# resubLoss

Classification error by resubstitution

## Syntax

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

## Description

L = resubLoss(ens) returns the resubstitution loss, meaning the loss computed for the data that fitcensemble used to create ens.

L = resubLoss(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 A classification ensemble created with fitcensemble.

### Name-Value 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.

learners

Indices of weak learners in the ensemble ranging from 1 to NumTrained. resubLoss uses only these learners for calculating loss.

Default: 1:NumTrained

lossfun

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'Misclassified rate in decimal
'exponential'Exponential loss
'hinge'Hinge loss
'logit'Logistic loss
'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

Character vector or string scalar representing the meaning of the output L:

• 'ensemble'L is a scalar value, the loss for the entire ensemble.

• 'individual'L is a vector with one element per trained learner.

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

Default: 'ensemble'

## Output Arguments

 L Classification 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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Train a classification ensemble of 100 decision trees using AdaBoostM2. Specify tree stumps as the weak learners.

t = templateTree('MaxNumSplits',1);

Estimate the resubstitution classification error.

loss = resubLoss(ens)
loss = 0.0333

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