# logp

Log unconditional probability density for naive Bayes classifier

## Description

lp = logp(Mdl,tbl) returns the log Unconditional Probability Density (lp) of the observations (rows) in tbl using the naive Bayes model Mdl. You can use lp to identify outliers in the training data.

example

lp = logp(Mdl,X) returns the log unconditional probability density of the observations (rows) in X using the naive Bayes model Mdl.

## 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 petal measurements for 150 irises. Create Y as a cell array of character vectors that contains the corresponding iris species.

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: {3x4 cell}

Properties, Methods

Mdl is a trained ClassificationNaiveBayes classifier.

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

lp = logp(Mdl,X);

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
L = -6.9222
U
U = 3.0323
ind = find(TF)
ind = 4×1

61
118
119
132

Display the values of the outlier unconditional probability densities.

lp(ind)
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')

## Input Arguments

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Naive Bayes classification model, specified as a ClassificationNaiveBayes model object or CompactClassificationNaiveBayes model object returned by fitcnb or compact, respectively.

Sample data used to train the model, specified as a table. Each row of tbl corresponds to one observation, and each column corresponds to one predictor variable. tbl must contain all the predictors used to train Mdl. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed. Optionally, tbl can contain additional columns for the response variable and observation weights.

If you train Mdl using sample data contained in a table, then the input data for logp must also be in a table.

Predictor data, specified as a numeric matrix.

Each row of X corresponds to one observation (also known as an instance or example), and each column corresponds to one variable (also known as a feature). The variables in the columns of X must be the same as the variables that trained the Mdl classifier.

The length of Y and the number of rows of X must be equal.

Data Types: double | single

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### Unconditional Probability Density

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

In other words, the unconditional probability density is

$P\left({X}_{1},..,{X}_{P}\right)=\sum _{k=1}^{K}P\left({X}_{1},..,{X}_{P},Y=k\right)=\sum _{k=1}^{K}P\left({X}_{1},..,{X}_{P}|y=k\right)\pi \left(Y=k\right),$

where π(Y = k) is the class prior probability. The conditional distribution of the data given the class (P(X1,..,XP|y = k)) and the class prior probability distributions are training options (that is, you specify them when training the classifier).

### Prior Probability

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