logp - Log unconditional probability density for naive Bayes classifier - MATLAB (original) (raw)

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Log unconditional probability density for naive Bayes classifier

Syntax

Description

`lp` = logp([Mdl](#bue3d16%5Fsep%5Fshared-Mdl),[tbl](#bue3d16%5Fsep%5Fshared-tbl)) returns the log Unconditional Probability Density (lp) of the observations (rows) in tbl using the naive Bayes modelMdl. You can use lp to identify outliers in the training data.

`lp` = logp([Mdl](#bue3d16%5Fsep%5Fshared-Mdl),[X](#bue3d16%5Fsep%5Fshared-X)) returns the log unconditional probability density of the observations (rows) inX using the naive Bayes modelMdl.

example

Examples

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Compute the unconditional probability densities of the in-sample observations of a naive Bayes classifier model.

Load the fisheriris data set. Create X as a numeric matrix that contains four measurements for 150 irises. Create Y as a cell array of character vectors that contains the corresponding iris species.

load fisheriris X = meas; Y = species;

Train a naive Bayes classifier using the predictors X and class labels Y. A recommended practice is to specify the class names. fitcnb assumes that each predictor is conditionally and normally distributed.

Mdl = fitcnb(X,Y,'ClassNames',{'setosa','versicolor','virginica'})

Mdl = ClassificationNaiveBayes ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 DistributionNames: {'normal' 'normal' 'normal' 'normal'} DistributionParameters: {3×4 cell}

Properties, Methods

Mdl is a trained ClassificationNaiveBayes classifier.

Compute the unconditional probability densities of the in-sample observations.

Identify indices of observations that have very small or very large log unconditional probabilities (ind). Display lower (L) and upper (U) thresholds used by the outlier detection method.

[TF,L,U] = isoutlier(lp); L

Display the values of the outlier unconditional probability densities.

ans = 4×1

-7.8995 -8.4765 -6.9854 -7.8969

All the outliers are smaller than the lower outlier detection threshold.

Plot the unconditional probability densities.

histogram(lp) hold on xline(L,'k--') hold off xlabel('Log unconditional probability') ylabel('Frequency') title('Histogram: Log Unconditional Probability')

More About

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The unconditional probability density of the predictors is the density's distribution marginalized over the classes.

In other words, the unconditional probability density is

where π(Y = k) is the class prior probability. The conditional distribution of the data given the class (P(_X_1,..,XP|y = k)) and the class prior probability distributions are training options (that is, you specify them when training the classifier).

The prior probability of a class is the assumed relative frequency with which observations from that class occur in a population.

Version History

Introduced in R2014b