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Out-of-bag error for bagged regression ensemble model



L = oobLoss(ens) returns the mean squared error L for the out-of-bag data in the bagged regression ensemble model ens. The interpretation of L depends on the loss function (LossFun). In general, better classifiers yield smaller classification loss values.

L = oobLoss(ens,Name=Value) specifies additional options using one or more name-value arguments. For example, you can specify the indices of the weak learners to use for calculating the error, the aggregation level for the output, and to perform computations in parallel.


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

Load the carsmall data set and select engine displacement, horsepower, and vehicle weight as predictors.

load carsmall
X = [Displacement Horsepower Weight];

Train an ensemble of bagged regression trees.

ens = fitrensemble(X,MPG,'Method','Bag');

Find the out-of-bag error.

L = oobLoss(ens)
L = 16.9551

Input Arguments

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Bagged regression ensemble model, specified as a RegressionBaggedEnsemble model object trained with fitrensemble.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: oobLoss(ens,Learners=[1 2 3 5],UseParallel=true) specifies to use the first, second, third, and fifth learners in the ensemble in oobLoss, and to perform computations in parallel.

Indices of weak learners in the ensemble to use in oobLoss, specified as a vector of positive integers in the range [1:ens.NumTrained]. By default, all learners are used.

Example: Learners=[1 2 4]

Data Types: single | double

Loss function, specified as "mse" (mean squared error) or as a function handle. If you pass a function handle fun, oobLoss calls it as


where Y, Yfit, and W are numeric vectors of the same length.

  • Y is the observed response.

  • Yfit is the predicted response.

  • W is the observation weights.

The returned value of fun(Y,Yfit,W) must be a scalar.

Example: LossFun="mse"

Example: LossFun=@Lossfun

Data Types: char | string | function_handle

Aggregation level for the output, specified as "ensemble", "individual", or "cumulative".

"ensemble"The output is a scalar value, the loss for the entire ensemble.
"individual"The output is a vector with one element per trained learner.
"cumulative"The output is a vector in which element J is obtained by using learners 1:J from the input list of learners.

Example: Mode="individual"

Data Types: char | string

Flag to run in parallel, specified as a numeric or logical 1 (true) or 0 (false). If you specify UseParallel=true, the oobLoss function executes for-loop iterations by using parfor. The loop runs in parallel when you have Parallel Computing Toolbox™.

Example: UseParallel=true

Data Types: logical

More About

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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, fitrensemble generates many bootstrap replicas of the dataset and grows decision trees on these replicas. fitrensemble 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 takes 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.

Extended Capabilities

Version History

Introduced in R2012b