Load theionospheredata set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

loadionosphererng(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'});

SVMModelis a trainedClassificationSVMclassifier.'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: {1x34 cell} ResponseName: 'Y' NumObservations: 351 KFold: 10 Partition: [1x1 cvpartition] ClassNames: {'b' 'g'} ScoreTransform: 'none' Properties, Methods

CVSVMModelis aClassificationPartitionedModelcross-validated classifier. During cross-validation, the software completes these steps:

Display the first model inCVSVMModel.Trained.

FirstModel = CVSVMModel.Trained{1}

FirstModel = CompactClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: 'none' Alpha: [78x1 double] Bias: -0.2208 KernelParameters: [1x1 struct] Mu: [0.8888 0 0.6320 0.0406 0.5931 0.1205 0.5361 ... ] Sigma: [0.3149 0 0.5033 0.4441 0.5255 0.4663 0.4987 ... ] SupportVectors: [78x34 double] SupportVectorLabels: [78x1 double] Properties, Methods

FirstModelis the first of the 10 trained classifiers. It is aCompactClassificationSVMclassifier.

You can estimate the generalization error by passingCVSVMModeltokfoldLoss.

Specify a holdout sample proportion for cross-validation. By default,crossvaluses 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 theionospheredata set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

loadionosphere

Remove the first two predictors for stability.

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

Train a naive Bayes classifier using the predictorsXand class labelsY. A recommended practice is to specify the class names.'b'is the negative class and'g'is the positive class.fitcnbassumes that each predictor is conditionally and normally distributed.

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

Mdlis a trainedClassificationNaiveBayesclassifier.

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

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

CVMdl = ClassificationPartitionedModel CrossValidatedModel: 'NaiveBayes' PredictorNames: {1x32 cell} ResponseName: 'Y' NumObservations: 351 KFold: 1 Partition: [1x1 cvpartition] ClassNames: {'b' 'g'} ScoreTransform: 'none' Properties, Methods

CVMdlis aClassificationPartitionedModelcross-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} Properties, Methods

TrainedModelis aCompactClassificationNaiveBayesclassifier.

Estimate the generalization error by passingCVMdltokfoldloss.

kfoldLoss(CVMdl)

ans = 0.2095

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

减少通过选择fi泛化误差ve 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%.

Train a regression generalized additive model (GAM) by usingfitrgam, and create a cross-validated GAM by usingcrossvaland the holdout option. Then, usekfoldPredict预测反应为validation-fold observations using a model trained on training-fold observations.

Load thepatientsdata set.

loadpatients

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');

Mdlis aRegressionGAMmodel object.

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

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

CVMdl = RegressionPartitionedGAM CrossValidatedModel: 'GAM' PredictorNames: {1x6 cell} CategoricalPredictors: [3 5 6] ResponseName: 'Systolic' NumObservations: 100 KFold: 1 Partition: [1x1 cvpartition] NumTrainedPerFold: [1x1 struct] ResponseTransform: 'none' IsStandardDeviationFit: 0 Properties, Methods

Thecrossvalfunction creates aRegressionPartitionedGAMmodel objectCVMdlwith the holdout option. During cross-validation, the software completes these steps:

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 usingkfoldPredict. The function predicts responses for the validation-fold observations by using the model trained on the training-fold observations. The function assignsNaNto 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)

ans=8×3 tableObseraction 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