--- title: "ContingencyTable" language: "en" type: "Method" summary: "ContingencyTable (Machine Learning Method) Method for LearnDistribution. Use a table to store the probabilities of a nominal vector for each possible outcome. A contingency table models the probability distribution of a nominal vector space by storing a probability value for each possible outcome. If the data is unidimensional, the distribution corresponds to a categorical distribution. The following options can be given: If the data contains numerical values, they are discretized. The resulting distribution is still a valid distribution in the original space. Information[LearnedDistribution[\\[Ellipsis]],MethodOption] can be used to extract the values of options chosen by the automation system. LearnDistribution[\\[Ellipsis],FeatureExtractor->Minimal] can be used to remove most preprocessing and directly access the method." keywords: - Machine Learning - Classification - Logistic function canonical_url: "https://reference.wolfram.com/language/ref/method/ContingencyTable.html" source: "Wolfram Language Documentation" --- # "ContingencyTable" (Machine Learning Method) * Method for ``LearnDistribution``. * Use a table to store the probabilities of a nominal vector for each possible outcome. --- ## Details & Suboptions * A contingency table models the probability distribution of a nominal vector space by storing a probability value for each possible outcome. * If the data is unidimensional, the distribution corresponds to a categorical distribution. * The following options can be given: "AdditiveSmoothing" [`Automatic`](https://reference.wolfram.com/language/ref/Automatic.en.md) value to be added to each count * If the data contains numerical values, they are discretized. The resulting distribution is still a valid distribution in the original space. * ``Information[LearnedDistribution[…], "MethodOption"]`` can be used to extract the values of options chosen by the automation system. * ``LearnDistribution[…, FeatureExtractor -> "Minimal"]`` can be used to remove most preprocessing and directly access the method. --- ## Examples (4) ### Basic Examples (3) Train a contingency-table distribution on a nominal dataset: ```wl In[1]:= ld = LearnDistribution[{"A", "A", "B", "B", "B"}, Method -> "ContingencyTable"] Out[1]= LearnedDistribution[Association["ExampleNumber" -> 5, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Nominal"]], "Output" -> Association["f1" -> Associati ... 87, -0.5581045242273198}, "LeftBoundary" -> -0.8482875978539917, "LeftScale" -> 0.04164962654198675, "LeftTailNorm" -> 0.10714285714285714]], "Entropy" -> Around[0.6820133850147919, 0.020306153124905864], "EntropySampleSize" -> 56]] ``` Look at the distribution ``Information`` : ```wl In[2]:= Information[ld] Out[2]= MachineLearning`MLInformationObject[LearnedDistribution[Association["ExampleNumber" -> 5, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Nominal"]], "O ... .5581287164962436}, "LeftBoundary" -> -0.8478507247066664, "LeftScale" -> 0.03621212688039488, "LeftTailNorm" -> 0.10294117647058823]], "Entropy" -> Around[0.6774168640087993, 0.018115682147101412], "EntropySampleSize" -> 68]]] ``` Obtain options information: ```wl In[3]:= Information[ld, "MethodOption"] Out[3]= Method -> {"ContingencyTable", "AdditiveSmoothing" -> 1} ``` Obtain an option value directly: ```wl In[4]:= Information[ld, "AdditiveSmoothing"] Out[4]= 1 ``` Compute the probabilities for the values ``"A"`` and ``"B"`` : ```wl In[5]:= PDF[ld, "A"] Out[5]= 0.428571 In[6]:= PDF[ld, "B"] Out[6]= 0.571429 ``` Generate new samples: ```wl In[7]:= RandomVariate[ld, 10] Out[7]= {"A", "B", "A", "B", "A", "B", "B", "B", "A", "B"} ``` --- Train a contingency-table distribution on a numeric dataset: ```wl In[1]:= ld = LearnDistribution[{1.2, 2.1, 3.5, 4.3}, Method -> "ContingencyTable"] Out[1]= LearnedDistribution[Association["ExampleNumber" -> 4, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> Association["f1" -> Associa ... 5946821074114402, -0.5943034615151463}, "LeftBoundary" -> -1.4934068319758655, "LeftScale" -> 0.0008207380195640971, "LeftTailNorm" -> 0.125]], "Entropy" -> Around[1.1647162356455172, 0.0882542889133266], "EntropySampleSize" -> 24]] ``` Look at the distribution ``Information`` : ```wl In[2]:= Information[ld] Out[2]= MachineLearning`MLInformationObject[LearnedDistribution[Association["ExampleNumber" -> 4, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... 821074114402, -0.5943034615151463}, "LeftBoundary" -> -1.4934068319758655, "LeftScale" -> 0.0008207380195640971, "LeftTailNorm" -> 0.125]], "Entropy" -> Around[1.1647162356455172, 0.0882542889133266], "EntropySampleSize" -> 24]]] ``` Compute the probability density for a new example: ```wl In[3]:= PDF[ld, 1.3] Out[3]= 0.550055 ``` Plot the PDF along with the training data: ```wl In[4]:= Show[Plot[PDF[ld, x], {x, -2, 8}, Filling -> Bottom], NumberLinePlot[{1.2, 2.1, 3.5, 4.3}, Spacings -> 0, PlotStyle -> Red]] Out[4]= [image] ``` Generate and visualize new samples: ```wl In[5]:= Histogram[RandomVariate[ld, 10000], 50] Out[5]= [image] ``` --- Train a contingency-table distribution on a two-dimensional dataset: ```wl In[1]:= iris = ExampleData[{"MachineLearning", "FisherIris"}, "Data"][[All, 1, {1, 3}]]; In[2]:= ld = LearnDistribution[iris, Method -> "ContingencyTable"] Out[2]= LearnedDistribution[Association["ExampleNumber" -> 150, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "NumericalVector", "Length" -> 2]], "Output" -> ... -> CompressedData["«620»"], "LeftBoundary" -> -2.5125888451725027, "LeftScale" -> 0.408908418811996, "LeftTailNorm" -> 0.02072538860103627]], "Entropy" -> Around[2.268940957994351, 0.042260501401623164], "EntropySampleSize" -> 772]] ``` Plot the PDF along with the training data: ```wl In[3]:= Show[ContourPlot[PDF[ld, {x, y}], {x, 4, 8}, {y, 1, 7}, PlotRange -> All, Contours -> 10], ListPlot[iris, PlotStyle -> Red]] Out[3]= [image] ``` Use ``SynthesizeMissingValues`` to impute missing values using the learned distribution: ```wl In[4]:= SynthesizeMissingValues[ld, {5.5, Missing[]}] Out[4]= {5.5, 4.39872} In[5]:= Histogram[Table[Last@SynthesizeMissingValues[ld, {5.5, Missing[]}], 1000]] Out[5]= [image] ``` ### Options (1) #### "AdditiveSmoothing" (1) Train a contingency-table distribution on a nominal dataset without any smoothing: ```wl In[1]:= ld = LearnDistribution[{"A", "A", "B", "B", "B"}, Method -> {"ContingencyTable", "AdditiveSmoothing" -> 0}] Out[1]= LearnedDistribution[Association["ExampleNumber" -> 5, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Nominal"]], "Output" -> Association["f1" -> Associati ... 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}], "LogPDFDistribution" -> Missing[], "Entropy" -> Around[0.7072859632994796, 0.11770779776346137], "EntropySampleSize" -> 3]] ``` Compute the probabilities for the values ``"A"`` and ``"B"`` : ```wl In[2]:= PDF[ld, {"A", "B"}] Out[2]= {0.4, 0.6} ``` Compare with the probabilities obtained after adding 1 and 10 counts to each outcome: ```wl In[3]:= ld = LearnDistribution[{"A", "A", "B", "B", "B"}, Method -> {"ContingencyTable", "AdditiveSmoothing" -> 1}] Out[3]= LearnedDistribution[Association["ExampleNumber" -> 5, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Nominal"]], "Output" -> Association["f1" -> Associati ... 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}], "LogPDFDistribution" -> Missing[], "Entropy" -> Around[0.7003970336970156, 0.08281274035887244], "EntropySampleSize" -> 3]] In[4]:= PDF[ld, {"A", "B"}] Out[4]= {0.428571, 0.571429} In[5]:= ld = LearnDistribution[{"A", "A", "B", "B", "B"}, Method -> {"ContingencyTable", "AdditiveSmoothing" -> 10}] Out[5]= LearnedDistribution[Association["ExampleNumber" -> 5, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Nominal"]], "Output" -> Association["f1" -> Associati ... , "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}], "LogPDFDistribution" -> Missing[], "Entropy" -> Around[0.7204235231045195, 0.013644591495560496], "EntropySampleSize" -> 3]] In[6]:= PDF[ld, {"A", "B"}] Out[6]= {0.48, 0.52} ``` ## See Also * [`LearnDistribution`](https://reference.wolfram.com/language/ref/LearnDistribution.en.md) * [`LearnedDistribution`](https://reference.wolfram.com/language/ref/LearnedDistribution.en.md) * [`AnomalyDetection`](https://reference.wolfram.com/language/ref/AnomalyDetection.en.md) * [`SynthesizeMissingValues`](https://reference.wolfram.com/language/ref/SynthesizeMissingValues.en.md) * [`RandomVariate`](https://reference.wolfram.com/language/ref/RandomVariate.en.md) * [`PDF`](https://reference.wolfram.com/language/ref/PDF.en.md) * [`RarerProbability`](https://reference.wolfram.com/language/ref/RarerProbability.en.md) * [`DecisionTree`](https://reference.wolfram.com/language/ref/method/DecisionTree.en.md) * [`KernelDensityEstimation`](https://reference.wolfram.com/language/ref/method/KernelDensityEstimation.en.md) * [`NaiveBayes`](https://reference.wolfram.com/language/ref/method/NaiveBayes.en.md) ## Related Links * [An Elementary Introduction to the Wolfram Language: Machine Learning](https://www.wolfram.com/language/elementary-introduction/22-machine-learning.html) ## History * [Introduced in 2019 (12.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn120.en.md)