# logp

Log unconditional probability density for naive Bayes classifier

## Description

returns the log Unconditional Probability Density (`lp`

= logp(`Mdl`

,`tbl`

)`lp`

) of the observations (rows) in `tbl`

using the naive Bayes model `Mdl`

. You can use `lp`

to identify outliers in the training data.

## Examples

### Compute Unconditional Probability Densities of Observations

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.

```
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: {3x4 cell}

`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

`Mdl`

— Naive Bayes classification model

`ClassificationNaiveBayes`

model object | `CompactClassificationNaiveBayes`

model object

Naive Bayes classification model, specified as a `ClassificationNaiveBayes`

model object or `CompactClassificationNaiveBayes`

model object returned by `fitcnb`

or `compact`

,
respectively.

`tbl`

— Sample data

table

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.

`X`

— Predictor data

numeric matrix

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`

## More About

### 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

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

where *π*(*Y* = *k*) is the class prior probability. The conditional distribution of the data given the class (*P*(*X*_{1},..,*X _{P}*|

*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.

## Version History

**Introduced in R2014b**

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