ScoreSVMModel = fitSVMPosterior (SVMModel) returns the two-class SVM classifier SVMModel with the transformation from the score of the second class, SVMModel.ClassNames(2), to its posterior probability stored in its ScoreTransform property, so that predict, or kfoldPredict for a cross-validated model, returns posterior probabilities, the two columns summing to 1. SVMModel is a ClassificationSVM, a CompactClassificationSVM or a ClassificationPartitionedModel cross-validating an SVM, and ScoreSVMModel is of the same class.

The transformation is fitted to scores of observations the model was not trained on:

• For a ClassificationSVM, scores from cross-validating it, 10-fold unless one of the options below says otherwise.
• For a ClassificationPartitionedModel, its own out-of-fold scores, from the partition it was built with; no option may be given.
• With predictors X and their classes Y, the scores the model gives X, without cross-validation; a CompactClassificationSVM holds no training data and needs them. X may also be a table Tbl, matched to the predictors by variable name, with the classes in the variable ResponseVarName names, in Y, or in the variable the model was fitted on. Rows whose score is NaN are left out.

Only one of these options may be given, and only with a ClassificationSVM and no data. The transformation is one of three:

• A sigmoid 1 / (1 + exp (A * s + B)) of the score s when the scores of the two classes overlap, with A and B fitted by maximum likelihood, as a logistic regression of the class on the score. Neither the observation weights nor the prior enter the fit, as in MATLAB.
• A step function when the scores separate the classes: 0 below the largest score of the first class, 1 above the smallest score of the second, and SVMModel.Prior(2) between, with a warning.
• A constant when one class has prior probability 0, posterior 1 for the other class.

A ScoreTransform already set on SVMModel is reset to 'none' first, with a warning. The property holds the transformation as '@(S)sigmoid(S,A,B)', '@(S)step(S,LowerBound,UpperBound,PositiveClassProbability)' or '@(S)constant(S,K)', K being the index of the predicted class. Each parameter is written exactly, in the fewest significant digits that read back to it, where MATLAB shows seven, so a model saved and reloaded predicts as before. The folds of a cross-validated model keep 'none', the transformation being applied to the scores they give together.

[ScoreSVMModel, ScoreTransform] = fitSVMPosterior (…) also returns the parameters in a structure whose field Type is 'sigmoid', with fields Slope and Intercept, 'step', with fields LowerBound, UpperBound and PositiveClassProbability, or 'constant', with the field PredictedClass.

Reference: J. Platt. Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In Advances in Large Margin Classifiers, MIT Press, 2000.

See also: ClassificationSVM.fitPosterior, CompactClassificationSVM.fitPosterior, fitcsvm, cvpartition

Source Code: fitSVMPosterior