oobLoss
Outofbag classification error
Syntax
L = oobLoss(ens)
L = oobLoss(ens,Name,Value)
Description
returns the
classification error for L
= oobLoss(ens
)ens
computed for outofbag data.
computes error with additional options specified
by one or more L
= oobLoss(ens
,Name,Value
)Name,Value
pair arguments. You can specify several namevalue
pair arguments in any order as
Name1,Value1,…,NameN,ValueN
.
Input Arguments

A classification bagged ensemble, constructed with 
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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.
Learners
— Indices of weak learners
[1:ens.NumTrained]
(default)  vector of positive integers
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
lossfun
—
Loss function, specified as the commaseparated pair consisting
of 'LossFun'
and a builtin loss function name
or function handle.
The following table lists the available loss functions. Specify one using its corresponding character vector or string scalar.
Value Description "binodeviance"
Binomial deviance "classifcost"
Observed misclassification cost "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) "quadratic"
Quadratic loss '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 inX
andK
be the number of distinct classes (numel(ens.ClassNames)
,ens
is the input model). Your function must have this signaturewhere:lossvalue =
lossfun
(C,S,W,Cost)The output argument
lossvalue
is a scalar.You choose the function name (
lossfun
).C
is ann
byK
logical matrix with rows indicating which class the corresponding observation belongs. The column order corresponds to the class order inens.ClassNames
.Construct
C
by settingC(p,q) = 1
if observationp
is in classq
, for each row. Set all other elements of rowp
to0
.S
is ann
byK
numeric matrix of classification scores. The column order corresponds to the class order inens.ClassNames
.S
is a matrix of classification scores, similar to the output ofpredict
.W
is ann
by1 numeric vector of observation weights. If you passW
, the software normalizes them to sum to1
.Cost
is a KbyK
numeric matrix of misclassification costs. For example,Cost = ones(K)  eye(K)
specifies a cost of0
for correct classification, and1
for misclassification.
Specify your function using
'LossFun',@
.lossfun
For more details on loss functions, see Classification Loss.
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 elementJ
is obtained by using learners1:J
from the input list of learners.
UseParallel
—
Indication to perform inference in parallel, specified as false
(compute
serially) or true
(compute in parallel). Parallel computation
requires Parallel Computing Toolbox™. Parallel inference can be faster than serial inference, especially for
large datasets. Parallel computation is supported only for tree learners.
Output Arguments

Classification
loss of the outofbag observations, a scalar. 
Examples
Estimate OutOfBag Error
Load Fisher's iris data set.
load fisheriris
Grow a bag of 100 classification trees.
ens = fitcensemble(meas,species,'Method','Bag');
Estimate the outofbag classification error.
L = oobLoss(ens)
L = 0.0400
More About
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,
fitcensemble
generates many bootstrap
replicas of the dataset and grows decision trees on these replicas. fitcensemble
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 "outofbag" observations.
For each observation, oobLoss
estimates the outofbag
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 outofbag error by comparing the outofbag predicted responses
against the true responses for all observations used for training.
This outofbag average is an unbiased estimator of the true ensemble
error.
Classification Loss
Classification loss functions measure the predictive inaccuracy of classification models. When you compare the same type of loss among many models, a lower loss indicates a better predictive model.
Consider the following scenario.
L is the weighted average classification loss.
n is the sample size.
For binary classification:
y_{j} is the observed class label. The software codes it as –1 or 1, indicating the negative or positive class (or the first or second class in the
ClassNames
property), respectively.f(X_{j}) is the positiveclass classification score for observation (row) j of the predictor data X.
m_{j} = y_{j}f(X_{j}) is the classification score for classifying observation j into the class corresponding to y_{j}. Positive values of m_{j} indicate correct classification and do not contribute much to the average loss. Negative values of m_{j} indicate incorrect classification and contribute significantly to the average loss.
For algorithms that support multiclass classification (that is, K ≥ 3):
y_{j}^{*} is a vector of K – 1 zeros, with 1 in the position corresponding to the true, observed class y_{j}. 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 theClassNames
property of the input model.f(X_{j}) 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.m_{j} = y_{j}^{*}′f(X_{j}). Therefore, m_{j} is the scalar classification score that the model predicts for the true, observed class.
The weight for observation j is w_{j}. The software normalizes the observation weights so that they sum to the corresponding prior class probability stored in the
Prior
property. Therefore,$$\sum _{j=1}^{n}{w}_{j}}=1.$$
Given this scenario, the following table describes the supported loss functions that you can specify by using the LossFun
namevalue argument.
Loss Function  Value of LossFun  Equation 

Binomial deviance  "binodeviance"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left\{1+\mathrm{exp}\left[2{m}_{j}\right]\right\}}.$$ 
Observed misclassification cost  "classifcost"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}}{c}_{{y}_{j}{\widehat{y}}_{j}},$$ where $${\widehat{y}}_{j}$$ is the class label corresponding to the class with the maximal score, and $${c}_{{y}_{j}{\widehat{y}}_{j}}$$ is the userspecified cost of classifying an observation into class $${\widehat{y}}_{j}$$ when its true class is y_{j}. 
Misclassified rate in decimal  "classiferror"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}}I\left\{{\widehat{y}}_{j}\ne {y}_{j}\right\},$$ where I{·} is the indicator function. 
Crossentropy loss  "crossentropy" 
The weighted crossentropy loss is $$L={\displaystyle \sum _{j=1}^{n}\frac{{\tilde{w}}_{j}\mathrm{log}({m}_{j})}{Kn}},$$ where the weights $${\tilde{w}}_{j}$$ are normalized to sum to n instead of 1. 
Exponential loss  "exponential"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{exp}\left({m}_{j}\right)}.$$ 
Hinge loss  "hinge"  $$L={\displaystyle \sum}_{j=1}^{n}{w}_{j}\mathrm{max}\left\{0,1{m}_{j}\right\}.$$ 
Logit loss  "logit"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left(1+\mathrm{exp}\left({m}_{j}\right)\right)}.$$ 
Minimal expected misclassification cost  "mincost" 
The software computes the weighted minimal expected classification cost using this procedure for observations j = 1,...,n.
The weighted average of the minimal expected misclassification cost loss is $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{c}_{j}}.$$ 
Quadratic loss  "quadratic"  $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{\left(1{m}_{j}\right)}^{2}}.$$ 
If you use the default cost matrix (whose element value is 0 for correct classification
and 1 for incorrect classification), then the loss values for
"classifcost"
, "classiferror"
, and
"mincost"
are identical. For a model with a nondefault cost matrix,
the "classifcost"
loss is equivalent to the "mincost"
loss most of the time. These losses can be different if prediction into the class with
maximal posterior probability is different from prediction into the class with minimal
expected cost. Note that "mincost"
is appropriate only if classification
scores are posterior probabilities.
This figure compares the loss functions (except "classifcost"
,
"crossentropy"
, and "mincost"
) over the score
m for one observation. Some functions are normalized to pass through
the point (0,1).
Extended Capabilities
Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.
To run in parallel, set the UseParallel
namevalue argument to
true
in the call to this function.
For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
Version History
R2022a: oobLoss
returns a different value for a model with a nondefault cost matrix
If you specify a nondefault cost matrix when you train the input model object, the oobLoss
function returns a different value compared to previous releases.
The oobLoss
function uses the
observation weights stored in the W
property. Also, the function uses the
cost matrix stored in the Cost
property if you specify the
LossFun
namevalue argument as "classifcost"
or
"mincost"
. The way the function uses the W
and
Cost
property values has not changed. However, the property values stored in the input model object have changed for a
model with a nondefault cost matrix, so the function might return a different value.
For details about the property value change, see Cost property stores the userspecified cost matrix.
If you want the software to handle the cost matrix, prior
probabilities, and observation weights in the same way as in previous releases, adjust the prior
probabilities and observation weights for the nondefault cost matrix, as described in Adjust Prior Probabilities and Observation Weights for Misclassification Cost Matrix. Then, when you train a
classification model, specify the adjusted prior probabilities and observation weights by using
the Prior
and Weights
namevalue arguments, respectively,
and use the default cost matrix.
See Also
loss
 oobEdge
 oobMargin
 oobPredict
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