resubLoss
Resubstitution classification loss
Description
returns the Classification Loss by resubstitution (L), or
the in-sample classification loss, for the trained classification model
L
= resubLoss(Mdl
)Mdl
using the training data stored in Mdl.X
and
the corresponding class labels stored in Mdl.Y
.
The interpretation of L
depends on the loss function
('LossFun'
) and weighting scheme (Mdl.W
). In
general, better classifiers yield smaller classification loss values. The default
'LossFun'
value varies depending on the model object
Mdl
.
specifies additional options using one or more name-value arguments. For example,
L
= resubLoss(Mdl
,Name,Value
)'LossFun','binodeviance'
sets the loss function to the binomial
deviance function.
Examples
Determine Resubstitution Loss of Naive Bayes Classifier
Determine the in-sample classification error (resubstitution loss) of a naive Bayes classifier. In general, a smaller loss indicates a better classifier.
Load the fisheriris
data set. Create X
as a numeric matrix that contains four measurements for 150 irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris
X = meas;
Y = species;
Train a naive Bayes classifier using the predictors X
and class labels Y
. A recommended practice is to specify the class names. fitcnb
assumes that each predictor is conditionally and normally distributed.
Mdl = fitcnb(X,Y,'ClassNames',{'setosa','versicolor','virginica'})
Mdl = ClassificationNaiveBayes ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 DistributionNames: {'normal' 'normal' 'normal' 'normal'} DistributionParameters: {3x4 cell}
Mdl
is a trained ClassificationNaiveBayes
classifier.
Estimate the in-sample classification error.
L = resubLoss(Mdl)
L = 0.0400
The naive Bayes classifier misclassifies 4% of the training observations.
Determine Resubstitution Hinge Loss of SVM Classifier
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
Train a support vector machine (SVM) classifier. Standardize the data and specify that 'g'
is the positive class.
SVMModel = fitcsvm(X,Y,'ClassNames',{'b','g'},'Standardize',true);
SVMModel
is a trained ClassificationSVM
classifier.
Estimate the in-sample hinge loss.
L = resubLoss(SVMModel,'LossFun','hinge')
L = 0.1603
The hinge loss is 0.1603
. Classifiers with hinge losses close to 0 are preferred.
Compare GAMs by Examining Classification Loss
Train a generalized additive model (GAM) that contains both linear and interaction terms for predictors, and estimate the classification loss with and without interaction terms. Specify whether to include interaction terms when estimating the classification loss for training and test data.
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
Partition the data set into two sets: one containing training data, and the other containing new, unobserved test data. Reserve 50 observations for the new test data set.
rng('default') % For reproducibility n = size(X,1); newInds = randsample(n,50); inds = ~ismember(1:n,newInds); XNew = X(newInds,:); YNew = Y(newInds);
Train a GAM using the predictors X
and class labels Y
. A recommended practice is to specify the class names. Specify to include the 10 most important interaction terms.
Mdl = fitcgam(X(inds,:),Y(inds),'ClassNames',{'b','g'},'Interactions',10)
Mdl = ClassificationGAM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: 'logit' Intercept: 2.0026 Interactions: [10x2 double] NumObservations: 301
Mdl
is a ClassificationGAM
model object.
Compute the resubstitution classification loss both with and without interaction terms in Mdl
. To exclude interaction terms, specify 'IncludeInteractions',false
.
resubl = resubLoss(Mdl)
resubl = 0
resubl_nointeraction = resubLoss(Mdl,'IncludeInteractions',false)
resubl_nointeraction = 0
Estimate the classification loss both with and without interaction terms in Mdl
.
l = loss(Mdl,XNew,YNew)
l = 0.0615
l_nointeraction = loss(Mdl,XNew,YNew,'IncludeInteractions',false)
l_nointeraction = 0.0615
Including interaction terms does not change the classification loss for Mdl
. The trained model classifies all training samples correctly and misclassifies approximately 6% of the test samples.
Input Arguments
Mdl
— Classification machine learning model
full classification model object
Classification machine learning model, specified as a full classification model object, as given in the following table of supported models.
Model | Classification Model Object |
---|---|
Generalized additive model | ClassificationGAM |
k-nearest neighbor model | ClassificationKNN |
Naive Bayes model | ClassificationNaiveBayes |
Neural network model | ClassificationNeuralNetwork |
Support vector machine for one-class and binary classification | ClassificationSVM |
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value 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.
Example: resubLoss(Mdl,'LossFun','logit')
estimates the logit
resubstitution loss.
IncludeInteractions
— Flag to include interaction terms
true
| false
Flag to include interaction terms of the model, specified as true
or
false
. This argument is valid only for a generalized
additive model (GAM). That is, you can specify this argument only when
Mdl
is ClassificationGAM
.
The default value is true
if Mdl
contains interaction
terms. The value must be false
if the model does not contain interaction
terms.
Data Types: logical
LossFun
— Loss function
'binodeviance'
| 'classifcost'
| 'classiferror'
| 'crossentropy'
| 'exponential'
| 'hinge'
| 'logit'
| 'mincost'
| 'quadratic'
| function handle
Loss function, specified as a built-in loss function name or a function handle.
The default value depends on the model type of Mdl
.
The default value is
'classiferror'
ifMdl
is aClassificationSVM
object.The default value is
'mincost'
ifMdl
is aClassificationKNN
,ClassificationNaiveBayes
, orClassificationNeuralNetwork
object.If
Mdl
is aClassificationGAM
object, the default value is'mincost'
if theScoreTransform
property of the input model object (
) isMdl
.ScoreTransform'logit'
; otherwise, the default value is'classiferror'
.
'classiferror'
and 'mincost'
are equivalent
when you use the default cost matrix. See Classification Loss for more
information.
This 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 'crossentropy'
Cross-entropy loss (for neural networks only) 'exponential'
Exponential loss 'hinge'
Hinge loss 'logit'
Logistic loss 'mincost'
Minimal expected misclassification cost (for classification scores that are posterior probabilities) 'quadratic'
Quadratic loss To specify a custom loss function, use function handle notation. The function must have this form:
lossvalue =
lossfun
(C,S,W,Cost)The output argument
lossvalue
is a scalar.You specify the function name (
lossfun
).C
is ann
-by-K
logical matrix with rows indicating the class to which the corresponding observation belongs.n
is the number of observations inTbl
orX
, andK
is the number of distinct classes (numel(Mdl.ClassNames)
). The column order corresponds to the class order inMdl.ClassNames
. CreateC
by settingC(p,q) = 1
, if observationp
is in classq
, for each row. Set all other elements of rowp
to0
.S
is ann
-by-K
numeric matrix of classification scores. The column order corresponds to the class order inMdl.ClassNames
.S
is a matrix of classification scores, similar to the output ofpredict
.W
is ann
-by-1 numeric vector of observation weights.Cost
is aK
-by-K
numeric matrix of misclassification costs. For example,Cost = ones(K) – eye(K)
specifies a cost of0
for correct classification and1
for misclassification.
Example: 'LossFun','binodeviance'
Data Types: char
| string
| function_handle
More About
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 positive-class 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
name-value 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 user-specified 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. |
Cross-entropy loss | "crossentropy" |
The weighted cross-entropy 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).
Algorithms
resubLoss
computes the classification loss according to the
corresponding loss
function of the object (Mdl
). For
a model-specific description, see the loss
function reference pages in
the following table.
Model | Classification Model Object (Mdl ) | loss Object Function |
---|---|---|
Generalized additive model | ClassificationGAM | loss |
k-nearest neighbor model | ClassificationKNN | loss |
Naive Bayes model | ClassificationNaiveBayes | loss |
Neural network model | ClassificationNeuralNetwork | loss |
Support vector machine for one-class and binary classification | ClassificationSVM | loss |
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
This function fully supports GPU arrays for a trained classification model specified as a
ClassificationKNN
orClassificationSVM
object.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2012aR2023b: Observations with missing predictor values are used in resubstitution and cross-validation computations
Starting in R2023b, the following classification model object functions use observations with missing predictor values as part of resubstitution ("resub") and cross-validation ("kfold") computations for classification edges, losses, margins, and predictions.
In previous releases, the software omitted observations with missing predictor values from the resubstitution and cross-validation computations.
R2022a: resubLoss
returns a different value for a ClassificationSVM
model with a nondefault cost matrix
If you specify a nondefault cost matrix when you train the input model object for an SVM model, the resubLoss
function returns a different value compared to previous releases.
The resubLoss
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
name-value 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 ClassificationSVM
model object with a nondefault cost matrix, so the
function can return a different value.
For details about the property value change, see Cost property stores the user-specified 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
name-value arguments, respectively,
and use the default cost matrix.
R2022a: Default LossFun
value has changed for ClassificationGAM
and
ClassificationNeuralNetwork
Starting in R2022a, the default value of the LossFun
name-value
argument has changed for both a generalized additive model (GAM) and a neural network model,
so that the resubLoss
function uses the "mincost"
option (minimal expected misclassification cost) as the default when a classification object
uses posterior probabilities for classification scores.
If the input model object
Mdl
is aClassificationGAM
object, the default value is"mincost"
if theScoreTransform
property ofMdl
(
) isMdl
.ScoreTransform'logit'
; otherwise, the default value is"classiferror"
.If
Mdl
is aClassificationNeuralNetwork
object, the default value is"mincost"
.
In previous releases, the default value was
"classiferror"
.
You do not need to make any changes to your code if you use the default cost matrix (whose element value is 0 for correct classification and 1 for incorrect classification). The "mincost"
option is equivalent to the "classiferror"
option for the default cost matrix.
See Also
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