gradient_descent_step by step.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "df6c8355",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8f41abfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y=make_regression(n_samples=4,n_features=1,n_informative=1,n_targets=1,noise=80,random_state=13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f273a2c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  7.21786552,  16.04609925, -27.83756166, 144.36688189])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1b874b07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.71239066,  0.45181234, -0.04450308,  0.75376638])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3a0e2404",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2a77af47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "477c3f6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x249286ab7f0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f43d9b20",
   "metadata": {},
   "outputs": [],
   "source": [
    "#lets apply ols\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a74aa8ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg=LinearRegression()\n",
    "reg.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c9782680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([78.35063668])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f2f6142b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.15963284313262"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "244765f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2492a0ce850>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y)\n",
    "plt.plot(X,reg.predict(X),color=\"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "915a6f39",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets apply Gradient Descent assuming slope is constant m = 78.35\n",
    "# and let's assume the starting value for intercept b = 0\n",
    "\n",
    "y_pred=((78.35*X)+100).reshape(4) #lets b=100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "db69cf58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9d595374",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 44.18419163, 135.39949674,  96.51318381, 159.05759577])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "dc8a96b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2492a152c40>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y)\n",
    "plt.plot(X,reg.predict(X),color=\"red\",label=\"ols\")\n",
    "plt.plot(X,y_pred,color=\"b\",label=\"mera\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8ba65ad2",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 78.35\n",
    "b=100\n",
    "loss_slope= -2 * sum(y-m*X.ravel()-b) #for using rable loss_slopw will be 1 diamention"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1fe87e06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "590.7223659179078"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "89cb3d22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "59.072236591790784"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr=.1\n",
    "step_size=loss_slope*lr\n",
    "step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3cabe834",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.927763408209216"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b=b-step_size\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "16b3db9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2492a1d9fa0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred1=((78.35*X)+b).reshape(4)\n",
    "plt.scatter(X,y)\n",
    "plt.plot(X,reg.predict(X),color=\"red\",label=\"ols\")\n",
    "plt.plot(X,y_pred1,color=\"b\",label=\"b={}\".format(b))\n",
    "plt.plot(X,y_pred,color=\"y\",label=\"b=0\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6cad79c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "loss_slope= -2 * sum(y-m*X.ravel()-b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fd1bfad3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "118.14447318358157"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5c014a3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.814447318358157"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "step_size=loss_slope*lr\n",
    "step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "652301a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "b=b-step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a988277e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.11331608985106"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f78581e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2492a234c70>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred2=((78.35*X)+b).reshape(4)\n",
    "plt.scatter(X,y)\n",
    "plt.plot(X,reg.predict(X),color=\"red\",label=\"ols\")\n",
    "plt.plot(X,y_pred2,color=\"#5C5858\",label=\"b=20.927763408209216\")\n",
    "plt.plot(X,y_pred1,color=\"b\",label=\"b={}\".format(b))\n",
    "plt.plot(X,y_pred,color=\"y\",label=\"b=0\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ff64b717",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-45.782671307790594"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss_slope=-2*sum(y-X.ravel()-b)\n",
    "loss_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "88982bee",
   "metadata": {},
   "outputs": [],
   "source": [
    "step_size=loss_slope*lr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0f52802c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.57826713077906"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "e2714a99",
   "metadata": {},
   "outputs": [],
   "source": [
    "b=b-step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e5ec0e2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2492a2f8190>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred3=((78.35*X)+b).reshape(4)\n",
    "plt.scatter(X,y)\n",
    "plt.plot(X,reg.predict(X),color=\"red\",label=\"ols\")\n",
    "\n",
    "plt.plot(X,y_pred3,color=\"#5C5859\",label=\"b={}\".format(b))\n",
    "plt.plot(X,y_pred2,color=\"#5C5858\",label=\"b=20.927763408209216\")\n",
    "plt.plot(X,y_pred1,color=\"b\",label=\"b={}\".format(b))\n",
    "plt.plot(X,y_pred,color=\"y\",label=\"b=0\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d52508b8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "dba43dca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2492a34c8e0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "b=-100\n",
    "m=78.35\n",
    "lr=.1\n",
    "epochs=10\n",
    "for i in range(epochs):\n",
    "    loss_slope= -2* sum(y-m*X.ravel()-b)\n",
    "    b=b- (lr*loss_slope)\n",
    "    y_pred=m*X+b\n",
    "    plt.plot(X,y_pred)\n",
    "plt.scatter(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1e25688",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}