knn_based_recommendation.ipynb

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      "cell_type": "markdown",
      "source": [
        "#KNN BASED RECOMMENDATION SYSTEM"
      ],
      "metadata": {
        "id": "bt1GslpHtR65"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Movie Recommendation"
      ],
      "metadata": {
        "id": "Dz9oLy5a3hBE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip install fuzzywuzzy"
      ],
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          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting fuzzywuzzy\n",
            "  Downloading fuzzywuzzy-0.18.0-py2.py3-none-any.whl (18 kB)\n",
            "Installing collected packages: fuzzywuzzy\n",
            "Successfully installed fuzzywuzzy-0.18.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "from scipy.sparse import csr_matrix\n",
        "from fuzzywuzzy import process\n",
        "from sklearn.neighbors import NearestNeighbors\n",
        "import numpy as np"
      ],
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        {
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          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/fuzzywuzzy/fuzz.py:11: UserWarning: Using slow pure-python SequenceMatcher. Install python-Levenshtein to remove this warning\n",
            "  warnings.warn('Using slow pure-python SequenceMatcher. Install python-Levenshtein to remove this warning')\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df_movies = pd.read_csv(\n",
        "    movies_filename,\n",
        "    usecols=['movieId', 'title'],\n",
        "    dtype={'movieId': 'int32', 'title': 'str'})\n",
        "\n",
        "df_ratings = pd.read_csv(\n",
        "    ratings_filename,\n",
        "    usecols=['userId', 'movieId', 'rating'],\n",
        "    dtype={'userId': 'int32', 'movieId': 'int32', 'rating': 'float32'})    "
      ],
      "metadata": {
        "id": "MK8bPiwy4TQ5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.sparse import csr_matrix\n",
        "# pivot ratings into movie features\n",
        "df_movie_features = df_ratings.pivot(\n",
        "    index='movieId',\n",
        "    columns='userId',\n",
        "    values='rating'\n",
        ").fillna(0)\n",
        "# convert dataframe of movie features to scipy sparse matrix\n",
        "mat_movie_features = csr_matrix(df_movie_features.values)"
      ],
      "metadata": {
        "id": "JE-YGozx9eYx"
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      "execution_count": null,
      "outputs": []
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      "source": [
        "df_movie_features.head()"
      ],
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          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.neighbors import NearestNeighbors\n",
        "model_knn = NearestNeighbors(metric='cosine', algorithm='brute', n_neighbors=20, n_jobs=-1)"
      ],
      "metadata": {
        "id": "zvQ1Fiym4GtV"
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      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "movies_users=df_ratings.pivot(index='movieId', columns='userId',values='rating').fillna(0)\n",
        "mat_movies_users=csr_matrix(movies_users.values)"
      ],
      "metadata": {
        "id": "4ss8aXU14ZtI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mat_movies_users"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "chd8lxGp8_4j",
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<9724x610 sparse matrix of type '<class 'numpy.float32'>'\n",
              "\twith 100836 stored elements in Compressed Sparse Row format>"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model_knn= NearestNeighbors(metric='cosine', algorithm='brute', n_neighbors=20)"
      ],
      "metadata": {
        "id": "nof190964beC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model_knn.fit(mat_movies_users)"
      ],
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              "NearestNeighbors(algorithm='brute', metric='cosine', n_neighbors=20)"
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            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Recommender(movie_name) => List of Movies recommended\n",
        "\n",
        "def recommender(movie_name, data,model, n_recommendations ):\n",
        "    model.fit(data)\n",
        "    idx=process.extractOne(movie_name, df_movies['title'])[2]\n",
        "    print('Movie Selected: ',df_movies['title'][idx], 'Index: ',idx)\n",
        "    print('Searching for recommendations.....')\n",
        "    distances, indices=model.kneighbors(data[idx], n_neighbors=n_recommendations)\n",
        "    for i in indices:\n",
        "        print(df_movies['title'][i].where(i!=idx))\n",
        "    \n",
        "recommender('iron man', mat_movies_users, model_knn,20)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Re8oDftn5G_V",
        "outputId": "612b795b-09e5-4955-ccae-e02c8ba7f5df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Movie Selected:  Iron Man (2008) Index:  6743\n",
            "Searching for recommendations.....\n",
            "6743                                            NaN\n",
            "7197                                  Garage (2007)\n",
            "7195                        Merry Madagascar (2009)\n",
            "7354                             A-Team, The (2010)\n",
            "6726                         Superhero Movie (2008)\n",
            "7137                         Thirst (Bakjwi) (2009)\n",
            "7026                                 Scorpio (1973)\n",
            "7571                                 Win Win (2011)\n",
            "3880                  Look Who's Talking Now (1993)\n",
            "6388    After the Wedding (Efter brylluppet) (2006)\n",
            "7601                       Idiots and Angels (2008)\n",
            "6755                Nina's Heavenly Delights (2006)\n",
            "7022                                   Earth (2007)\n",
            "7338                          Blue Valentine (2010)\n",
            "4421                         What's Up, Doc? (1972)\n",
            "6195                             Silent Hill (2006)\n",
            "5885                                   Crash (2004)\n",
            "3740                              Motel Hell (1980)\n",
            "7378           Serbian Film, A (Srpski film) (2010)\n",
            "7289                            Generation X (1996)\n",
            "Name: title, dtype: object\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Rating prediction"
      ],
      "metadata": {
        "id": "WPeosTY13dhm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install surprise"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NI61c97jDXvK",
        "outputId": "5072e56e-3a98-4ed8-efc3-0576d61c7bee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting surprise\n",
            "  Downloading surprise-0.1-py2.py3-none-any.whl (1.8 kB)\n",
            "Collecting scikit-surprise (from surprise)\n",
            "  Downloading scikit-surprise-1.1.3.tar.gz (771 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m772.0/772.0 kB\u001b[0m \u001b[31m10.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: joblib>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-surprise->surprise) (1.2.0)\n",
            "Requirement already satisfied: numpy>=1.17.3 in /usr/local/lib/python3.10/dist-packages (from scikit-surprise->surprise) (1.22.4)\n",
            "Requirement already satisfied: scipy>=1.3.2 in /usr/local/lib/python3.10/dist-packages (from scikit-surprise->surprise) (1.10.1)\n",
            "Building wheels for collected packages: scikit-surprise\n",
            "  Building wheel for scikit-surprise (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for scikit-surprise: filename=scikit_surprise-1.1.3-cp310-cp310-linux_x86_64.whl size=3095463 sha256=1b91945f2db8e16e71185ade9fefcef09b67b71ad4b5e25f273a25b75b19d6fd\n",
            "  Stored in directory: /root/.cache/pip/wheels/a5/ca/a8/4e28def53797fdc4363ca4af740db15a9c2f1595ebc51fb445\n",
            "Successfully built scikit-surprise\n",
            "Installing collected packages: scikit-surprise, surprise\n",
            "Successfully installed scikit-surprise-1.1.3 surprise-0.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from surprise import Dataset\n",
        "from surprise.model_selection import cross_validate\n",
        "from surprise.prediction_algorithms import KNNBaseline, KNNBasic, KNNWithMeans, KNNWithZScore\n",
        "from surprise import accuracy\n",
        "from surprise.model_selection import train_test_split"
      ],
      "metadata": {
        "id": "vOxRW63YDV-M"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def convert_traintest_dataframe_forsurprise(training_dataframe, testing_dataframe):\n",
        "    reader = Reader(rating_scale=(0, 5))\n",
        "    trainset = Dataset.load_from_df(training_dataframe[['userId', 'movieId', 'rating']], reader)\n",
        "    testset = Dataset.load_from_df(testing_dataframe[['userId', 'movieId', 'rating']], reader)\n",
        "    trainset = trainset.construct_trainset(trainset.raw_ratings)\n",
        "    testset = testset.construct_testset(testset.raw_ratings)\n",
        "    return trainset, testset"
      ],
      "metadata": {
        "id": "ZNU4gGn_EAmu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def recommendation(algo, trainset, testset):\n",
        "  # Train the algorithm on the trainset, and predict ratings for the testset\n",
        "  algo.fit(trainset)\n",
        "\n",
        "  # Predictions on testing set\n",
        "  test_predictions = algo.test(testset)\n",
        "  test_rmse = accuracy.rmse(test_predictions)\n",
        "  test_mae = accuracy.mae(test_predictions)\n",
        "  \n",
        "  return test_rmse, test_mae, test_predictions"
      ],
      "metadata": {
        "id": "JjaG4JzaEDso"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#KNNBaseline\n",
        "sim_options = {'name': 'pearson',\n",
        "               'user_based': False  # compute  similarities between items\n",
        "               }\n",
        "algo = KNNBaseline(k=20,sim_options=sim_options)\n",
        "test_knn_rmse, test_knn_mae, test_knn_pred = recommendation(algo, trainset, testset)\n",
        "     "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VyxLg2FzEKl5",
        "outputId": "fe45cff2-fcb6-4a64-f1d5-fb800de1ae84"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimating biases using als...\n",
            "Computing the pearson similarity matrix...\n",
            "Done computing similarity matrix.\n",
            "RMSE: 0.9016\n",
            "MAE:  0.7079\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#KNNBaseline\n",
        "sim_options = {'name': 'pearson',\n",
        "              'user_based': True  # compute similarities between users\n",
        "               }\n",
        "algo = KNNBaseline(k=20,sim_options=sim_options)\n",
        "test_knn_rmse, test_knn_mae, test_knn_pred = recommendation(algo, trainset, testset)"
      ],
      "metadata": {
        "id": "8BSI6R-QxU6Z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0b23be3b-13ea-402b-a3d9-46b3e96909e7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimating biases using als...\n",
            "Computing the pearson similarity matrix...\n",
            "Done computing similarity matrix.\n",
            "RMSE: 0.9087\n",
            "MAE:  0.7162\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "test_knn_pred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p5J6HYXfEa9F",
        "outputId": "988cea53-1208-44ec-aec9-ddebae70d6c5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              " Prediction(uid='4611', iid='1968', r_ui=4.0, est=3.1802917088489835, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='386', iid='3753', r_ui=1.0, est=3.352990917715468, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1153', iid='1971', r_ui=2.0, est=1.5931389224769328, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3242', iid='1220', r_ui=2.0, est=4.2613637541732725, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2105', iid='337', r_ui=3.0, est=3.7165142136418314, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1928', iid='1196', r_ui=4.0, est=3.8800629318922786, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3300', iid='2058', r_ui=3.0, est=3.822139501377374, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2005', iid='3081', r_ui=5.0, est=2.7589208243719883, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='601', iid='3063', r_ui=1.0, est=2.333078852147022, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1805', iid='555', r_ui=4.0, est=4.387867198816288, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5905', iid='1676', r_ui=2.0, est=2.8233931628690434, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3970', iid='3255', r_ui=5.0, est=3.9404949958110476, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2129', iid='3784', r_ui=1.0, est=3.5194246794398873, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5545', iid='1193', r_ui=5.0, est=4.948416450421349, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5759', iid='492', r_ui=3.0, est=3.6526835996676583, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5728', iid='719', r_ui=3.0, est=2.8026352419537637, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1261', iid='3717', r_ui=5.0, est=3.4652297564745167, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3454', iid='1378', r_ui=4.0, est=3.649964015751899, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1010', iid='2924', r_ui=4.0, est=3.1462447698960583, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3792', iid='830', r_ui=3.0, est=2.9469456902638345, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1266', iid='1834', r_ui=4.0, est=3.8406675055059947, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1223', iid='2762', r_ui=2.0, est=4.49037987910753, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1896', iid='1254', r_ui=5.0, est=4.512165335537112, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1303', iid='2628', r_ui=1.0, est=2.8630793615168937, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5503', iid='2763', r_ui=3.0, est=3.793101292476977, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1676', iid='520', r_ui=3.0, est=2.9212853750820713, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5551', iid='1219', r_ui=5.0, est=3.688286961303762, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4277', iid='154', r_ui=3.0, est=4.351788695110298, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='999', iid='3767', r_ui=3.0, est=1.938578991382126, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5282', iid='1784', r_ui=3.0, est=3.487438298041595, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1447', iid='348', r_ui=5.0, est=3.7112044199065064, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1968', iid='1196', r_ui=5.0, est=3.6166074332291123, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2811', iid='3435', r_ui=3.0, est=3.9467226852528965, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2837', iid='2359', r_ui=5.0, est=3.8579235811245733, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2157', iid='2028', r_ui=2.0, est=4.210903362399729, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='566', iid='1214', r_ui=3.0, est=3.1047472461386163, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3916', iid='125', r_ui=4.0, est=4.416376225069393, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5599', iid='2692', r_ui=5.0, est=4.092015354867307, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3871', iid='3524', r_ui=3.0, est=3.4018992931621472, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4418', iid='223', r_ui=4.0, est=4.079655090567477, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1968', iid='144', r_ui=2.0, est=2.7708285616418658, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='319', iid='1268', r_ui=3.0, est=3.2604436949704505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5582', iid='2936', r_ui=5.0, est=4.550556054129778, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5736', iid='1537', r_ui=3.0, est=4.5083642552257714, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='17', iid='2288', r_ui=4.0, est=4.1544286888196575, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='319', iid='3100', r_ui=3.0, est=3.554762696375418, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4085', iid='1991', r_ui=3.0, est=2.5813968739000694, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1120', iid='312', r_ui=4.0, est=2.8818696985884893, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5111', iid='1798', r_ui=4.0, est=2.373841881331059, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5147', iid='791', r_ui=4.0, est=2.7139663050595124, details={'actual_k': 1, 'was_impossible': False}),\n",
              " Prediction(uid='2608', iid='428', r_ui=5.0, est=4.228043361552319, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5709', iid='3686', r_ui=2.0, est=3.2915355877111847, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='429', iid='2000', r_ui=3.0, est=3.4281304625546625, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5240', iid='2762', r_ui=5.0, est=4.360761128814571, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4729', iid='17', r_ui=5.0, est=4.015234936043446, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5975', iid='2353', r_ui=4.0, est=3.659125450259929, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2809', iid='34', r_ui=5.0, est=4.230482799953698, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4018', iid='3404', r_ui=4.0, est=3.6112067474405816, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4022', iid='289', r_ui=2.0, est=2.880437646426533, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2060', iid='520', r_ui=2.0, est=2.509680004858626, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4041', iid='1573', r_ui=4.0, est=3.4430384154561744, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5084', iid='466', r_ui=3.0, est=2.528699685575602, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1470', iid='1870', r_ui=1.0, est=2.9131739955336737, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1387', iid='911', r_ui=2.0, est=4.085641147331608, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4472', iid='1968', r_ui=3.0, est=3.82171540234694, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1694', iid='2872', r_ui=4.0, est=3.6884758399588664, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3411', iid='750', r_ui=3.0, est=3.7454079393371718, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5747', iid='3479', r_ui=3.0, est=3.572416367234172, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4388', iid='2501', r_ui=5.0, est=4.370480767965837, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='858', iid='1371', r_ui=3.0, est=3.882363115551778, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5792', iid='745', r_ui=5.0, est=4.345837161223629, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='934', iid='3089', r_ui=4.0, est=4.025015224224518, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1904', iid='2294', r_ui=3.0, est=3.2493827851438546, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3499', iid='1589', r_ui=5.0, est=3.7857632308504017, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5555', iid='2', r_ui=4.0, est=2.629688014622533, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4233', iid='1233', r_ui=4.0, est=4.181413968482557, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2478', iid='908', r_ui=5.0, est=3.9010731022997254, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1050', iid='1370', r_ui=2.0, est=3.144569029674509, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2265', iid='780', r_ui=3.0, est=3.57385520476392, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3509', iid='3549', r_ui=2.0, est=3.6100147891475727, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1167', iid='1265', r_ui=4.0, est=3.7377819299357413, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1230', iid='2826', r_ui=4.0, est=4.080141203917671, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1770', iid='3051', r_ui=3.0, est=2.7745456567391895, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1150', iid='663', r_ui=2.0, est=2.7576698424563033, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2060', iid='842', r_ui=5.0, est=2.5481178117175043, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='802', iid='2642', r_ui=2.0, est=2.4044951958608616, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='484', iid='2881', r_ui=4.0, est=3.764775396430548, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='687', iid='539', r_ui=4.0, est=3.7813786118013084, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1129', iid='1198', r_ui=5.0, est=4.79498568299003, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1926', iid='3199', r_ui=3.0, est=3.9406277226440234, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5319', iid='3802', r_ui=3.0, est=2.476784756730486, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='300', iid='2028', r_ui=5.0, est=4.907822202022019, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4150', iid='1390', r_ui=3.0, est=2.768270156309416, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2244', iid='2085', r_ui=1.0, est=3.33785951720953, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='243', iid='933', r_ui=5.0, est=4.051616359534731, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3416', iid='3489', r_ui=3.0, est=3.439146533984928, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1465', iid='1339', r_ui=4.0, est=3.228966910807908, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2436', iid='3039', r_ui=4.0, est=3.9511329855699056, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2551', iid='1967', r_ui=4.0, est=3.552708704594389, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='869', iid='1171', r_ui=4.0, est=3.9675026994673965, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3829', iid='2546', r_ui=2.0, est=2.3161638961407425, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4543', iid='2664', r_ui=4.0, est=3.8730563950492853, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1680', iid='3510', r_ui=4.0, est=3.710096343100127, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5599', iid='3257', r_ui=3.0, est=2.802321735899266, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='631', iid='2664', r_ui=4.0, est=3.908727524435245, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='8', iid='741', r_ui=5.0, est=4.137899678496785, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4747', iid='2959', r_ui=3.0, est=3.757231766550963, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3163', iid='481', r_ui=4.0, est=3.6916940517187062, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2277', iid='837', r_ui=5.0, est=3.4357971645377345, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1396', iid='1923', r_ui=4.0, est=3.4965228420052643, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='984', iid='2447', r_ui=4.0, est=2.6793484393557705, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2612', iid='2420', r_ui=2.0, est=2.817883091432393, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2860', iid='3300', r_ui=4.0, est=3.4403871740292846, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='587', iid='3468', r_ui=3.0, est=3.9230091123168513, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='78', iid='2096', r_ui=3.0, est=3.372573132917881, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1150', iid='1355', r_ui=3.0, est=1.8245008382742407, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='967', iid='3476', r_ui=3.0, est=4.058687796722094, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5724', iid='1235', r_ui=5.0, est=4.18752880047938, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4085', iid='1754', r_ui=4.0, est=3.943467509735563, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3320', iid='1025', r_ui=4.0, est=3.6619215004457564, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2878', iid='2078', r_ui=3.0, est=3.885219163834928, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4852', iid='3091', r_ui=5.0, est=4.305417170715674, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4558', iid='923', r_ui=5.0, est=4.866827952675045, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='729', iid='2405', r_ui=4.0, est=2.824987052795662, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1018', iid='3671', r_ui=4.0, est=4.319513985572338, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2589', iid='453', r_ui=3.0, est=2.881755776554878, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1470', iid='2406', r_ui=4.0, est=3.0070316282912595, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5361', iid='2429', r_ui=4.0, est=2.9807154610801345, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5776', iid='813', r_ui=1.0, est=2.90479076443884, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3151', iid='793', r_ui=1.0, est=4.359882710176377, details={'actual_k': 4, 'was_impossible': False}),\n",
              " Prediction(uid='151', iid='1088', r_ui=5.0, est=3.380888006545666, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2514', iid='3476', r_ui=2.0, est=4.111129935731874, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3829', iid='1270', r_ui=3.0, est=3.434373276783108, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4085', iid='2872', r_ui=4.0, est=4.3710107087900125, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5750', iid='2925', r_ui=5.0, est=4.019451360637945, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4972', iid='2762', r_ui=5.0, est=4.296896628889561, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5128', iid='1337', r_ui=3.0, est=3.682076195928369, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='571', iid='2105', r_ui=3.0, est=3.7939862698432854, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3243', iid='543', r_ui=5.0, est=4.264836926128119, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3312', iid='3889', r_ui=3.0, est=2.2526099544897344, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1677', iid='2706', r_ui=4.0, est=4.033584060832187, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='245', iid='608', r_ui=3.0, est=3.7453986592362174, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5339', iid='2028', r_ui=5.0, est=4.4477456280026395, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3658', iid='942', r_ui=5.0, est=4.7006608506032395, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2010', iid='3258', r_ui=1.0, est=1.5985172694973064, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1483', iid='3698', r_ui=2.0, est=2.505676532731404, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4580', iid='3819', r_ui=3.0, est=3.9604302557987556, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1069', iid='1401', r_ui=1.0, est=2.714463419079487, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3007', iid='3618', r_ui=4.0, est=2.9343774375729548, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2907', iid='1348', r_ui=4.0, est=4.368046307644242, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1202', iid='1207', r_ui=5.0, est=4.479368977658012, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1448', iid='1923', r_ui=5.0, est=3.908253240530958, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1539', iid='480', r_ui=4.0, est=4.311014760224301, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5556', iid='2700', r_ui=5.0, est=3.201162751939896, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1255', iid='927', r_ui=4.0, est=4.520553182283839, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1776', iid='2291', r_ui=4.0, est=3.6630871223731303, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='588', iid='2321', r_ui=3.0, est=3.8251069657710732, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4884', iid='3448', r_ui=4.0, est=4.1739989248208085, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4222', iid='959', r_ui=4.0, est=3.945103490888316, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5302', iid='2806', r_ui=3.0, est=2.5976677429505117, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3807', iid='1240', r_ui=4.0, est=3.839122143588501, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='498', iid='1267', r_ui=4.0, est=4.103457500618078, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3780', iid='1968', r_ui=5.0, est=4.317188752396035, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3931', iid='1097', r_ui=3.0, est=3.522813359621912, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2785', iid='2478', r_ui=2.0, est=2.548639203739811, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3391', iid='1059', r_ui=5.0, est=3.669885391379659, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1605', iid='2542', r_ui=4.0, est=3.7500756948978697, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4174', iid='924', r_ui=5.0, est=3.992904384737508, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5759', iid='2393', r_ui=3.0, est=3.3805351679701463, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='927', iid='1197', r_ui=5.0, est=3.5031011932494933, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1698', iid='2070', r_ui=4.0, est=4.24565795603353, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5908', iid='494', r_ui=3.0, est=3.4643016884487037, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='842', iid='2013', r_ui=4.0, est=3.4988496971195304, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3673', iid='1307', r_ui=4.0, est=4.0195272629453, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5428', iid='1573', r_ui=4.0, est=3.97117601002903, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='123', iid='2245', r_ui=4.0, est=3.2826062573078496, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3401', iid='7', r_ui=5.0, est=2.933741829176787, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1044', iid='1238', r_ui=5.0, est=4.183485268403789, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1845', iid='97', r_ui=4.0, est=3.643758908492421, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='939', iid='3617', r_ui=4.0, est=3.4645462278579924, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5929', iid='2740', r_ui=4.0, est=2.7558609364199094, details={'actual_k': 10, 'was_impossible': False}),\n",
              " Prediction(uid='4277', iid='2916', r_ui=5.0, est=4.009071017521631, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1068', iid='2247', r_ui=3.0, est=3.654941854283926, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3824', iid='3698', r_ui=3.0, est=2.550552172453426, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5653', iid='1265', r_ui=4.0, est=3.790952272363667, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4502', iid='1617', r_ui=4.0, est=4.3902874575234065, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='731', iid='1885', r_ui=4.0, est=3.89232953213396, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2002', iid='296', r_ui=4.0, est=4.483491316695408, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2768', iid='1748', r_ui=2.0, est=3.8190791143332548, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1597', iid='1405', r_ui=4.0, est=3.081228249146829, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5412', iid='1918', r_ui=4.0, est=2.945079954662309, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2063', iid='3898', r_ui=3.0, est=2.2643532730511353, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1401', iid='1084', r_ui=5.0, est=3.8836914014969417, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='798', iid='2033', r_ui=5.0, est=3.4153549911671996, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5074', iid='1892', r_ui=2.0, est=3.260939031856955, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2793', iid='32', r_ui=4.0, est=4.64765512020933, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3262', iid='2706', r_ui=1.0, est=3.6173756686324174, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='783', iid='2700', r_ui=5.0, est=3.729237399359886, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3569', iid='2702', r_ui=4.0, est=2.366313211252526, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='980', iid='1265', r_ui=3.0, est=3.075795208709538, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3481', iid='1044', r_ui=3.0, est=3.5371690043416124, details={'actual_k': 17, 'was_impossible': False}),\n",
              " Prediction(uid='4889', iid='1393', r_ui=3.0, est=4.3726461306882305, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4686', iid='541', r_ui=4.0, est=4.32122665494495, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4043', iid='708', r_ui=4.0, est=3.2287830135291657, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1008', iid='2701', r_ui=3.0, est=2.1511040868500397, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='394', iid='2617', r_ui=3.0, est=3.2815581391556665, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5731', iid='858', r_ui=5.0, est=5, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4647', iid='3730', r_ui=5.0, est=4.2690779423769, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='332', iid='1784', r_ui=5.0, est=3.7340876340925586, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4663', iid='1172', r_ui=2.0, est=3.9556486744166546, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5347', iid='3699', r_ui=4.0, est=2.944652396535154, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3443', iid='1210', r_ui=3.0, est=3.6525924635116707, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1088', iid='317', r_ui=3.0, est=3.0536567443751514, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5948', iid='2372', r_ui=4.0, est=3.1718510464484395, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='734', iid='2713', r_ui=3.0, est=2.813187308844624, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1803', iid='423', r_ui=3.0, est=3.237338214478167, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5678', iid='1097', r_ui=5.0, est=3.417667939356959, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5664', iid='1717', r_ui=1.0, est=3.171558525382333, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='383', iid='2531', r_ui=3.0, est=2.764004143008783, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2136', iid='2321', r_ui=4.0, est=3.856109315891775, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3320', iid='2268', r_ui=4.0, est=3.938165834490064, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5289', iid='3470', r_ui=4.0, est=4.675131172438309, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='796', iid='1953', r_ui=3.0, est=3.3081983972151, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='438', iid='1581', r_ui=4.0, est=2.5996491836233706, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4049', iid='2000', r_ui=3.0, est=3.953824465004676, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4309', iid='2976', r_ui=2.0, est=3.0703057013257666, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5287', iid='1378', r_ui=4.0, est=3.840963824981215, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3274', iid='1967', r_ui=4.0, est=3.2587749237703494, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3808', iid='3471', r_ui=5.0, est=3.956106754752577, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4058', iid='1917', r_ui=4.0, est=2.3198142943241424, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5910', iid='412', r_ui=5.0, est=3.36251988450964, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1764', iid='3740', r_ui=5.0, est=4.070248261307088, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3014', iid='296', r_ui=5.0, est=4.227804135445523, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4069', iid='1244', r_ui=5.0, est=4.462563846038474, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1730', iid='3565', r_ui=4.0, est=3.7972138000639952, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4781', iid='3421', r_ui=2.0, est=4.308556088192284, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1632', iid='3671', r_ui=4.0, est=3.0415916716370055, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1267', iid='117', r_ui=3.0, est=3.2907876440967265, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3551', iid='3101', r_ui=5.0, est=3.2772978528256482, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3941', iid='2046', r_ui=2.0, est=3.1574762925667312, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2440', iid='2976', r_ui=3.0, est=3.0850555908080857, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1756', iid='2805', r_ui=3.0, est=2.603897504866014, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='509', iid='569', r_ui=3.0, est=2.530123238477527, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4725', iid='2770', r_ui=3.0, est=3.120844231623265, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1884', iid='674', r_ui=4.0, est=3.075435214682639, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4083', iid='2917', r_ui=4.0, est=3.704755499619314, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4738', iid='3508', r_ui=3.0, est=3.797236031584758, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2754', iid='236', r_ui=3.0, est=3.372674998493015, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5301', iid='3113', r_ui=3.0, est=2.4696520610881514, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1211', iid='3706', r_ui=3.0, est=3.9423028859465705, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5643', iid='2436', r_ui=3.0, est=2.9082549012823793, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5367', iid='188', r_ui=2.0, est=2.3954152904254613, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1016', iid='2997', r_ui=4.0, est=4.1040231045988085, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='655', iid='2194', r_ui=2.0, est=3.0663402135837012, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3300', iid='2019', r_ui=5.0, est=5, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='166', iid='2194', r_ui=4.0, est=4.340443918155501, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1749', iid='1958', r_ui=1.0, est=2.133843680033057, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4868', iid='235', r_ui=4.0, est=3.453593937695155, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5530', iid='1516', r_ui=4.0, est=3.307316173001766, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2857', iid='1965', r_ui=3.0, est=3.7254737489982723, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='270', iid='457', r_ui=4.0, est=4.3545416742408065, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2994', iid='204', r_ui=2.0, est=2.3083963210245355, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3309', iid='1285', r_ui=3.0, est=3.966996380180349, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2896', iid='2279', r_ui=2.0, est=3.1529355568599944, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='655', iid='1189', r_ui=4.0, est=3.578835709045383, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4305', iid='1968', r_ui=4.0, est=3.9084242428361264, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4234', iid='1292', r_ui=3.0, est=3.9311392077780636, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3290', iid='2668', r_ui=1.0, est=1.8265489620801851, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3452', iid='3755', r_ui=4.0, est=3.7977960312202117, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1753', iid='3721', r_ui=3.0, est=3.0317588041382475, details={'actual_k': 15, 'was_impossible': False}),\n",
              " Prediction(uid='4354', iid='946', r_ui=4.0, est=3.8818037055707713, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5279', iid='3512', r_ui=3.0, est=3.1423877396903803, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='678', iid='1387', r_ui=3.0, est=4.536366742369251, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3829', iid='71', r_ui=1.0, est=1, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5047', iid='2013', r_ui=2.0, est=3.46732845420894, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3408', iid='1197', r_ui=5.0, est=4.214326650353151, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='702', iid='2659', r_ui=4.0, est=2.6879039384852232, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3248', iid='1226', r_ui=5.0, est=4.008306009670854, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1941', iid='317', r_ui=4.0, est=3.1592088862972334, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3483', iid='1265', r_ui=4.0, est=4.170438062810621, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5762', iid='2081', r_ui=3.0, est=4.584168185843942, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3507', iid='1127', r_ui=4.0, est=3.3301767603152297, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4451', iid='2003', r_ui=2.0, est=2.50521520284992, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3600', iid='3361', r_ui=4.0, est=3.972772305941042, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2909', iid='3766', r_ui=4.0, est=3.0516960893615295, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2996', iid='70', r_ui=2.0, est=3.235928420318044, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2636', iid='1265', r_ui=4.0, est=3.5054809902005504, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5494', iid='368', r_ui=4.0, est=3.1126547274729823, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='824', iid='2728', r_ui=5.0, est=4.527138772962882, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1074', iid='3230', r_ui=5.0, est=3.5574376068441738, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5317', iid='2067', r_ui=5.0, est=4.595309409636064, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1057', iid='1396', r_ui=3.0, est=3.587331121488277, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4458', iid='104', r_ui=3.0, est=3.0918539737767152, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='680', iid='2706', r_ui=4.0, est=3.7465861648501044, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='565', iid='3481', r_ui=4.0, est=3.5116079047813336, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4153', iid='2167', r_ui=3.0, est=3.670746199661439, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3718', iid='1395', r_ui=2.0, est=3.2387684359338444, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3129', iid='1911', r_ui=3.0, est=2.65147938816422, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1125', iid='509', r_ui=4.0, est=3.3858523871436828, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5504', iid='780', r_ui=5.0, est=4.115103595911089, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3800', iid='858', r_ui=5.0, est=4.7931154675748315, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2666', iid='3623', r_ui=2.0, est=3.7031278362382816, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='117', iid='741', r_ui=5.0, est=4.359121963266236, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4973', iid='1286', r_ui=4.0, est=3.502670533275775, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5754', iid='1033', r_ui=4.0, est=3.1144512397558484, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1470', iid='579', r_ui=2.0, est=2.9229510542664316, details={'was_impossible': False}),\n",
              " Prediction(uid='3309', iid='1641', r_ui=4.0, est=4.073315762176598, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3807', iid='1407', r_ui=5.0, est=3.6857963815630534, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1556', iid='2470', r_ui=2.0, est=2.7122800476320594, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5096', iid='2750', r_ui=5.0, est=3.3829116826044423, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3012', iid='14', r_ui=1.0, est=2.432129884993949, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5287', iid='2668', r_ui=3.0, est=2.8374163046242358, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4008', iid='3624', r_ui=4.0, est=3.1306747451675054, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5900', iid='2686', r_ui=4.0, est=3.910148981938123, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1571', iid='480', r_ui=3.0, est=4.088869721761332, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3903', iid='1288', r_ui=3.0, est=4.043174269872335, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='549', iid='3343', r_ui=2.0, est=2.4940858303241744, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2203', iid='3439', r_ui=3.0, est=2.9278464334421286, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4735', iid='3362', r_ui=4.0, est=4.037073950858186, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4206', iid='1', r_ui=5.0, est=4.620919802893461, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='157', iid='2763', r_ui=3.0, est=3.8710270284319535, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1889', iid='1215', r_ui=3.0, est=4.006079156330124, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4933', iid='3912', r_ui=3.0, est=1.9884971888960745, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2293', iid='899', r_ui=5.0, est=4.683669013390515, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4728', iid='2616', r_ui=2.0, est=2.2335662182982814, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2100', iid='919', r_ui=5.0, est=4.551600372712225, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4386', iid='1013', r_ui=4.0, est=3.6745246259426834, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='284', iid='534', r_ui=5.0, est=3.7656583984532768, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1922', iid='2496', r_ui=4.0, est=3.0659640784180273, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5555', iid='376', r_ui=3.0, est=2.9989867522683866, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='855', iid='1732', r_ui=4.0, est=3.6477760983822685, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='731', iid='3448', r_ui=3.0, est=3.8193005587067677, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4257', iid='2706', r_ui=3.0, est=3.588557742165302, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='651', iid='969', r_ui=5.0, est=4.40974472877954, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5350', iid='2006', r_ui=4.0, est=2.7522462547524347, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5908', iid='553', r_ui=5.0, est=3.971511589538751, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2641', iid='1028', r_ui=4.0, est=4.148887170606544, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='696', iid='1962', r_ui=4.0, est=3.895384344624231, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='148', iid='2021', r_ui=3.0, est=4.232420051226491, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='368', iid='1120', r_ui=4.0, est=3.823961403947505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3039', iid='898', r_ui=5.0, est=4.816014563957774, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2497', iid='3524', r_ui=5.0, est=4.191482002790509, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5399', iid='2600', r_ui=5.0, est=3.8088548590096716, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4124', iid='3477', r_ui=4.0, est=3.261620617149258, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='780', iid='2410', r_ui=3.0, est=2.736182949249553, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4451', iid='162', r_ui=4.0, est=3.4887998044033672, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1150', iid='104', r_ui=2.0, est=2.2411811819180913, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5395', iid='1019', r_ui=3.0, est=3.7728696618015003, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2918', iid='2433', r_ui=4.0, est=3.4151324597109216, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3329', iid='1266', r_ui=5.0, est=3.451158670098021, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2870', iid='1643', r_ui=3.0, est=2.9603350951414544, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1496', iid='1883', r_ui=3.0, est=3.2949834235854656, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3228', iid='2959', r_ui=5.0, est=3.529283880834144, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5561', iid='317', r_ui=3.0, est=2.7564108994198504, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='556', iid='708', r_ui=4.0, est=3.3769465748969476, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2077', iid='1042', r_ui=2.0, est=3.3022265604886667, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='791', iid='2005', r_ui=5.0, est=3.5441678752566808, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='48', iid='2860', r_ui=2.0, est=2.946389454354298, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4808', iid='1923', r_ui=3.0, est=3.957075242176122, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2419', iid='2871', r_ui=4.0, est=3.7718110650727636, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1360', iid='1580', r_ui=3.0, est=3.6593982260795364, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4655', iid='3408', r_ui=3.0, est=3.6515856474913075, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5605', iid='2803', r_ui=3.0, est=2.8500612345129905, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5021', iid='3723', r_ui=4.0, est=3.6711518431328485, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1437', iid='3152', r_ui=5.0, est=4.453761337463589, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2939', iid='1127', r_ui=4.0, est=3.6606817455954146, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3233', iid='1276', r_ui=5.0, est=4.472685126750593, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='666', iid='508', r_ui=3.0, est=3.913984080968658, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='143', iid='377', r_ui=2.0, est=3.4782008162139593, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4227', iid='674', r_ui=1.0, est=2.345428477927562, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2803', iid='2268', r_ui=4.0, est=3.7688233692496156, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4022', iid='2076', r_ui=2.0, est=3.15088403534713, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3808', iid='342', r_ui=5.0, est=3.4809066367318335, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5501', iid='3608', r_ui=4.0, est=3.03695817561976, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3972', iid='1127', r_ui=5.0, est=3.9565010772052784, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1015', iid='2126', r_ui=3.0, est=2.9287224030673555, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3672', iid='2087', r_ui=4.0, est=3.091517200975754, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='565', iid='589', r_ui=4.0, est=3.9818301972827297, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='447', iid='594', r_ui=5.0, est=4.936357032835375, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2016', iid='2294', r_ui=4.0, est=3.841922056312654, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2870', iid='348', r_ui=1.0, est=2.975328050500239, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4446', iid='2054', r_ui=2.0, est=2.48903950020337, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4167', iid='3022', r_ui=5.0, est=4.638843690398916, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1912', iid='266', r_ui=1.0, est=1.9924612945515738, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1056', iid='2826', r_ui=5.0, est=3.546054389699417, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1199', iid='1784', r_ui=4.0, est=3.9638961847426635, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4300', iid='2137', r_ui=4.0, est=3.6514885152477987, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3648', iid='3259', r_ui=2.0, est=3.1329385974695505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3985', iid='1719', r_ui=4.0, est=3.7324949513750174, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2938', iid='1680', r_ui=5.0, est=4.206285012218331, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5015', iid='2948', r_ui=5.0, est=3.849219334882514, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1202', iid='3827', r_ui=3.0, est=3.281246841994079, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1072', iid='296', r_ui=5.0, est=4.811550090040197, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1675', iid='2617', r_ui=4.0, est=3.2356522611643066, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1884', iid='3505', r_ui=4.0, est=3.661248591859696, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='923', iid='2858', r_ui=4.0, est=4.297383090460495, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2394', iid='2716', r_ui=3.0, est=4.257903225075181, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1194', iid='3827', r_ui=4.0, est=2.945112976013183, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3401', iid='181', r_ui=1.0, est=1, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1181', iid='1086', r_ui=3.0, est=3.3048313014461357, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4792', iid='1211', r_ui=3.0, est=4.371534768157672, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='103', iid='552', r_ui=2.0, est=4.294199993292464, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3393', iid='2872', r_ui=3.0, est=3.7009999175823776, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3819', iid='3175', r_ui=4.0, est=3.672456620763928, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4344', iid='1094', r_ui=4.0, est=3.592702262478208, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='623', iid='3751', r_ui=5.0, est=4.390681683763479, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1545', iid='1036', r_ui=2.0, est=3.5175655918740536, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2219', iid='3545', r_ui=2.0, est=4.13061469805613, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4336', iid='1644', r_ui=5.0, est=3.680589841159007, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2873', iid='3526', r_ui=3.0, est=3.7399311900244094, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3173', iid='2532', r_ui=4.0, est=3.3433167031120243, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4171', iid='1358', r_ui=4.0, est=4.245661869525186, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2810', iid='1831', r_ui=4.0, est=2.8540991247492307, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5654', iid='1225', r_ui=5.0, est=4.373957446559806, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1465', iid='3686', r_ui=3.0, est=3.660101542880725, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3737', iid='1242', r_ui=4.0, est=4.398635901274471, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3401', iid='1036', r_ui=5.0, est=3.614395448459484, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2129', iid='2694', r_ui=3.0, est=3.004623015101664, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3844', iid='196', r_ui=2.0, est=3.4985441853580834, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='137', iid='2492', r_ui=3.0, est=2.6191270124418824, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='454', iid='3793', r_ui=3.0, est=3.2604683636020644, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4480', iid='3354', r_ui=1.0, est=2.1174033502174407, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4215', iid='1617', r_ui=5.0, est=4.523691821583043, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1303', iid='2616', r_ui=1.0, est=2.3836672628139044, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5978', iid='1303', r_ui=5.0, est=3.8129096036452235, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1988', iid='2676', r_ui=3.0, est=2.948851877456545, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3539', iid='236', r_ui=4.0, est=3.9308523400480557, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='809', iid='1562', r_ui=5.0, est=2.882357524273617, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3630', iid='1779', r_ui=2.0, est=2.6773375712212713, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3927', iid='2355', r_ui=5.0, est=3.98858369528615, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1635', iid='3082', r_ui=4.0, est=3.0611895217424676, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3453', iid='2858', r_ui=5.0, est=4.1019285749971495, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4775', iid='2762', r_ui=5.0, est=4.115900691093763, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3957', iid='2001', r_ui=3.0, est=4.005259157836021, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1050', iid='424', r_ui=3.0, est=2.094017865411159, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2137', iid='1580', r_ui=5.0, est=4.232662643363193, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2638', iid='3210', r_ui=3.0, est=3.4768729333115784, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3679', iid='300', r_ui=2.0, est=3.6922919372335126, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2020', iid='3168', r_ui=4.0, est=3.7537808934858785, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3581', iid='2916', r_ui=3.0, est=3.24609222576382, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='380', iid='1394', r_ui=5.0, est=3.663278547119775, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='689', iid='1936', r_ui=5.0, est=4.156153402931549, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3860', iid='1408', r_ui=5.0, est=4.018399055582332, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1449', iid='1219', r_ui=5.0, est=4.165402101419537, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4271', iid='1136', r_ui=4.0, est=3.7895925420542262, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4472', iid='1499', r_ui=1.0, est=2.526169228228487, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1100', iid='2394', r_ui=1.0, est=2.669881287757895, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5107', iid='858', r_ui=3.0, est=3.9080129967107187, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5020', iid='3753', r_ui=2.0, est=4.315089503061814, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2150', iid='3081', r_ui=2.0, est=3.494903542143377, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3847', iid='293', r_ui=4.0, est=3.538165076420467, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4213', iid='1676', r_ui=4.0, est=3.7274109953828254, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4808', iid='2991', r_ui=3.0, est=3.2724230227254036, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5277', iid='357', r_ui=3.0, est=3.4466225826156984, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='970', iid='2571', r_ui=5.0, est=4.320100085523505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5345', iid='205', r_ui=4.0, est=3.6794984205308374, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3592', iid='2053', r_ui=3.0, est=2.869826492476721, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='753', iid='2761', r_ui=4.0, est=4.599992527333381, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2909', iid='778', r_ui=5.0, est=4.566481306522692, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1035', iid='235', r_ui=5.0, est=3.6247721529169, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4268', iid='2942', r_ui=4.0, est=2.7727089961702234, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5560', iid='3608', r_ui=1.0, est=2.8037007326577963, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='509', iid='1189', r_ui=5.0, est=4.2998041129537805, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='352', iid='1750', r_ui=2.0, est=2.156523541931506, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3793', iid='2431', r_ui=3.0, est=2.9556890588801914, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3475', iid='141', r_ui=3.0, est=3.0618258002330974, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2042', iid='2203', r_ui=4.0, est=3.9820820386599136, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2909', iid='415', r_ui=4.0, est=2.681593250898477, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1980', iid='2400', r_ui=4.0, est=2.900967577568657, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2881', iid='2291', r_ui=3.0, est=3.9220038696470114, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3415', iid='1270', r_ui=5.0, est=3.7505862790454176, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2130', iid='3555', r_ui=3.0, est=4.0753026979525275, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2340', iid='2366', r_ui=5.0, est=4.277627000175542, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1299', iid='442', r_ui=3.0, est=3.246081459341268, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1281', iid='1233', r_ui=3.0, est=4.1348791698631, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3671', iid='1722', r_ui=4.0, est=3.645740169168692, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3741', iid='2692', r_ui=3.0, est=3.965555356707199, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='769', iid='919', r_ui=4.0, est=3.7782345129015362, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5689', iid='2605', r_ui=3.0, est=2.8450976655625193, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3201', iid='3591', r_ui=4.0, est=4.171142922279806, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2012', iid='1257', r_ui=4.0, est=3.6952903815862608, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2583', iid='2376', r_ui=5.0, est=4.236261784518801, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3526', iid='724', r_ui=2.0, est=2.6963638787740805, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4210', iid='1831', r_ui=3.0, est=2.9585494885426153, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4408', iid='2795', r_ui=3.0, est=3.4852625278565834, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5142', iid='2371', r_ui=5.0, est=4.049770210963106, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2230', iid='282', r_ui=3.0, est=2.804502936021734, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1022', iid='3060', r_ui=5.0, est=4.033347724879463, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1457', iid='1631', r_ui=4.0, est=3.9579550121129206, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2092', iid='1291', r_ui=3.0, est=3.642172931552932, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2124', iid='1307', r_ui=3.0, est=4.580837887113494, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3308', iid='1282', r_ui=5.0, est=3.755846132876329, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4055', iid='52', r_ui=4.0, est=3.4288610885136364, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3391', iid='3668', r_ui=4.0, est=4.1029890099220125, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5652', iid='22', r_ui=5.0, est=3.1678685043668837, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2641', iid='3177', r_ui=2.0, est=2.631756916287515, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4662', iid='497', r_ui=5.0, est=3.624791466937419, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5881', iid='306', r_ui=5.0, est=4.623847989185441, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3384', iid='1210', r_ui=4.0, est=3.703320606328879, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4079', iid='3545', r_ui=1.0, est=3.8953952761217616, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3377', iid='662', r_ui=4.0, est=3.633742397800816, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='166', iid='1968', r_ui=5.0, est=3.686947362813098, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5394', iid='322', r_ui=2.0, est=3.906427727472561, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3635', iid='2943', r_ui=2.0, est=4.0247273815056746, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4089', iid='1673', r_ui=4.0, est=3.825021252929314, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='984', iid='3355', r_ui=5.0, est=3.1543408736944882, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5502', iid='3689', r_ui=2.0, est=1.9642417147608286, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4375', iid='1974', r_ui=4.0, est=4.210253288852332, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5100', iid='3045', r_ui=5.0, est=3.716302791018933, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2029', iid='543', r_ui=4.0, est=2.756762129390316, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3182', iid='3499', r_ui=5.0, est=3.719310549134025, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='192', iid='2443', r_ui=2.0, est=3.342905017863095, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1194', iid='1013', r_ui=3.0, est=3.351400474761694, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3147', iid='1422', r_ui=3.0, est=3.184021840291874, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4897', iid='2720', r_ui=3.0, est=2.041996621401779, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='654', iid='34', r_ui=4.0, est=3.560752504444608, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2240', iid='1198', r_ui=5.0, est=4.72106474280789, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3423', iid='377', r_ui=4.0, est=4.229612871145617, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='438', iid='1073', r_ui=4.0, est=4.239813754858113, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4131', iid='2890', r_ui=5.0, est=4.494617142848009, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='678', iid='1867', r_ui=2.0, est=2.7807618747428835, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4006', iid='541', r_ui=5.0, est=4.277853331941197, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2055', iid='2941', r_ui=3.0, est=4.059326413900659, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5555', iid='1274', r_ui=2.0, est=3.451344081539938, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5996', iid='2100', r_ui=4.0, est=4.004037191922427, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5411', iid='2908', r_ui=2.0, est=3.484925283490133, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1050', iid='1060', r_ui=4.0, est=3.613235391773339, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1579', iid='549', r_ui=4.0, est=3.891850686567306, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5888', iid='1379', r_ui=1.0, est=2.08082402591149, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3491', iid='2355', r_ui=4.0, est=4.374597003153243, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1097', iid='1784', r_ui=3.0, est=3.9529085014902896, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2352', iid='3476', r_ui=4.0, est=3.793094858246728, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4807', iid='589', r_ui=5.0, est=3.9646161835580354, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4238', iid='1269', r_ui=3.0, est=4.496926728484401, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3719', iid='2694', r_ui=3.0, est=3.0424396088927903, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1271', iid='2100', r_ui=4.0, est=3.983538178800382, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2478', iid='1265', r_ui=4.0, est=3.5385387864932487, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5468', iid='434', r_ui=2.0, est=2.4830378443477894, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1998', iid='898', r_ui=5.0, est=4.24464280293852, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3044', iid='1059', r_ui=3.0, est=4.417668861636522, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5100', iid='1095', r_ui=5.0, est=4.1848957197129755, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4524', iid='2003', r_ui=5.0, est=3.275221489693561, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3259', iid='1409', r_ui=3.0, est=3.412359408712264, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3553', iid='3107', r_ui=5.0, est=4.064724572585662, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2195', iid='840', r_ui=3.0, est=2.379775761229518, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3309', iid='2144', r_ui=4.0, est=3.860402218678361, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2514', iid='2206', r_ui=5.0, est=4.508115865112411, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2279', iid='3929', r_ui=5.0, est=4.377327876311957, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1837', iid='111', r_ui=5.0, est=4.424710226176114, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1741', iid='593', r_ui=5.0, est=4.747013754431273, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4354', iid='1747', r_ui=4.0, est=3.556445343860095, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1088', iid='3901', r_ui=3.0, est=2.633228201968015, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3769', iid='720', r_ui=5.0, est=4.962739443064798, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3315', iid='1608', r_ui=4.0, est=3.7798712084877004, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='817', iid='2353', r_ui=4.0, est=4.566778755799108, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4613', iid='782', r_ui=4.0, est=3.750156106719778, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5229', iid='1957', r_ui=3.0, est=4.573455625820628, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='6016', iid='3358', r_ui=4.0, est=3.7734565099102317, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5915', iid='1210', r_ui=5.0, est=4.037012213901774, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5395', iid='1206', r_ui=5.0, est=4.145207012772159, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3077', iid='480', r_ui=4.0, est=3.6482363676896177, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3971', iid='2054', r_ui=3.0, est=3.1544586431298236, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1333', iid='2456', r_ui=1.0, est=2.1014828578375453, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5519', iid='1012', r_ui=3.0, est=3.403778266032627, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3610', iid='2124', r_ui=2.0, est=2.026083619533125, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='854', iid='490', r_ui=4.0, est=2.893162061903074, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2610', iid='3354', r_ui=3.0, est=2.695000507133241, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1761', iid='1210', r_ui=2.0, est=2.834403309053797, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4302', iid='3763', r_ui=3.0, est=4.139629205905234, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1449', iid='3269', r_ui=2.0, est=2.134250166982981, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5268', iid='342', r_ui=4.0, est=3.5610730618922624, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5614', iid='535', r_ui=4.0, est=3.8093239812349395, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3823', iid='3115', r_ui=3.0, est=2.904429626022603, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1254', iid='1496', r_ui=3.0, est=3.581034530193307, details={'actual_k': 11, 'was_impossible': False}),\n",
              " Prediction(uid='2583', iid='2762', r_ui=5.0, est=4.936734558759394, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3067', iid='3392', r_ui=5.0, est=2.331128772578545, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4957', iid='2478', r_ui=3.0, est=2.365020391842033, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2943', iid='2985', r_ui=5.0, est=3.3493653613394967, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4086', iid='480', r_ui=4.0, est=4.747306608650439, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3940', iid='2687', r_ui=4.0, est=3.3601694911578193, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4818', iid='1214', r_ui=3.0, est=4.39075288161842, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5886', iid='48', r_ui=2.0, est=2.3808552342671634, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4009', iid='1085', r_ui=5.0, est=3.490759064999668, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5858', iid='1304', r_ui=4.0, est=4.062183865612247, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3242', iid='1801', r_ui=2.0, est=2.696676059733215, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5878', iid='1616', r_ui=4.0, est=2.943899368504439, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2103', iid='3821', r_ui=4.0, est=2.819326180260015, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3680', iid='2959', r_ui=4.0, est=4.1140679325673135, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='979', iid='168', r_ui=3.0, est=3.572427406113882, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1068', iid='1393', r_ui=5.0, est=4.114043535411482, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1128', iid='2870', r_ui=3.0, est=3.4354298608838167, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3605', iid='3081', r_ui=3.0, est=3.645109069032895, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3999', iid='2114', r_ui=4.0, est=3.699114917357335, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3507', iid='1220', r_ui=4.0, est=4.148844813019698, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1284', iid='2468', r_ui=4.0, est=3.130838304467206, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5249', iid='534', r_ui=4.0, est=4.183399512915751, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2620', iid='316', r_ui=4.0, est=3.4857658247235332, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='31', iid='905', r_ui=5.0, est=4.374377116381597, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3519', iid='1509', r_ui=4.0, est=3.278504102078989, details={'actual_k': 14, 'was_impossible': False}),\n",
              " Prediction(uid='340', iid='914', r_ui=4.0, est=3.6086590881223892, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1969', iid='616', r_ui=5.0, est=3.6981445439325937, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2962', iid='3379', r_ui=4.0, est=3.4103661523798046, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='963', iid='2324', r_ui=4.0, est=4.19077708336524, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3589', iid='2494', r_ui=4.0, est=3.2557454547847833, details={'actual_k': 14, 'was_impossible': False}),\n",
              " Prediction(uid='3125', iid='2385', r_ui=1.0, est=2.3277607758962167, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4268', iid='2420', r_ui=2.0, est=3.2083564802246665, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='349', iid='47', r_ui=5.0, est=4.21610205575183, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4062', iid='2023', r_ui=4.0, est=3.6871931577758263, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2740', iid='2363', r_ui=1.0, est=3.2232451440368552, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4042', iid='1036', r_ui=4.0, est=3.887828321739029, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='442', iid='2144', r_ui=4.0, est=4.317288550520941, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='259', iid='2686', r_ui=4.0, est=4.288790771903876, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2368', iid='140', r_ui=4.0, est=4.022287467078224, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1108', iid='1193', r_ui=5.0, est=4.689648049121997, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4193', iid='1610', r_ui=5.0, est=4.116797949632291, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5439', iid='3788', r_ui=3.0, est=3.6187711030402316, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4612', iid='2996', r_ui=2.0, est=3.5462283427683734, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='353', iid='2333', r_ui=5.0, est=3.9131447707856175, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5759', iid='2529', r_ui=3.0, est=3.336398611570474, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='678', iid='3489', r_ui=4.0, est=3.144126660940932, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1733', iid='1846', r_ui=5.0, est=3.2117712410066805, details={'actual_k': 16, 'was_impossible': False}),\n",
              " Prediction(uid='5566', iid='2311', r_ui=2.0, est=3.0645521935175086, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2043', iid='3555', r_ui=5.0, est=3.135088383963938, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1943', iid='292', r_ui=3.0, est=3.208315697454212, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5483', iid='2690', r_ui=4.0, est=3.801707197285534, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5447', iid='2757', r_ui=5.0, est=4.281194708872157, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4816', iid='1293', r_ui=5.0, est=4.8163528484585045, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1418', iid='546', r_ui=2.0, est=1.5638071177440183, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3929', iid='1129', r_ui=4.0, est=3.333335905404029, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1127', iid='3354', r_ui=2.0, est=2.229910369698431, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1546', iid='597', r_ui=3.0, est=3.6669236498775524, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1203', iid='3263', r_ui=3.0, est=3.686577634144853, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1873', iid='1959', r_ui=4.0, est=3.5851069662195463, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3647', iid='2628', r_ui=4.0, est=3.4388825374941216, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5460', iid='1199', r_ui=5.0, est=4.793851708462879, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5882', iid='1374', r_ui=5.0, est=3.655045240789061, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='6013', iid='3408', r_ui=5.0, est=3.8883980158470797, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5151', iid='2026', r_ui=3.0, est=2.149008019830389, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2979', iid='588', r_ui=4.0, est=3.8955916073570585, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4416', iid='1242', r_ui=5.0, est=4.640377051808987, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2063', iid='1974', r_ui=4.0, est=3.0699988839760177, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='531', iid='3194', r_ui=3.0, est=3.145691797133716, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4607', iid='1094', r_ui=4.0, est=3.3708605974532637, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4053', iid='2641', r_ui=2.0, est=2.8532912644613235, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1506', iid='2069', r_ui=3.0, est=3.65352507790509, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='352', iid='1230', r_ui=5.0, est=4.248369541249985, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2157', iid='919', r_ui=5.0, est=4.269465438598976, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='308', iid='2054', r_ui=3.0, est=2.7184417852434386, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='903', iid='2716', r_ui=3.0, est=3.617663860248128, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5956', iid='208', r_ui=2.0, est=2.3585186394931146, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3957', iid='2529', r_ui=5.0, est=3.935200944313598, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5536', iid='2916', r_ui=3.0, est=3.3410129433463545, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='58', iid='2144', r_ui=3.0, est=4.22017297412154, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5473', iid='3082', r_ui=3.0, est=3.168021522724607, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='500', iid='954', r_ui=4.0, est=4.233076574626909, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1599', iid='1588', r_ui=1.0, est=2.8469619007577505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1740', iid='1269', r_ui=3.0, est=4.314087499446593, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2012', iid='1017', r_ui=3.0, est=3.301779145196067, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3007', iid='185', r_ui=2.0, est=2.553966821203041, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5880', iid='908', r_ui=2.0, est=3.608618890186928, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2734', iid='2565', r_ui=4.0, est=4.405877053843813, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='733', iid='924', r_ui=4.0, est=4.442373957661075, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3922', iid='1784', r_ui=2.0, est=3.5888261932730168, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='216', iid='933', r_ui=3.0, est=3.9151652759853626, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5543', iid='441', r_ui=4.0, est=4.117685344122508, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4448', iid='2393', r_ui=3.0, est=3.763169631631753, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2484', iid='647', r_ui=3.0, est=3.327589694590074, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3789', iid='1270', r_ui=4.0, est=4.080143432065863, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3359', iid='3252', r_ui=1.0, est=3.2992438370163386, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1335', iid='3430', r_ui=2.0, est=2.3143904139946994, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4238', iid='1884', r_ui=4.0, est=3.61460407782528, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1887', iid='2716', r_ui=3.0, est=3.4139891524626567, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1589', iid='29', r_ui=4.0, est=4.532937743162465, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='474', iid='105', r_ui=2.0, est=3.1893301979453943, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4718', iid='1023', r_ui=4.0, est=3.9673391231614827, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2337', iid='110', r_ui=3.0, est=4.425211049415359, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3044', iid='539', r_ui=5.0, est=4.127441232180697, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2177', iid='1449', r_ui=4.0, est=3.907894959075991, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1912', iid='1199', r_ui=2.0, est=3.178673498375041, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5728', iid='898', r_ui=5.0, est=4.884545975728146, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1354', iid='2496', r_ui=4.0, est=3.2977751780220914, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5614', iid='1345', r_ui=5.0, est=3.619536909677425, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5466', iid='273', r_ui=3.0, est=3.02485790624117, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3508', iid='1127', r_ui=4.0, est=3.8683782808488223, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='330', iid='3793', r_ui=3.0, est=4.066930497583243, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2634', iid='1401', r_ui=3.0, est=3.5258788047442633, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4914', iid='1584', r_ui=3.0, est=3.865026832468865, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1880', iid='1620', r_ui=3.0, est=3.0799482481327525, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3824', iid='3941', r_ui=3.0, est=1.6740626175574032, details={'actual_k': 12, 'was_impossible': False}),\n",
              " Prediction(uid='1087', iid='3036', r_ui=2.0, est=3.1827318922082726, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1328', iid='377', r_ui=3.0, est=3.2720927934946227, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1086', iid='2861', r_ui=4.0, est=3.3293227008077877, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4557', iid='800', r_ui=5.0, est=4.047558418952359, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4353', iid='3751', r_ui=5.0, est=3.756093897804408, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1203', iid='3785', r_ui=3.0, est=3.346629972015414, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4425', iid='608', r_ui=4.0, est=3.89388691771145, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5140', iid='3703', r_ui=3.0, est=3.420775677985385, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4549', iid='2389', r_ui=1.0, est=2.8542742932904326, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2926', iid='1061', r_ui=4.0, est=3.36676396297871, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3018', iid='605', r_ui=4.0, est=3.176160350471724, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5847', iid='551', r_ui=5.0, est=3.4845973112546984, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3164', iid='2694', r_ui=3.0, est=2.648961661300922, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='6003', iid='1641', r_ui=5.0, est=4.247398427924402, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4510', iid='3156', r_ui=3.0, est=2.3729540303678176, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2304', iid='2470', r_ui=4.0, est=3.782542758350444, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1306', iid='31', r_ui=3.0, est=3.631933353111129, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1301', iid='480', r_ui=5.0, est=3.5378281228580626, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2176', iid='2804', r_ui=5.0, est=4.7676231946020415, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1287', iid='2762', r_ui=5.0, est=4.687271718628259, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='352', iid='1801', r_ui=4.0, est=2.4535638226269807, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1599', iid='1394', r_ui=4.0, est=4.044322524541588, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='770', iid='1249', r_ui=5.0, est=3.6775884311069817, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2533', iid='609', r_ui=4.0, est=3.351181929383527, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5989', iid='3477', r_ui=3.0, est=3.6110261862919337, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='78', iid='2384', r_ui=4.0, est=3.578728910017636, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4026', iid='1203', r_ui=3.0, est=4.094978072943468, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='662', iid='596', r_ui=2.0, est=3.469455661207587, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4508', iid='502', r_ui=1.0, est=1.8123585240269091, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5458', iid='1213', r_ui=5.0, est=4.531508770102216, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4779', iid='906', r_ui=5.0, est=4.391778489881609, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='398', iid='112', r_ui=3.0, est=3.302715510733754, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='524', iid='3316', r_ui=1.0, est=2.6483688445825235, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3743', iid='2953', r_ui=3.0, est=2.266871713815684, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2541', iid='3043', r_ui=2.0, est=2.2298547844840284, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5682', iid='1552', r_ui=4.0, est=3.7224721170527144, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2599', iid='616', r_ui=2.0, est=2.904881123625744, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2872', iid='3298', r_ui=3.0, est=3.2875073109001685, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4663', iid='1246', r_ui=3.0, est=3.16665651688621, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1001', iid='647', r_ui=3.0, est=3.355822384836477, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1181', iid='2643', r_ui=2.0, est=1, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4531', iid='3174', r_ui=4.0, est=2.937836087208248, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3110', iid='2970', r_ui=4.0, est=3.6541147371967937, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2164', iid='527', r_ui=3.0, est=4.665808290185532, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1880', iid='799', r_ui=2.0, est=3.077477944352565, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4953', iid='2826', r_ui=4.0, est=3.7747424595830776, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1029', iid='3751', r_ui=3.0, est=3.397657738570461, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2682', iid='1689', r_ui=3.0, est=2.6010710786848477, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3272', iid='2455', r_ui=4.0, est=3.692148572687082, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3471', iid='511', r_ui=3.0, est=2.4969997041450966, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='303', iid='1645', r_ui=1.0, est=3.2300264463489126, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5156', iid='2243', r_ui=5.0, est=4.35798622183713, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='631', iid='733', r_ui=3.0, est=3.8534706165704438, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2436', iid='471', r_ui=4.0, est=4.01862348178806, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4655', iid='1683', r_ui=3.0, est=4.003758585699917, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4099', iid='541', r_ui=4.0, est=4.19180587122839, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2689', iid='2381', r_ui=1.0, est=2.7952518254071697, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='850', iid='909', r_ui=4.0, est=4.074478082750154, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1010', iid='2888', r_ui=1.0, est=1.696211161727942, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3109', iid='3755', r_ui=3.0, est=3.3409214480665304, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3984', iid='112', r_ui=4.0, est=3.6318831628915054, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1137', iid='2210', r_ui=4.0, est=3.8652649206605827, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3705', iid='2747', r_ui=3.0, est=3.270168314288448, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1778', iid='3005', r_ui=3.0, est=4.013540608207812, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5039', iid='3518', r_ui=1.0, est=1.7269886042020166, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2103', iid='2719', r_ui=4.0, est=2.675431608653463, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5394', iid='2356', r_ui=4.0, est=3.1348146389986242, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5977', iid='1234', r_ui=4.0, est=4.365094114325285, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1168', iid='32', r_ui=4.0, est=3.504052694021285, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5517', iid='2186', r_ui=5.0, est=4.597898068872484, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='135', iid='3793', r_ui=5.0, est=3.9930115054312436, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2776', iid='3463', r_ui=2.0, est=1.995758388972588, details={'actual_k': 7, 'was_impossible': False}),\n",
              " Prediction(uid='2509', iid='635', r_ui=4.0, est=3.3331886451952895, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4028', iid='2109', r_ui=5.0, est=3.865650449193819, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4335', iid='337', r_ui=2.0, est=3.6048215177558403, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1041', iid='1176', r_ui=5.0, est=4.554678693382019, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1407', iid='373', r_ui=3.0, est=4.348887545761813, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='881', iid='2918', r_ui=5.0, est=4.1580576657968145, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2206', iid='1717', r_ui=1.0, est=2.891219179554902, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4119', iid='3263', r_ui=3.0, est=3.0808696863482985, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2609', iid='1620', r_ui=5.0, est=4.24196243698167, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2583', iid='1086', r_ui=4.0, est=5, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1645', iid='784', r_ui=1.0, est=3.5773892567147874, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3526', iid='2160', r_ui=3.0, est=3.2802779421886035, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3520', iid='2422', r_ui=1.0, est=2.0123609924451342, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3885', iid='1223', r_ui=5.0, est=4.810257196945652, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='662', iid='2858', r_ui=5.0, est=4.159238968541815, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1503', iid='3479', r_ui=3.0, est=3.602618573913097, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='408', iid='1197', r_ui=5.0, est=4.4851476666116765, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3731', iid='1372', r_ui=2.0, est=2.91640840357088, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3843', iid='1456', r_ui=1.0, est=2.2085138247035707, details={'actual_k': 17, 'was_impossible': False}),\n",
              " Prediction(uid='1231', iid='903', r_ui=3.0, est=4.350285469701907, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='6025', iid='195', r_ui=3.0, est=3.0155034581214712, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4999', iid='3361', r_ui=3.0, est=4.149158310197785, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3793', iid='788', r_ui=2.0, est=3.058443241869994, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3308', iid='296', r_ui=1.0, est=4.38256956404629, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5296', iid='3152', r_ui=5.0, est=4.167802354306588, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3618', iid='1953', r_ui=3.0, est=3.872970969049399, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3295', iid='2722', r_ui=4.0, est=3.4285474979523305, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4810', iid='1370', r_ui=3.0, est=2.6592906675958803, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3885', iid='2717', r_ui=2.0, est=2.8731441471024, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5162', iid='2879', r_ui=3.0, est=3.057446160017075, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1985', iid='2367', r_ui=2.0, est=2.586949825550612, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1958', iid='288', r_ui=4.0, est=3.22924014374128, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1062', iid='1220', r_ui=5.0, est=4.821380318860112, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1303', iid='1748', r_ui=5.0, est=3.4636696845597763, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='697', iid='2739', r_ui=3.0, est=3.854414713931149, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5430', iid='648', r_ui=1.0, est=3.7230085516707705, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='169', iid='413', r_ui=4.0, est=2.8417494876625793, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5428', iid='1672', r_ui=4.0, est=4.342347723958253, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5121', iid='2671', r_ui=4.0, est=3.621313647166588, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='362', iid='380', r_ui=3.0, est=3.0302028586708873, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3260', iid='1263', r_ui=5.0, est=4.410780276703898, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1897', iid='1082', r_ui=3.0, est=3.7839257507307362, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2156', iid='3254', r_ui=4.0, est=2.77339785874726, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2750', iid='1233', r_ui=3.0, est=4.543409707778488, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1376', iid='3752', r_ui=3.0, est=3.627781157905705, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1417', iid='457', r_ui=4.0, est=4.095086898997581, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5085', iid='1358', r_ui=5.0, est=4.411265443429472, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3836', iid='2153', r_ui=2.0, est=1.9603099505576405, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1064', iid='3160', r_ui=4.0, est=3.9753301483297108, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4058', iid='3256', r_ui=2.0, est=3.5750503797405697, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3266', iid='1093', r_ui=3.0, est=4.028724766732491, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='702', iid='1269', r_ui=5.0, est=4.197583981681297, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2149', iid='89', r_ui=3.0, est=3.3707074397301233, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1218', iid='3844', r_ui=3.0, est=3.4912509710112154, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2909', iid='3576', r_ui=3.0, est=3.922582375218955, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3809', iid='1210', r_ui=5.0, est=4.623286605312646, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1100', iid='1019', r_ui=3.0, est=2.549287828744373, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1857', iid='558', r_ui=4.0, est=2.846231723959914, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3469', iid='1377', r_ui=3.0, est=2.8962553403033255, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5522', iid='3211', r_ui=3.0, est=3.901712015476568, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4404', iid='1611', r_ui=2.0, est=3.475548904628179, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='392', iid='3424', r_ui=4.0, est=3.5028114216336856, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2073', iid='1206', r_ui=5.0, est=4.181404423487314, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1632', iid='1090', r_ui=4.0, est=3.484158734599901, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='621', iid='1617', r_ui=3.0, est=4.001517751931965, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5107', iid='2527', r_ui=3.0, est=2.6375856148819827, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='546', iid='1191', r_ui=3.0, est=2.43946240659275, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5300', iid='2289', r_ui=5.0, est=4.720285275790451, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1896', iid='928', r_ui=4.0, est=4.448392391222734, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1059', iid='1172', r_ui=3.0, est=3.5894212054682315, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2105', iid='1732', r_ui=5.0, est=3.8027679227403715, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1033', iid='3273', r_ui=4.0, est=2.557136788974011, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1687', iid='1713', r_ui=5.0, est=3.620178174760893, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4605', iid='3260', r_ui=3.0, est=2.8452743746906117, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3471', iid='2501', r_ui=3.0, est=3.9117612831264776, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4306', iid='3660', r_ui=2.0, est=3.2412405047771116, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4847', iid='858', r_ui=4.0, est=4.38721405372473, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1140', iid='2782', r_ui=3.0, est=3.3820977955050044, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='436', iid='2628', r_ui=2.0, est=3.555757391099866, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3380', iid='3545', r_ui=4.0, est=4.261652407155429, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4020', iid='1610', r_ui=3.0, est=3.5557277150325945, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5475', iid='1127', r_ui=1.0, est=4.15898587297606, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5246', iid='3160', r_ui=4.0, est=3.8921302852450124, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4578', iid='3186', r_ui=3.0, est=3.797618993759172, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5907', iid='919', r_ui=3.0, est=3.674944131211997, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5855', iid='531', r_ui=4.0, est=4.117460930974647, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1984', iid='2018', r_ui=4.0, est=3.4164983346236673, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='19', iid='457', r_ui=3.0, est=4.406734508013583, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1260', iid='164', r_ui=4.0, est=3.815512156892797, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1988', iid='2946', r_ui=4.0, est=3.4897809662930093, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3927', iid='627', r_ui=3.0, est=3.9552944397131773, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1105', iid='2028', r_ui=4.0, est=4.220521288918135, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3741', iid='1580', r_ui=4.0, est=3.4666211299139604, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4908', iid='344', r_ui=3.0, est=3.0261513032862766, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1387', iid='2085', r_ui=2.0, est=2.7407284867162787, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5572', iid='431', r_ui=3.0, est=3.7252863820235986, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3486', iid='1220', r_ui=4.0, est=4.52211871048488, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5536', iid='1265', r_ui=3.0, est=3.1186639981663973, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1680', iid='3770', r_ui=5.0, est=3.74844953220292, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5542', iid='615', r_ui=5.0, est=4.911673279753178, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5738', iid='1973', r_ui=2.0, est=1.6010501113966171, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1698', iid='3724', r_ui=4.0, est=4.167131766068038, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3539', iid='514', r_ui=4.0, est=4.052783387292514, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5954', iid='181', r_ui=1.0, est=1.4437012259139055, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5306', iid='432', r_ui=1.0, est=2.5165011632307626, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1151', iid='562', r_ui=1.0, est=3.5955232654675475, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1922', iid='1983', r_ui=3.0, est=2.5802407741103153, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1246', iid='1960', r_ui=4.0, est=4.389637348002995, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5886', iid='3444', r_ui=3.0, est=2.603418188236526, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2456', iid='1265', r_ui=3.0, est=2.9551277930977866, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5220', iid='2912', r_ui=3.0, est=3.232444868218561, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5847', iid='912', r_ui=4.0, est=4.981865642928106, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1465', iid='2422', r_ui=2.0, est=2.1019025091130508, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2840', iid='1866', r_ui=4.0, est=2.134326635204428, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4481', iid='1693', r_ui=4.0, est=3.187263754466831, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5736', iid='1259', r_ui=4.0, est=4.377003606204412, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1983', iid='2944', r_ui=5.0, est=4.8527547254903425, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4335', iid='3169', r_ui=3.0, est=3.4201002140094494, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3371', iid='1884', r_ui=1.0, est=3.541209650055773, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4510', iid='3105', r_ui=3.0, est=3.215730830778266, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1194', iid='223', r_ui=4.0, est=3.8773677405205453, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4287', iid='517', r_ui=4.0, est=3.6507586520689226, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3988', iid='587', r_ui=4.0, est=3.8519709464106966, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3229', iid='3719', r_ui=3.0, est=3.3555531443208197, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1227', iid='535', r_ui=4.0, est=4.205224297266133, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3505', iid='1221', r_ui=4.0, est=4.047015667577286, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3942', iid='1805', r_ui=3.0, est=2.5390973312785574, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2181', iid='3927', r_ui=4.0, est=3.2456381393597464, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='190', iid='2599', r_ui=5.0, est=4.033311350552715, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1869', iid='583', r_ui=1.0, est=3.6894884700310127, details={'actual_k': 14, 'was_impossible': False}),\n",
              " Prediction(uid='2967', iid='2384', r_ui=4.0, est=3.0758560828177, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5367', iid='1188', r_ui=3.0, est=3.125166215831329, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3382', iid='1784', r_ui=3.0, est=4.020583004236363, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5321', iid='1079', r_ui=3.0, est=3.6214453065499415, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1880', iid='1371', r_ui=3.0, est=2.790100946358647, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2567', iid='1206', r_ui=4.0, est=3.80522916853263, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3036', iid='1307', r_ui=5.0, est=4.490918181909718, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4828', iid='2266', r_ui=2.0, est=3.016820080379483, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4958', iid='1291', r_ui=5.0, est=3.8033833520174984, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1099', iid='89', r_ui=2.0, est=2.7808686423685547, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='710', iid='2985', r_ui=4.0, est=3.1630057568547683, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3650', iid='1200', r_ui=5.0, est=4.334731472147037, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5889', iid='1211', r_ui=1.0, est=4.369919297576842, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5605', iid='2542', r_ui=3.0, est=3.4243458680814096, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='161', iid='1073', r_ui=3.0, est=4.189740546961557, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3789', iid='858', r_ui=5.0, est=4.628913837848008, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2114', iid='3623', r_ui=3.0, est=3.2900021087867377, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2590', iid='1584', r_ui=4.0, est=3.945862308323221, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2678', iid='1219', r_ui=5.0, est=4.117233986415679, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='235', iid='1267', r_ui=5.0, est=4.885888196528238, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1051', iid='1073', r_ui=5.0, est=4.2132707570731425, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5643', iid='361', r_ui=2.0, est=2.7666347410904764, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='181', iid='2470', r_ui=4.0, est=2.8898988957419363, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5121', iid='2353', r_ui=3.0, est=4.064693625953085, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2576', iid='724', r_ui=3.0, est=2.7590595348208633, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2050', iid='3481', r_ui=4.0, est=4.364812464323522, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1425', iid='1010', r_ui=2.0, est=3.2238765663180544, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='741', iid='1991', r_ui=4.0, est=2.9890849077596853, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='249', iid='349', r_ui=5.0, est=3.9680829084508926, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1675', iid='1993', r_ui=1.0, est=1.6265935608899542, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3138', iid='2018', r_ui=3.0, est=3.691791044823694, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2073', iid='2245', r_ui=3.0, est=3.5986067604210534, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4181', iid='2694', r_ui=2.0, est=2.5774062978260823, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1206', iid='316', r_ui=4.0, est=3.7926212620373496, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3804', iid='1221', r_ui=5.0, est=4.075180007601355, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='1746', iid='3000', r_ui=5.0, est=5, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='453', iid='953', r_ui=4.0, est=4.407391251059556, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='415', iid='920', r_ui=5.0, est=3.875976295563505, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5461', iid='2926', r_ui=4.0, est=3.4528549181368287, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3732', iid='3703', r_ui=4.0, est=3.109829754008539, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4083', iid='922', r_ui=4.0, est=4.155878686558032, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3391', iid='1527', r_ui=5.0, est=3.86289884783088, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2453', iid='2829', r_ui=2.0, est=3.109584312075457, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5077', iid='1294', r_ui=5.0, est=3.811799504046951, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3313', iid='151', r_ui=4.0, est=3.65984114607954, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4656', iid='586', r_ui=4.0, est=3.489965511843185, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5333', iid='1892', r_ui=3.0, est=3.563197851269804, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5512', iid='1380', r_ui=5.0, est=4.250522855627126, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4169', iid='2067', r_ui=3.0, est=4.446549463695147, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4139', iid='1192', r_ui=4.0, est=3.969162847269958, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='2195', iid='1704', r_ui=5.0, est=4.207171040811396, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='4026', iid='500', r_ui=3.0, est=2.9618755788540856, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3503', iid='2492', r_ui=2.0, est=2.9887034264270906, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3989', iid='2302', r_ui=3.0, est=3.8697364612810987, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='5717', iid='858', r_ui=4.0, est=4.608890546449559, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='53', iid='3654', r_ui=5.0, est=4.4887634534200425, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='631', iid='2378', r_ui=1.0, est=2.9216167665217636, details={'actual_k': 20, 'was_impossible': False}),\n",
              " Prediction(uid='3983', iid='380', r_ui=4.0, est=3.367699510751049, details={'actual_k': 20, 'was_impossible': False}),\n",
              " ...]"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "df = pd.DataFrame(test_knn_pred)\n",
        "df.rename(columns = {'uid': 'user_id','iid': 'item_id','r_ui':'og_rating','est':'pred_rating'}, inplace = True)"
      ],
      "metadata": {
        "id": "_G1_lheGF8c1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.drop(['details'], axis = 1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "rRypI3NpGoBr",
        "outputId": "363aef3e-422f-46e9-99de-7fcf8d988b23"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       user_id item_id  og_rating  pred_rating\n",
              "0         4048    1839        3.0     2.671259\n",
              "1         1181    2871        3.0     3.189054\n",
              "2          451    2612        4.0     4.760734\n",
              "3          673    2818        1.0     1.000000\n",
              "4         4524    2699        3.0     3.163891\n",
              "...        ...     ...        ...          ...\n",
              "200037    2059    2717        2.0     2.436918\n",
              "200038     343    2080        5.0     4.792007\n",
              "200039    3868    2641        3.0     3.002048\n",
              "200040    3243     165        4.0     3.778784\n",
              "200041    3808     580        4.0     2.802598\n",
              "\n",
              "[200042 rows x 4 columns]"
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              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-bc2009ec-84f5-4738-a931-a00f0f4d1612 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-bc2009ec-84f5-4738-a931-a00f0f4d1612');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "precision, recall, f_score = precision_recall_fmeasure(mat_movies_users, 3.5)\n",
        "ndcg_measure = ndcg(mat_movies_users)\n",
        "print(\"The precision is \", precision)\n",
        "print(\"The recall is \", recall)\n",
        "print(\"The f-score is \", f_score)\n",
        "print(\"The NDCG value is \", ndcg_measure)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kPdP3ksNqzMD",
        "outputId": "376990a5-710b-4e71-f30d-b0593ee5030e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The precision is  0.9\n",
            "The recall is  0.58\n",
            "The f-score is  0.7\n",
            "The NDCG value is  0.97\n"
          ]
        }
      ]
    }
  ]
}