# Documentation

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# kfoldLoss

Classification loss for observations not used for training

## Syntax

L = kfoldLoss(ens)
L = kfoldLoss(ens,Name,Value)

## Description

L = kfoldLoss(ens) returns loss obtained by cross-validated classification model ens. For every fold, this method computes classification loss for in-fold observations using a model trained on out-of-fold observations.

L = kfoldLoss(ens,Name,Value) calculates loss with additional options specified by one or more Name,Value pair arguments. You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

## Input Arguments

 ens Object of class ClassificationPartitionedEnsemble. Create ens with fitensemble along with one of the cross-validation options: 'crossval', 'kfold', 'holdout', 'leaveout', or 'cvpartition'. Alternatively, create ens from a classification ensemble with crossval.

### 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 single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'folds'

Indices of folds ranging from 1 to ens.KFold. Use only these folds for predictions.

Default: 1:ens.KFold

'lossfun'

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

• The following lists available loss functions. Specify one using its corresponding character vector.

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.

• Bagged and subspace ensembles return posterior probabilities by default (ens.Method is 'Bag' or 'Subspace').

• If the ensemble method is 'AdaBoostM1', 'AdaBoostM2', GentleBoost, or 'LogitBoost', then, to use posterior probabilities as classification scores, you must specify the double-logit score transform by entering

ens.ScoreTransform = 'doublelogit';

• For all other ensemble methods, the software does not support posterior probabilities as classification scores.

• 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(ens.ClassNames), ens 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 ens.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 ens.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.

Default: 'classiferror'

'mode'

A character vector for determining the output of kfoldLoss:

• 'average'L is a scalar, the loss averaged over all folds.

• 'individual'L is a vector of length ens.KFold, where each entry is the loss for a fold.

• 'cumulative'L is a vector in which element J is obtained by using learners 1:J from the input list of learners.

Default: 'average'

## Output Arguments

 L Loss, by default the fraction of misclassified data. L can be a vector, and can mean different things, depending on the name-value pair settings.

## Examples

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Cross-validate the ensemble using 10-fold cross-validation.

cvens = crossval(ens);

Estimate the cross-validated classification error.

L = kfoldLoss(cvens)
L =

0.0655

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