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Class: ClassificationBaggedEnsemble

Out-of-bag classification error


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


L = oobloss(ens) returns the classification 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


A classification 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.


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

Default: 1:NumTrained


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.

    'binodeviance'Binomial deviance
    'classiferror'Classification error
    'mincost'Minimal expected misclassification cost (for classification scores that are posterior probabilities)

    'mincost' is appropriate for classification scores that are posterior probabilities. Bagged ensembles return posterior probabilities as classification scores by default.

  • 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)

    • 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.

    Specify your function using 'LossFun',@lossfun.

For more details on loss functions, see Classification Loss.

Default: 'classiferror'


Character vector 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


Classification loss 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.


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.

Classification Loss

Classification loss functions measure the predictive inaccuracy of classification models. When comparing the same type of loss among many models, lower loss indicates a better predictive model.

Suppose that:

  • L is the weighted average classification loss.

  • n is the sample size.

  • For binary classification:

    • yj is the observed class label. The software codes it as –1 or 1 indicating the negative or positive class, respectively.

    • f(Xj) is the raw classification score for observation (row) j of the predictor data X.

    • mj = yjf(Xj) is the classification score for classifying observation j into the class corresponding to yj. Positive values of mj indicate correct classification and do not contribute much to the average loss. Negative values of mj indicate incorrect classification and contribute to the average loss.

  • For algorithms that support multiclass classification (that is, K ≥ 3):

    • yj* is a vector of K – 1 zeros, and a 1 in the position corresponding to the true, observed class yj. For example, if the true class of the second observation is the third class and K = 4, then y*2 = [0 0 1 0]′. The order of the classes corresponds to the order in the ClassNames property of the input model.

    • f(Xj) is the length K vector of class scores for observation j of the predictor data X. The order of the scores corresponds to the order of the classes in the ClassNames property of the input model.

    • mj = yj*f(Xj). Therefore, mj is the scalar classification score that the model predicts for the true, observed class.

  • The weight for observation j is wj. The software normalizes the observation weights so that they sum to the corresponding prior class probability. The software also normalizes the prior probabilities so they sum to 1. Therefore,


The supported loss functions are:

  • Binomial deviance, specified using 'LossFun','binodeviance'. Its equation is


  • Exponential loss, specified using 'LossFun','exponential'. Its equation is


  • Classification error, specified using 'LossFun','classiferror'. It is the weighted fraction of misclassified observations, with equation


    y^j is the class label corresponding to the class with the maximal posterior probability. I{x} is the indicator function.

  • Hinge loss, specified using 'LossFun','hinge'. Its equation is


  • Logit loss, specified using 'LossFun','logit'. Its equation is


  • Minimal cost, specified using 'LossFun','mincost'. The software computes the weighted minimal cost using this procedure for observations j = 1,...,n:

    1. Estimate the 1-by-K vector of expected classification costs for observation j


      f(Xj) is the column vector of class posterior probabilities for binary and multiclass classification. C is the cost matrix the input model stores in the property Cost.

    2. For observation j, predict the class label corresponding to the minimum, expected classification cost:


    3. Using C, identify the cost incurred (cj) for making the prediction.

    The weighted, average, minimum cost loss is


  • Quadratic loss, specified using 'LossFun','quadratic'. Its equation is


This figure compares some of the loss functions for one observation over m (some functions are normalized to pass through [0,1]).


expand all

Load Fisher's iris data set.

load fisheriris

Grow a bag of 100 classification trees.

rng(1) % For reproducibility
ens = fitensemble(meas,species,'Bag',100,'Tree','type','classification');

Estimate the out-of-bag classification error.

L = oobLoss(ens)
L =


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