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fix typos, wording and clarify code examples
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sourceCode4 committed Jan 19, 2024
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48 changes: 24 additions & 24 deletions docs/src/tutorials/advanced_search.ipynb
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"There is also another search method called `search_best` which return both the solution and the possible error. The method returns the best program found so far. In this case, we can also see the error (`typemax(Int)`):"
"There is another search method called `search_best` which returns both the solution and the possible error. The method returns the best program found so far. In this case, we can also see the error (`typemax(Int)`):"
]
},
{
Expand All @@ -135,11 +135,11 @@
"source": [
"## Search methods\n",
"\n",
"We now show examples of using different search procedures, which are initialized by using different enumerators that are passed to the search function.\n",
"We now show examples of using different search procedures, which are initialized by passing different enumerators to the search function.\n",
"\n",
"### Breadth-First Search\n",
"\n",
"The breadth-first search will first enumerate all possible programs at the same depth before considering a program with a depth of one more. A tree of the grammar is returned with programs ordered in increasing sizes. We can first `collect` the programs that have a `max-depth` of 2 and a `max_size` of infinite (integer maximum value), where the starting symbol is of type `Real`. This function uses a default heuristic 'left-most first', such that the left-most child in the tree is always explored first."
"The breadth-first search will first enumerate all possible programs at the same depth before considering programs with a depth of one more. A tree of the grammar is returned with programs ordered in increasing sizes. We can first `collect` the programs that have a `max-depth` of 2 and a `max_size` of infinite (integer maximum value), where the starting symbol is of type `Real`. This function uses a default heuristic 'left-most first', such that the left-most child in the tree is always explored first."
]
},
{
Expand All @@ -159,7 +159,7 @@
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"We can test that this function returns the correct functions and all functions. "
"We can test that this function returns all and only the correct functions. "
]
},
{
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"\n",
"One of the stochastic search methods that is implemented is Metropolis-Hastings (MH), which samples from a distribution of programs based on the grammar. For more information on MH, see for example [this webpage](https://stephens999.github.io/fiveMinuteStats/MH_intro.html).\n",
"\n",
"The below example uses a simple arithmetic example. You can try running this code block multiple times, which will give different programs, as the search is stochastic. "
"The example below uses a simple arithmetic example. You can try running this code block multiple times, which will give different programs, as the search is stochastic. "
]
},
{
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"e = Meta.parse(\"x -> x * x + 4\")\n",
"problem, examples = create_problem(eval(e))\n",
"e = x -> x * x + 4\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_mh_enumerator(examples, mean_squared_error)\n",
"program, cost = search_best(grammar, problem, :X, enumerator=enumerator, error_function=mse_error_function, max_depth=3)"
]
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"source": [
"### Very Large Scale Neighbourhood Search \n",
"\n",
"The second implemented stochastic search method is VLSN, which search for a local optimum in the neighbourhood. For more information, see [this article](https://backend.orbit.dtu.dk/ws/portalfiles/portal/5293785/Pisinger.pdf).\n",
"The second implemented stochastic search method is VLSN, which searches for a local optimum in the neighbourhood. For more information, see [this article](https://backend.orbit.dtu.dk/ws/portalfiles/portal/5293785/Pisinger.pdf).\n",
"\n",
"Given the same grammar as before, we can try with some simple examples."
"Given the same grammar as before, we can try it with some simple examples."
]
},
{
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"e = Meta.parse(\"x -> 10\")\n",
"e = x -> 10\n",
"max_depth = 2\n",
"problem, examples = create_problem(eval(e))\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_vlsn_enumerator(examples, mean_squared_error, max_depth)\n",
"program, cost = search_best(grammar, problem, :X, enumerator=enumerator, error_function=mse_error_function, max_depth=max_depth)\n"
]
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"source": [
"e = Meta.parse(\"x -> x\")\n",
"e = x -> x\n",
"max_depth = 1\n",
"problem, examples = create_problem(eval(e))\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_vlsn_enumerator(examples, mean_squared_error, max_depth)\n",
"program, cost = search_best(grammar, problem, :X, enumerator=enumerator, error_function=mse_error_function, max_depth=max_depth)"
]
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"source": [
"### Simulated Annealing\n",
"\n",
"The third stochastic search method is called simulated annealing, is another hill-climbing method to find local optima. For more information, see [this page](https://www.cs.cmu.edu/afs/cs.cmu.edu/project/learn-43/lib/photoz/.g/web/glossary/anneal.html).\n",
"The third stochastic search method is called simulated annealing. This is another hill-climbing method to find local optima. For more information, see [this page](https://www.cs.cmu.edu/afs/cs.cmu.edu/project/learn-43/lib/photoz/.g/web/glossary/anneal.html).\n",
"\n",
"We try the example from earlier, but now we can additionally define the `initial_temperature` of the algorithm, which is 1 by default. Change the value below to see the effect."
]
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"e = Meta.parse(\"x -> x * x + 4\")\n",
"e = x -> x * x + 4\n",
"initial_temperature = 1\n",
"problem, examples = create_problem(eval(e))\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_sa_enumerator(examples, mean_squared_error, initial_temperature)\n",
"program, cost = search_best(grammar, problem, :X, enumerator=enumerator, error_function=mse_error_function, max_depth=3) "
]
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"metadata": {},
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"source": [
"e = Meta.parse(\"x -> x * x + 4\")\n",
"e = x -> x * x + 4\n",
"initial_temperature = 2\n",
"problem, examples = create_problem(eval(e))\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_sa_enumerator(examples, mean_squared_error, initial_temperature)\n",
"program, cost = @time search_best(grammar, problem, :X, enumerator=enumerator, error_function=mse_error_function, max_depth=3)"
]
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"metadata": {},
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"source": [
"e = Meta.parse(\"x -> 3 * x * x + (x + 2)\")\n",
"problem, examples = create_problem(eval(e))\n",
"e = x -> 3 * x * x + (x + 2)\n",
"problem, examples = create_problem(e)\n",
"enumerator = get_genetic_enumerator(examples, \n",
" initial_population_size = 10,\n",
" mutation_probability = 0.8,\n",
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