logp

Log unconditional probability density for discriminant analysis classifier

Syntax

lp = logp(Mdl,Tbl)

lp = logp(Mdl,X)

Description

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

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

Examples

Compute Log Unconditional Probability Density of an Observation

Construct a discriminant analysis classifier for Fisher's iris data, and examine its prediction for an average measurement.

Load Fisher's iris data and construct a default discriminant analysis classifier.

load fisheriris
Mdl = fitcdiscr(meas,species);

Find the log probability of the discriminant model applied to an average iris.

logpAverage = logp(Mdl,mean(meas))

logpAverage = 
-1.7254

Input Arguments

Mdl — Trained discriminant analysis classifier

ClassificationDiscriminant model object | CompactClassificationDiscriminant model object

Trained discriminant analysis classifier, specified as a ClassificationDiscriminant model object trained with fitcdiscr, or a CompactClassificationDiscriminant model object created with compact.

Tbl — Sample data

table

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

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

Data Types: table

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. Each row of X corresponds to one observation, and each column corresponds to one predictor variable. Categorical predictor variables are not supported. The variables in the columns of X must be the same as the variables used to train Mdl. The number of rows in X must equal the number of rows in Y.

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

Data Types: single | double

More About

Unconditional Probability Density

The unconditional probability density of a point x of a discriminant analysis model is

$$P(x)={\displaystyle \sum _{k=1}^{K}P(k)P(x|k),}$$

where P(k) is the prior probability of class k, P(x|k) is the conditional density of x given class k, and K is the total number of classes. The conditional density function of the multivariate normal with 1-by-d mean μ_k and d-by-d covariance Σ_k at a 1-by-d point x is

$$P\left(x|k\right)=\frac{1}{{\left({\left(2\pi \right)}^d\left|{\Sigma }_k\right|\right)}^{1/2}}\exp \left(-\frac{1}{2}\left(x-{\mu }_k\right){\Sigma }_k^{-1}{\left(x-{\mu }_k\right)}^T\right),$$

where $$\left|{\Sigma }_k\right|$$ is the determinant of Σ_k, and $${\Sigma }_k^{-1}$$ is the inverse matrix.

Version History

Introduced in R2011b