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

Classification ensemble created with 

Matrix of data to classify. Each row of 

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: 

Function handle or string representing a loss function. Builtin loss functions:
You can write your own loss function in the syntax described in Loss Functions. Default: 

String representing the meaning of the output
Default: 

A logical matrix of size When Default: 

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

Loss, by default the fraction of misclassified data. 
The default classification error is the fraction of the data X
that ens
misclassifies,
where Y
are the true classifications.
Weighted classification error is the sum of weight i times
the Boolean value that is 1
when tree
misclassifies
the ith row of X
, divided by
the sum of the weights.
The builtin loss functions are:
'binodeviance'
— For binary
classification, assume the classes y_{n} are 1
and 1
.
With weight vector w normalized to have sum 1
,
and predictions of row n of data X as f(X_{n}),
the binomial deviance is
$$\sum {w}_{n}\mathrm{log}\left(1+\mathrm{exp}\left(2{y}_{n}f\left({X}_{n}\right)\right)\right)}.$$
'classiferror'
— Fraction
of misclassified data, weighted by w.
'exponential'
— With the
same definitions as for 'binodeviance'
, the exponential
loss is
$$\sum {w}_{n}\mathrm{exp}\left({y}_{n}f\left({X}_{n}\right)\right)}.$$
'hinge'
— Classification
error measure that has the form
$$L=\frac{{\displaystyle \sum}_{j=1}^{n}{w}_{j}\mathrm{max}\left\{0,1{y}_{j}\prime f\left({X}_{j}\right)\right\}}{{\displaystyle \sum}_{j=1}^{n}{w}_{j}},$$
where:
w_{j} is weight j.
For binary classification, y_{j} = 1 for the positive class and 1 for the negative class. For problems where the number of classes K > 3, y_{j} is a vector of 0s, but with a 1 in the position corresponding to the true class, e.g., if the second observation is in the third class and K = 4, then y_{2} = [0 0 1 0]′.
$$f({X}_{j})$$ is, for binary classification, the posterior probability or, for K > 3, a vector of posterior probabilities for each class given observation j.
'mincost'
— Predict the
label with the smallest expected misclassification cost, with expectation
taken over the posterior probability, and cost as given by the Cost
property
of the classifier (a matrix). The loss is then the true misclassification
cost averaged over the observations.
To write your own loss function, create a function file of the form
function loss = lossfun(C,S,W,COST)
N
is the number of rows of ens
.X
.
K
is the number of classes in ens
,
represented in ens.ClassNames
.
C
is an N
byK
logical
matrix, with one true
per row for the true class.
The index for each class is its position in tree.ClassNames
.
S
is an N
byK
numeric
matrix. S
is a matrix of posterior probabilities
for classes with one row per observation, similar to the score
output
from predict
.
W
is a numeric vector with N
elements,
the observation weights.
COST
is a K
byK
numeric
matrix of misclassification costs. The default 'classiferror'
gives
a cost of 0
for correct classification, and 1
for
misclassification.
The output loss
should be a scalar.
Pass the function handle @
as
the value of the lossfun
lossfun
namevalue pair.
Create a compact classification ensemble for the ionosphere data, and find the fraction of training data that the ensemble misclassifies:
load ionosphere ada = fitensemble(X,Y,'AdaBoostM1',100,'tree'); adb = compact(ada); L = loss(adb,X,Y) L = 0.0085