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oobLoss

Class: RegressionBaggedEnsemble

Out-of-bag regression error

Syntax

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

Description

L = oobLoss(ens) returns the mean squared error for ens computed for out-of-bag data.

L = oobLoss(ens,Name,Value) computes error 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 regression bagged ensemble, constructed with fitensemble.

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.

'learners'

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

Default: 1:NumTrained

'lossfun'

Function handle for loss function, or the string 'mse', meaning mean squared error. If you pass a function handle fun, oobLoss calls it as

FUN(Y,Yfit,W)

where Y, Yfit, and W are numeric vectors of the same length. Y is the observed response, Yfit is the predicted response, and W is the observation weights.

Default: 'mse'

'mode'

String 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

Mean squared error of the out-of-bag observations, a scalar. L can be a vector, or can represent a different quantity, depending on the name-value settings.

Definitions

Out of Bag

Bagging, which stands for "bootstrap aggregation", is a type of ensemble learning. To bag a weak learner such as a decision tree on a dataset, fitensemble generates many bootstrap replicas of the dataset and grows decision trees on these replicas. fitensemble obtains each bootstrap replica by randomly selecting N observations out of N with replacement, where N is the dataset size. To find the predicted response of a trained ensemble, predict take an average over predictions from individual trees.

Drawing N out of N observations with replacement omits on average 37% (1/e) of observations for each decision tree. These are "out-of-bag" observations. For each observation, oobLoss estimates the out-of-bag prediction by averaging over predictions from all trees in the ensemble for which this observation is out of bag. It then compares the computed prediction against the true response for this observation. It calculates the out-of-bag error by comparing the out-of-bag predicted responses against the true responses for all observations used for training. This out-of-bag average is an unbiased estimator of the true ensemble error.

Examples

Compute the out-of-bag error for the carsmall data:

load carsmall
X = [Displacement Horsepower Weight];
ens = fitensemble(X,MPG,'bag',100,'Tree',...
    'type','regression');
L = oobLoss(ens)

L =
   17.0665

See Also

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