margin - Classification margins for generalized additive model (GAM) - MATLAB (original) (raw)

Classification margins for generalized additive model (GAM)

Since R2021a

Syntax

Description

`m` = margin([Mdl](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Mdl),[Tbl](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Tbl),[ResponseVarName](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-ResponseVarName)) returns the Classification Margin (m) for the generalized additive model Mdl using the predictor data inTbl and the true class labels inTbl.ResponseVarName.

m is returned as an _n_-by-1 numeric column vector, where n is the number of observations in the predictor data.

`m` = margin([Mdl](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Mdl),[Tbl](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Tbl),[Y](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Y)) uses the predictor data in table Tbl and the true class labels inY.

`m` = margin([Mdl](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Mdl),[X](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-X),[Y](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-Y)) uses the predictor data in matrix X and the true class labels inY.

example

`m` = margin(___,'IncludeInteractions',[includeInteractions](#mw%5F3d1a2c23-6f48-4e5b-a26e-93fc03f36740%5Fsep%5Fshared-includeInteractions)) specifies whether to include interaction terms in computations. You can specifyincludeInteractions in addition to any of the input argument combinations in the previous syntaxes.

example

Examples

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Estimate the test sample classification margins and edge of a generalized additive model. The test sample margins are the observed true class scores minus the false class scores, and the test sample edge is the mean of the margins.

Load the fisheriris data set. Create X as a numeric matrix that contains two sepal and two petal measurements for versicolor and virginica irises. Create Y as a cell array of character vectors that contains the corresponding iris species.

load fisheriris inds = strcmp(species,'versicolor') | strcmp(species,'virginica'); X = meas(inds,:); Y = species(inds,:);

Randomly partition observations into a training set and a test set with stratification, using the class information in Y. Specify a 30% holdout sample for testing.

rng('default') % For reproducibility cv = cvpartition(Y,'HoldOut',0.30);

Extract the training and test indices.

trainInds = training(cv); testInds = test(cv);

Specify the training and test data sets.

XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);

Train a GAM using the predictors XTrain and class labels YTrain. A recommended practice is to specify the class names.

Mdl = fitcgam(XTrain,YTrain,'ClassNames',{'versicolor','virginica'});

Mdl is a ClassificationGAM model object.

Estimate the test sample classification margins and edge.

m = margin(Mdl,XTest,YTest); e = edge(Mdl,XTest,YTest)

Display the histogram of the test sample classification margins.

histogram(m,length(unique(m)),'Normalization','probability') xlabel('Test Sample Margins') ylabel('Probability') title('Probability Distribution of the Test Sample Margins')

Figure contains an axes object. The axes object with title Probability Distribution of the Test Sample Margins, xlabel Test Sample Margins, ylabel Probability contains an object of type histogram.

Compare a GAM with linear terms to a GAM with both linear and interaction terms by examining the test sample margins and edge. Based solely on this comparison, the classifier with the highest margins and edge is the best model.

Load the ionosphere data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

Randomly partition observations into a training set and a test set with stratification, using the class information in Y. Specify a 30% holdout sample for testing.

rng('default') % For reproducibility cv = cvpartition(Y,'Holdout',0.30);

Extract the training and test indices.

trainInds = training(cv); testInds = test(cv);

Specify the training and test data sets.

XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);

Train a GAM that contains both linear and interaction terms for predictors. Specify to include all available interaction terms whose _p_-values are not greater than 0.05.

Mdl = fitcgam(XTrain,YTrain,'Interactions','all','MaxPValue',0.05)

Mdl = ClassificationGAM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: 'logit' Intercept: 3.0398 Interactions: [561×2 double] NumObservations: 246

Properties, Methods

Mdl is a ClassificationGAM model object. Mdl includes all available interaction terms.

Estimate the test sample margins and edge for Mdl.

M = margin(Mdl,XTest,YTest); E = edge(Mdl,XTest,YTest)

Estimate the test sample margins and edge for Mdl without including interaction terms.

M_nointeractions = margin(Mdl,XTest,YTest,'IncludeInteractions',false); E_nointeractions = edge(Mdl,XTest,YTest,'IncludeInteractions',false)

E_nointeractions = 0.7871

Display the distributions of the margins using box plots.

boxplot([M M_nointeractions],'Labels',{'Linear and Interaction Terms','Linear Terms Only'}) title('Box Plots of Test Sample Margins')

Figure contains an axes object. The axes object with title Box Plots of Test Sample Margins contains 14 objects of type line. One or more of the lines displays its values using only markers

The margins M and M_nointeractions have a similar distribution, but the test sample edge of the classifier with only linear terms is larger. Classifiers that yield relatively large margins are preferred.

Input Arguments

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Response variable name, specified as a character vector or string scalar containing the name of the response variable in Tbl. For example, if the response variable Y is stored in Tbl.Y, then specify it as'Y'.

Data Types: char | string

Data Types: single | double

More About

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The classification margin for binary classification is, for each observation, the difference between the classification score for the true class and the classification score for the false class.

If the margins are on the same scale (that is, the score values are based on the same score transformation), then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.

Version History

Introduced in R2021a