# Wolfram Mathematica

## Find the Optimal Parameters of a Classifier

Load a dataset and split it into a training set and a test set.

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```data = RandomSample[ ExampleData[{"MachineLearning", "Titanic"}, "Data"] ]; training = data[[;; 1000]]; test = data[[1001 ;;]];```

Define a function computing the performance of a classifier as a function of its (hyper) parameters.

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```loss[{c_, gamma_, b_, d_}] := -ClassifierMeasurements[ Classify[training, Method -> {"SupportVectorMachine", "KernelType" -> "Polynomial", "SoftMarginParameter" -> Exp[c], "GammaScalingParameter" -> Exp[gamma], "BiasParameter" -> Exp[b], "PolynomialDegree" -> d } ], test, "LogLikelihoodRate"];```

Define the possible value of the parameters.

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```region = ImplicitRegion[And[ -3. <= c <= 3., -3. <= gamma <= 3. , -1. <= b <= 2., 1 <= d <= 3 , d \[Element] Integers], { c, gamma, b, d}]```
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Search for a good set of parameters.

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`bmo = BayesianMinimization[loss, region]`
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`bmo["MinimumConfiguration"]`
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Train a classifier with these parameters.

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```Classify[training, Method -> {"SupportVectorMachine", "KernelType" -> "Polynomial", "SoftMarginParameter" -> Exp[2.979837222482109`], "GammaScalingParameter" -> Exp[-2.1506497693543025`], "BiasParameter" -> Exp[-0.9038364134482837`], "PolynomialDegree" -> 2} ]```
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