L = loss(ens,tbl,ResponseVarName)
L = loss(ens,tbl,Y)
L = loss(ens,X,Y)
L = loss(___,Name,Value)
returns
the classification error for ensemble L
= loss(ens
,tbl
,ResponseVarName
)ens
computed
using table of predictors tbl
and true class labels tbl.ResponseVarName
.
returns
the classification error for ensemble L
= loss(ens
,tbl
,Y
)ens
computed
using table of predictors tbl
and true class labels Y
.
returns
the classification error for ensemble L
= loss(ens
,X
,Y
)ens
computed
using matrix of predictors X
and true class labels Y
.
computes
classification error with additional options specified by one or more L
= loss(___,Name,Value
)Name,Value
pair
arguments, using any of the previous syntaxes.
When computing the loss, loss
normalizes the
class probabilities in ResponseVarName
or Y
to
the class probabilities used for training, stored in the Prior
property
of ens
.

Classification ensemble created with 

Sample data, specified as a table. Each row of If you trained 

Response variable name, specified as the name of a variable
in You must specify 

Matrix of data to classify. Each row of If you trained 

Classification of 
Specify optional commaseparated 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 Default:  

Loss function, specified as the commaseparated pair consisting
of
For more details on loss functions, see Classification Loss. Default:  

Meaning of the output
Default:  

A logical matrix of size When Default:  

Vector of observation weights, with nonnegative entries. The
length of Default: 

Classification loss, by default
the fraction of misclassified data. 
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:
y_{j} is the observed class label. The software codes it as –1 or 1 indicating the negative or positive class, respectively.
f(X_{j}) is the raw 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 to the average loss.
For algorithms that support multiclass classification (that is, K ≥ 3):
y_{j}^{*} is
a vector of K – 1 zeros, and a 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 the ClassNames
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. The software also normalizes the prior probabilities so they sum to 1. Therefore,
$$\sum _{j=1}^{n}{w}_{j}}=1.$$
The supported loss functions are:
Binomial deviance, specified using 'LossFun','binodeviance'
.
Its equation is
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left\{1+\mathrm{exp}\left[2{m}_{j}\right]\right\}}.$$
Exponential loss, specified using 'LossFun','exponential'
.
Its equation is
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{exp}\left({m}_{j}\right)}.$$
Classification error, specified using 'LossFun','classiferror'
.
It is the weighted fraction of misclassified observations, with equation
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}}I\left\{{\widehat{y}}_{j}\ne {y}_{j}\right\}.$$
$${\widehat{y}}_{j}$$ 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
$$L={\displaystyle \sum}_{j=1}^{n}{w}_{j}\mathrm{max}\left\{0,1{m}_{j}\right\}.$$
Logit loss, specified using 'LossFun','logit'
.
Its equation is
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left(1+\mathrm{exp}\left({m}_{j}\right)\right)}.$$
Minimal cost, specified using 'LossFun','mincost'
.
The software computes the weighted minimal cost using this procedure
for observations j = 1,...,n:
Estimate the 1byK vector of expected classification costs for observation j
$${\gamma}_{j}=f{\left({X}_{j}\right)}^{\prime}C.$$
f(X_{j})
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
.
For observation j, predict the class label corresponding to the minimum, expected classification cost:
$${\widehat{y}}_{j}=\underset{j=1,\mathrm{...},K}{\mathrm{min}}\left({\gamma}_{j}\right).$$
Using C, identify the cost incurred (c_{j}) for making the prediction.
The weighted, average, minimum cost loss is
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{c}_{j}}.$$
Quadratic loss, specified using 'LossFun','quadratic'
.
Its equation is
$$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{\left(1{m}_{j}\right)}^{2}}.$$
This figure compares some of the loss functions for one observation over m (some functions are normalized to pass through [0,1]).