Documentation

# loss

Classification error for naive Bayes classifier

## Description

L = loss(Mdl,tbl,ResponseVarName) returns the minimum classification loss (see Classification Loss), a scalar representing how well the trained naive Bayes classifier Mdl classifies the predictor data in table tbl) as compared to the true class labels in tbl.ResponseVarName.

loss normalizes the class probabilities in tbl.ResponseVarName to the prior class probabilities fitcnb used for training, stored in the Prior property of Mdl.

L = loss(Mdl,tbl,Y) returns the minimum classification loss (L), a scalar representing how well the trained naive Bayes classifier Mdl classifies the predictor data in table tbl) as compared to the true class labels in Y.

loss normalizes the class probabilities in Y to the prior class probabilities fitcnb used for training, stored in the Prior property of Mdl.

example

L = loss(Mdl,X,Y) returns the minimum classification loss (L), a scalar representing how well the trained naive Bayes classifier Mdl classifies the predictor data (X) as compared to the true class labels (Y).

loss normalizes the class probabilities in Y to the prior class probabilities fitcnb used for training, stored in the Prior property of Mdl.

example

L = loss(___,Name,Value) returns the classification loss with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes.

## Input Arguments

expand all

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

Sample data, specified as a table. Each row of tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, tbl can contain additional columns for the response variable and observation weights. tbl must contain all the predictors used to train Mdl. Multi-column 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 this method must also be in a table.

Data Types: table

Response variable name, specified as the name of a variable in tbl.

You must specify ResponseVarName as a character vector or string scalar. For example, if the response variable y is stored as tbl.y, then specify it as 'y'. Otherwise, the software treats all columns of tbl, including y, as predictors when training the model.

The response variable must be a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.

Data Types: char | string

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 making up the columns of X should be the same as the variables that trained Mdl.

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

Data Types: double | single

Class labels, specified as a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. Y must be the same as the data type of Mdl.ClassNames. (The software treats string arrays as cell arrays of character vectors.)

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

Data Types: categorical | char | string | logical | single | double | cell

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Loss function, specified as the comma-separated pair consisting of 'LossFun' and a built-in, loss-function name or function handle.

• The following table lists the available loss functions. Specify one using its corresponding character vector or string scalar.

ValueDescription
'binodeviance'Binomial deviance
'classiferror'Classification error
'exponential'Exponential
'hinge'Hinge
'logit'Logistic
'mincost'Minimal expected misclassification cost (for classification scores that are posterior probabilities)

'mincost' is appropriate for classification scores that are posterior probabilities. Naive Bayes models return posterior probabilities as classification scores by default (see predict).

• Specify your own function using function handle notation.

Suppose that n be the number of observations in X and K be the number of distinct classes (numel(Mdl.ClassNames), Mdl is the input model). Your function must have this signature

lossvalue = lossfun(C,S,W,Cost)
where:

• The output argument lossvalue is a scalar.

• You choose the function name (lossfun).

• C is an n-by-K logical matrix with rows indicating which class the corresponding observation belongs. The column order corresponds to the class order in Mdl.ClassNames.

Construct C by setting C(p,q) = 1 if observation p is in class q, for each row. Set all other elements of row p to 0.

• S is an n-by-K numeric matrix of classification scores. The column order corresponds to the class order in Mdl.ClassNames. S is a matrix of classification scores, similar to the output of predict.

• W is an n-by-1 numeric vector of observation weights. If you pass W, the software normalizes them to sum to 1.

• Cost is a K-by-K numeric matrix of misclassification costs. For example, Cost = ones(K) - eye(K) specifies a cost of 0 for correct classification, and 1 for misclassification.

For more details on loss functions, see Classification Loss.

Data Types: char | string | function_handle

Observation weights, specified as the comma-separated pair consisting of 'Weights' and a numeric vector or the name of a variable in tbl. The software weighs the observations in each row of X or tbl with the corresponding weight in Weights.

If you specify Weights as a vector, then the size of Weights must be equal to the number of rows of X or tbl.

If you specify Weights as the name of a variable in tbl, you must do so as a character vector or string scalar. For example, if the weights are stored as tbl.w, then specify Weights as 'w'. Otherwise, the software treats all columns of tbl, including tbl.w, as predictors.

If you do not specify your own loss function, then the software normalizes Weights to add up to 1.

Data Types: double | char | string

## Output Arguments

expand all

Classification loss, returned as a scalar. L is a generalization or resubstitution quality measure. Its interpretation depends on the loss function and weighting scheme, but, in general, better classifiers yield smaller loss values.

## Examples

expand all

X = meas;    % Predictors
Y = species; % Response
rng(1);      % For reproducibility

Train a naive Bayes classifier. Specify a 15% holdout sample for testing. It is good practice to specify the class order. Assume that each predictor is conditionally normally distributed given its label.

CVMdl = fitcnb(X,Y,'ClassNames',{'setosa','versicolor','virginica'},...
'Holdout',0.15);
CMdl = CVMdl.Trained{1}; % Extract the trained, compact classifier
testInds = test(CVMdl.Partition);   % Extract the test indices
XTest = X(testInds,:);
YTest = Y(testInds);

CVMdl is a ClassificationPartitionedModel classifier. It contains the property Trained, which is a 1-by-1 cell array holding a CompactClassificationNaiveBayes classifier that the software trained using the training set.

Determine how well the algorithm generalizes by estimating the test sample minimum cost loss.

L = loss(CMdl,XTest,YTest)
L = 0.0476

The test sample average classification cost is approximately 0.05.

You might improve the classification error by specifying better predictor distributions when you train the classifier.

X = meas;    % Predictors
Y = species; % Response
rng(1); % For reproducibility

Train a naive Bayes classifier. Specify a 15% holdout sample for testing. It is good practice to specify the class order. Assume that each predictor is conditionally normally distributed given its label.

CVMdl = fitcnb(X,Y,'ClassNames',{'setosa','versicolor','virginica'},...
'Holdout',0.15);
CMdl = CVMdl.Trained{1}; % Extract the trained, compact classifier
testInds = test(CVMdl.Partition);   % Extract the test indices
XTest = X(testInds,:);
YTest = Y(testInds);

CVMdl is a ClassificationPartitionedModel classifier. It contains the property Trained, which is a 1-by-1 cell array holding a CompactClassificationNaiveBayes classifier that the software trained using the training set.

Determine how well the algorithm generalizes by estimating the test sample classification error.

L = loss(CMdl,XTest,YTest,'LossFun','classiferror')
L = 0.0476

The classifier misclassified approximately 5% of the test sample observations.

expand all

## References

[1] Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning, second edition. Springer, New York, 2008.