L = loss(ens,X,Y)
L = loss(ens,X,Y,Name,Value)
When computing the loss,
loss normalizes the
class probabilities in
Y to the class probabilities
used for training, stored in the
Matrix of data to classify. Each row of
Specify optional comma-separated pairs of
Name is the argument
Value is the corresponding
Name must appear
inside single quotes (
You can specify several name and value pair
arguments in any order as
Indices of weak learners in the ensemble ranging from
Function handle or string representing a loss function. Built-in loss functions:
You can write your own loss function in the syntax described in Loss Functions.
String representing the meaning of the output
A logical matrix of size
Vector of observation weights, with nonnegative entries. The
Loss, by default the fraction of misclassified data.
The default classification error is the fraction of the data
Y are the true classifications.
Weighted classification error is the sum of weight i times
the Boolean value that is
the ith row of
X, divided by
the sum of the weights.
The built-in loss functions are:
'binodeviance' — For binary
classification, assume the classes yn are
With weight vector w normalized to have sum
and predictions of row n of data X as f(Xn),
the binomial deviance is
'classiferror' — Fraction
of misclassified data, weighted by w.
'exponential' — With the
same definitions as for
'binodeviance', the exponential
'hinge' — Classification
error measure that has the form
wj is weight j.
For binary classification, yj = 1 for the positive class and -1 for the negative class. For problems where the number of classes K > 3, yj 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 y2 = [0 0 1 0]′.
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
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
K is the number of classes in
C is an
matrix, with one
true per row for the true class.
The index for each class is its position in
S is an
S is a matrix of posterior probabilities
for classes with one row per observation, similar to the
W is a numeric vector with
the observation weights.
COST is a
matrix of misclassification costs. The default
a cost of
0 for correct classification, and
loss should be a scalar.
Pass the function handle
the value of the
lossfun name-value 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