crossval

Cross-validate machine learning model

Syntax

CVMdl = crossval(Mdl)

CVMdl = crossval(Mdl,Name=Value)

Description

CVMdl = crossval(Mdl) returns a cross-validated (partitioned) machine learning model (CVMdl) from a trained model (Mdl). By default, crossval uses 10-fold cross-validation on the training data.

CVMdl = crossval(Mdl,Name=Value) specifies additional options using one or more name-value arguments. For example, you can specify the fraction of data for holdout validation, and the number of folds to use in the cross-validated model.

Examples

Cross-Validate 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
rng(1); % For reproducibility

Train a support vector machine (SVM) classifier. Standardize the predictor data and specify the order of the classes.

SVMModel = fitcsvm(X,Y,'Standardize',true,'ClassNames',{'b','g'});

SVMModel is a trained ClassificationSVM classifier. 'b' is the negative class and 'g' is the positive class.

Cross-validate the classifier using 10-fold cross-validation.

CVSVMModel = crossval(SVMModel)

CVSVMModel = 
  ClassificationPartitionedModel
    CrossValidatedModel: 'SVM'
         PredictorNames: {'x1'  'x2'  'x3'  'x4'  'x5'  'x6'  'x7'  'x8'  'x9'  'x10'  'x11'  'x12'  'x13'  'x14'  'x15'  'x16'  'x17'  'x18'  'x19'  'x20'  'x21'  'x22'  'x23'  'x24'  'x25'  'x26'  'x27'  'x28'  'x29'  'x30'  'x31'  'x32'  'x33'  'x34'}
           ResponseName: 'Y'
        NumObservations: 351
                  KFold: 10
              Partition: [1x1 cvpartition]
             ClassNames: {'b'  'g'}
         ScoreTransform: 'none'

CVSVMModel is a ClassificationPartitionedModel cross-validated classifier. During cross-validation, the software completes these steps:

1. Randomly partition the data into 10 sets of equal size.

2. Train an SVM classifier on nine of the sets.

3. Repeat steps 1 and 2 k = 10 times. The software leaves out one partition each time and trains on the other nine partitions.

4. Combine generalization statistics for each fold.

Display the first model in CVSVMModel.Trained.

FirstModel = CVSVMModel.Trained{1}

FirstModel = 
  CompactClassificationSVM
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: {'b'  'g'}
           ScoreTransform: 'none'
                    Alpha: [78x1 double]
                     Bias: -0.2209
         KernelParameters: [1x1 struct]
                       Mu: [0.8888 0 0.6320 0.0406 0.5931 0.1205 0.5361 0.1286 0.5083 0.1879 0.4779 0.1567 0.3924 0.0875 0.3360 0.0789 0.3839 9.6066e-05 0.3562 -0.0308 0.3398 -0.0073 0.3590 -0.0628 0.4064 -0.0664 0.5535 -0.0749 0.3835 ... ] (1x34 double)
                    Sigma: [0.3149 0 0.5033 0.4441 0.5255 0.4663 0.4987 0.5205 0.5040 0.4780 0.5649 0.4896 0.6293 0.4924 0.6606 0.4535 0.6133 0.4878 0.6250 0.5140 0.6075 0.5150 0.6068 0.5222 0.5729 0.5103 0.5061 0.5478 0.5712 0.5032 ... ] (1x34 double)
           SupportVectors: [78x34 double]
      SupportVectorLabels: [78x1 double]

FirstModel is the first of the 10 trained classifiers. It is a CompactClassificationSVM classifier.

You can estimate the generalization error by passing CVSVMModel to kfoldLoss.

Specify Holdout Sample Proportion for Naive Bayes Cross-Validation

Specify a holdout sample proportion for cross-validation. By default, crossval uses 10-fold cross-validation to cross-validate a naive Bayes classifier. However, you have several other options for cross-validation. For example, you can specify a different number of folds or a holdout sample proportion.

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

Remove the first two predictors for stability.

X = X(:,3:end);
rng('default'); % For reproducibility

Train a naive Bayes classifier using the predictors X and class labels Y. A recommended practice is to specify the class names. 'b' is the negative class and 'g' is the positive class. fitcnb assumes that each predictor is conditionally and normally distributed.

Mdl = fitcnb(X,Y,'ClassNames',{'b','g'});

Mdl is a trained ClassificationNaiveBayes classifier.

Cross-validate the classifier by specifying a 30% holdout sample.

CVMdl = crossval(Mdl,'Holdout',0.3)

CVMdl = 
  ClassificationPartitionedModel
    CrossValidatedModel: 'NaiveBayes'
         PredictorNames: {'x1'  'x2'  'x3'  'x4'  'x5'  'x6'  'x7'  'x8'  'x9'  'x10'  'x11'  'x12'  'x13'  'x14'  'x15'  'x16'  'x17'  'x18'  'x19'  'x20'  'x21'  'x22'  'x23'  'x24'  'x25'  'x26'  'x27'  'x28'  'x29'  'x30'  'x31'  'x32'}
           ResponseName: 'Y'
        NumObservations: 351
                  KFold: 1
              Partition: [1x1 cvpartition]
             ClassNames: {'b'  'g'}
         ScoreTransform: 'none'

CVMdl is a ClassificationPartitionedModel cross-validated, naive Bayes classifier.

Display the properties of the classifier trained using 70% of the data.

TrainedModel = CVMdl.Trained{1}

TrainedModel = 
  CompactClassificationNaiveBayes
              ResponseName: 'Y'
     CategoricalPredictors: []
                ClassNames: {'b'  'g'}
            ScoreTransform: 'none'
         DistributionNames: {1x32 cell}
    DistributionParameters: {2x32 cell}

TrainedModel is a CompactClassificationNaiveBayes classifier.

Estimate the generalization error by passing CVMdl to kfoldloss.

kfoldLoss(CVMdl)

ans = 
0.2095

The out-of-sample misclassification error is approximately 21%.

Reduce the generalization error by choosing the five most important predictors.

idx = fscmrmr(X,Y);
Xnew = X(:,idx(1:5));

Train a naive Bayes classifier for the new predictor.

Mdlnew = fitcnb(Xnew,Y,'ClassNames',{'b','g'});

Cross-validate the new classifier by specifying a 30% holdout sample, and estimate the generalization error.

CVMdlnew = crossval(Mdlnew,'Holdout',0.3);
kfoldLoss(CVMdlnew)

ans = 
0.1429

The out-of-sample misclassification error is reduced from approximately 21% to approximately 14%.

Create Cross-Validated Regression GAM Using crossval

Train a regression generalized additive model (GAM) by using fitrgam, and create a cross-validated GAM by using crossval and the holdout option. Then, use kfoldPredict to predict responses for validation-fold observations using a model trained on training-fold observations.

Load the patients data set.

load patients

Create a table that contains the predictor variables (Age, Diastolic, Smoker, Weight, Gender, SelfAssessedHealthStatus) and the response variable (Systolic).

tbl = table(Age,Diastolic,Smoker,Weight,Gender,SelfAssessedHealthStatus,Systolic);

Train a GAM that contains linear terms for predictors.

Mdl = fitrgam(tbl,'Systolic');

Mdl is a RegressionGAM model object.

Cross-validate the model by specifying a 30% holdout sample.

rng('default') % For reproducibility
CVMdl = crossval(Mdl,'Holdout',0.3)

CVMdl = 
  RegressionPartitionedGAM
       CrossValidatedModel: 'GAM'
            PredictorNames: {'Age'  'Diastolic'  'Smoker'  'Weight'  'Gender'  'SelfAssessedHealthStatus'}
     CategoricalPredictors: [3 5 6]
              ResponseName: 'Systolic'
           NumObservations: 100
                     KFold: 1
                 Partition: [1x1 cvpartition]
         NumTrainedPerFold: [1x1 struct]
         ResponseTransform: 'none'
    IsStandardDeviationFit: 0

The crossval function creates a RegressionPartitionedGAM model object CVMdl with the holdout option. During cross-validation, the software completes these steps:

1. Randomly select and reserve 30% of the data as validation data, and train the model using the rest of the data.

2. Store the compact, trained model in the Trained property of the cross-validated model object RegressionPartitionedGAM.

You can choose a different cross-validation setting by using the 'CrossVal', 'CVPartition', 'KFold', or 'Leaveout' name-value argument.

Predict responses for the validation-fold observations by using kfoldPredict. The function predicts responses for the validation-fold observations by using the model trained on the training-fold observations. The function assigns NaN to the training-fold observations.

yFit = kfoldPredict(CVMdl);

Find the validation-fold observation indexes, and create a table containing the observation index, observed response values, and predicted response values. Display the first eight rows of the table.

idx = find(~isnan(yFit));
t = table(idx,tbl.Systolic(idx),yFit(idx), ...
    'VariableNames',{'Obseraction Index','Observed Value','Predicted Value'});
head(t)

    Obseraction Index    Observed Value    Predicted Value
    _________________    ______________    _______________

            1                 124              130.22     
            6                 121              124.38     
            7                 130              125.26     
           12                 115              117.05     
           20                 125              121.82     
           22                 123              116.99     
           23                 114                 107     
           24                 128              122.52     

Compute the regression error (mean squared error) for the validation-fold observations.

L = kfoldLoss(CVMdl)

L = 
43.8715

Cross-Validate ECOC Classifier

Cross-validate an ECOC classifier with SVM binary learners, and estimate the generalized classification error.

Load Fisher's iris data set. Specify the predictor data X and the response data Y.

load fisheriris
X = meas;
Y = species;
rng(1); % For reproducibility

Create an SVM template, and standardize the predictors.

t = templateSVM('Standardize',true)

t = 
Fit template for SVM.
    Standardize: 1

t is an SVM template. Most of the template object properties are empty. When training the ECOC classifier, the software sets the applicable properties to their default values.

Train the ECOC classifier, and specify the class order.

Mdl = fitcecoc(X,Y,'Learners',t,...
    'ClassNames',{'setosa','versicolor','virginica'});

Mdl is a ClassificationECOC classifier. You can access its properties using dot notation.

Cross-validate Mdl using 10-fold cross-validation.

CVMdl = crossval(Mdl);

CVMdl is a ClassificationPartitionedECOC cross-validated ECOC classifier.

Estimate the generalized classification error.

genError = kfoldLoss(CVMdl)

genError = 
0.0400

The generalized classification error is 4%, which indicates that the ECOC classifier generalizes fairly well.

Input Arguments

Mdl — Machine learning model

full regression model object | full classification model object

Machine learning model, specified as a full regression or classification model object, as given in the following tables of supported models.

Regression Model Object

Model	Full Regression Model Object
Regression ensemble model	RegressionEnsemble, RegressionBaggedEnsemble
Gaussian process regression (GPR) model	RegressionGP (If you supply a custom ActiveSet value in the call to fitrgp, then you cannot cross-validate the GPR model.)
Generalized additive model (GAM)	RegressionGAM
Neural network model	RegressionNeuralNetwork (If you use multiple response variables in the call to fitrnet, then you cannot cross-validate the neural network model.)
Support vector machine regression model	RegressionSVM
Regression tree model	RegressionTree

Classification Model Object

Model	Full Classification Model Object
Discriminant analysis classifier	ClassificationDiscriminant
Multiclass error-correcting output codes (ECOC) model	ClassificationECOC
Ensemble classifier	ClassificationEnsemble, ClassificationBaggedEnsemble
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
Binary decision tree for multiclass classification	ClassificationTree

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: crossval(Mdl,KFold=3) specifies to use three folds in the cross-validated model.

CVPartition — Cross-validation partition

[] (default) | cvpartition object

Cross-validation partition, specified as a cvpartition object that specifies the type of cross-validation and the indexing for the training and validation sets.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Suppose you create a random partition for 5-fold cross-validation on 500 observations by using cvp = cvpartition(500,KFold=5). Then, you can specify the cross-validation partition by setting CVPartition=cvp.

Holdout — Fraction of data for holdout validation

scalar value in the range (0,1)

Fraction of the data used for holdout validation, specified as a scalar value in the range (0,1). If you specify Holdout=p, then the software completes these steps:

1. Randomly select and reserve p*100% of the data as validation data, and train the model using the rest of the data.

2. Store the compact trained model in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Holdout=0.1

Data Types: double | single

KFold — Number of folds

10 (default) | positive integer value greater than 1

Number of folds to use in the cross-validated model, specified as a positive integer value greater than 1. If you specify KFold=k, then the software completes these steps:

1. Randomly partition the data into k sets.

2. For each set, reserve the set as validation data, and train the model using the other k – 1 sets.

3. Store the k compact trained models in a k-by-1 cell vector in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: KFold=5

Data Types: single | double

Leaveout — Leave-one-out cross-validation flag

"off" (default) | "on"

Leave-one-out cross-validation flag, specified as "on" or "off". If you specify Leaveout="on", then for each of the n observations (where n is the number of observations, excluding missing observations, specified in the NumObservations property of the model), the software completes these steps:

1. Reserve the one observation as validation data, and train the model using the other n – 1 observations.

2. Store the n compact trained models in an n-by-1 cell vector in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Leaveout="on"

Data Types: char | string

NPrint — Printout frequency

"off" (default) | positive integer

Printout frequency, specified as a positive integer or "off".

To track the number of folds trained by the software so far, specify a positive integer m. The software displays a message to the command line every time it finishes training m folds.

If you specify "off", the software does not display a message when it completes training folds.

Note

You can specify Nprint only if Mdl is a ClassificationEnsemble or RegressionEnsemble model object.

Example: NPrint=5

Data Types: single | double | char | string

Options — Options for computing in parallel

structure

Options for computing in parallel, specified as a structure. Create the Options structure using statset.

You need Parallel Computing Toolbox™ to run computations in parallel.

You can specify Options only if Mdl is a ClassificationECOC model object.

Example: Options=statset(UseParallel=true)

Data Types: struct

Output Arguments

CVMdl — Cross-validated machine learning model

cross-validated (partitioned) model object

Cross-validated machine learning model, returned as one of the cross-validated (partitioned) model objects in the following tables, depending on the input model Mdl.

Regression Model Object

Model	Regression Model (Mdl)	Cross-Validated Model (CVMdl)
Regression ensemble model	RegressionEnsemble, RegressionBaggedEnsemble	RegressionPartitionedEnsemble
Gaussian process regression model	RegressionGP	RegressionPartitionedGP
Generalized additive model	RegressionGAM	RegressionPartitionedGAM
Neural network model	RegressionNeuralNetwork	RegressionPartitionedNeuralNetwork
Support vector machine regression model	RegressionSVM	RegressionPartitionedSVM
Regression tree model	RegressionTree	RegressionPartitionedModel

Classification Model Object

Model	Classification Model (Mdl)	Cross-Validated Model (CVMdl)
Discriminant analysis classifier	ClassificationDiscriminant	ClassificationPartitionedModel
Multiclass error-correcting output codes (ECOC) model	ClassificationECOC	ClassificationPartitionedECOC
Ensemble classifier	ClassificationEnsemble, ClassificationBaggedEnsemble	ClassificationPartitionedEnsemble
Generalized additive model	ClassificationGAM	ClassificationPartitionedGAM
k-nearest neighbor model	ClassificationKNN	ClassificationPartitionedModel
Naive Bayes model	ClassificationNaiveBayes	ClassificationPartitionedModel
Neural network model	ClassificationNeuralNetwork	ClassificationPartitionedModel
Support vector machine for one-class and binary classification	ClassificationSVM	ClassificationPartitionedModel
Binary decision tree for multiclass classification	ClassificationTree	ClassificationPartitionedModel

Tips

• Assess the predictive performance of Mdl on cross-validated data using the kfold functions and properties of CVMdl, such as kfoldPredict, kfoldLoss, kfoldMargin, and kfoldEdge for classification, and kfoldPredict and kfoldLoss for regression.

• Return a partitioned classifier with stratified partitioning by using the name-value argument KFold or Holdout.

• Create a cvpartition object cvp using cvp = cvpartition(n,KFold=k). Return a partitioned classifier with nonstratified partitioning by using the name-value argument CVPartition=cvp.

Alternative Functionality

Instead of training a model and then cross-validating it, you can create a cross-validated model directly by using a fitting function and specifying one of these name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

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 ClassificationECOC, ClassificationEnsemble, ClassificationKNN, ClassificationNeuralNetwork, ClassificationSVM, or ClassificationTree object.

• This function fully supports GPU arrays for a trained regression model specified as a RegressionEnsemble, RegressionNeuralNetwork, RegressionSVM, or RegressionTree object.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a

R2024b: Specify GPU arrays for neural network models (requires Parallel Computing Toolbox)

crossval fully supports GPU arrays for RegressionNeuralNetwork and ClassificationNeuralNetwork.

R2023b: A cross-validated regression neural network model is a RegressionPartitionedNeuralNetwork object

Starting in R2023b, a cross-validated regression neural network model is a RegressionPartitionedNeuralNetwork object. In previous releases, a cross-validated regression neural network model was a RegressionPartitionedModel object.

You can create a RegressionPartitionedNeuralNetwork object in two ways:

• Create a cross-validated model from a regression neural network model object RegressionNeuralNetwork by using the crossval object function.

• Create a cross-validated model by using the fitrnet function and specifying one of the name-value arguments CrossVal, CVPartition, Holdout, KFold, or Leaveout.

R2022b: A cross-validated Gaussian process regression model is a RegressionPartitionedGP object

Starting in R2022b, a cross-validated Gaussian process regression (GPR) model is a RegressionPartitionedGP object. In previous releases, a cross-validated GPR model was a RegressionPartitionedModel object.

You can create a RegressionPartitionedGP object in two ways:

• Create a cross-validated model from a GPR model object RegressionGP by using the crossval object function.

• Create a cross-validated model by using the fitrgp function and specifying one of the name-value arguments CrossVal, CVPartition, Holdout, KFold, or Leaveout.

Regardless of whether you train a full or cross-validated GPR model first, you cannot specify an ActiveSet value in the call to fitrgp.