Documentation |
L = resubLoss(ens)
L = resubLoss(ens,Name,Value)
L = resubLoss(ens) returns the resubstitution loss, meaning the loss computed for the data that fitensemble used to create ens.
L = resubLoss(ens,Name,Value) calculates loss 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.
ens |
A classification ensemble created with fitensemble. |
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.
'learners' |
Indices of weak learners in the ensemble ranging from 1 to NumTrained. resubLoss uses only these learners for calculating loss. Default: 1:NumTrained |
'lossfun' |
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. Default: 'classiferror' |
'mode' |
String representing the meaning of the output L:
Default: 'ensemble' |
L |
Loss, by default the fraction of misclassified data. L can be a vector, and can mean different things, depending on the name-value pair settings. |
The default classification error is the fraction of the training data X that ens misclassifies.
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 built-in 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-by-K 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-by-K 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-by-K 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 @lossfun as the value of the lossfun name-value pair.
Compute the resubstitution loss for a classification ensemble for the Fisher iris data:
load fisheriris ens = fitensemble(meas,species,'AdaBoostM2',100,'Tree'); loss = resubLoss(ens) loss = 0.0333