selectModels

Choose subset of multiclass ECOC models composed of binary ClassificationLinear learners

Syntax

SubMdl = selectModels(Mdl,idx)

Description

SubMdl = selectModels(Mdl,idx) returns a subset of trained error-correcting output codes (ECOC) models composed of ClassificationLinear binary models from a set of multiclass ECOC models (Mdl) trained using various regularization strengths. The indices (idx) correspond to the regularization strengths in Mdl.BinaryLearners{1}.Lambda and specify which models to return.

SubMdl is returned as a CompactClassificationECOC model object.

Examples

Select Best Regularized Models

Choose a subset of trained ECOC models composed of linear binary learners with various regularization strengths.

Load the NLP data set.

load nlpdata

X is a sparse matrix of predictor data, and Y is a categorical vector of class labels.

Create a set of 11 logarithmically spaced regularization strengths from $$10^{-8}$$ through $$10^{-1}$$.

Lambda = logspace(-8,-1,11);

Create a linear classification model template that specifies optimizing the objective function using SpaRSA. Use lasso penalties with the strengths specified in Lambda.

t = templateLinear('Solver','sparsa','Regularization','lasso',...
    'Lambda',Lambda);

Hold out 30% of the data for testing. Identify the test-sample indices.

rng(1); % For reproducibility
cvp = cvpartition(Y,'Holdout',0.30);
idxTest = test(cvp);

Train an ECOC model composed of linear classification models. For quicker execution time, orient the predictor data so that individual observations correspond to columns.

X = X';
PMdl = fitcecoc(X,Y,'Learners',t,'ObservationsIn','columns','CVPartition',cvp);
Mdl = PMdl.Trained{1};
numel(Mdl.BinaryLearners{1}.Lambda)

ans = 11

Mdl is a CompactClassificationECOC model object. Because Lambda is an 11-dimensional vector of regularization strengths, you can think of Mdl as eleven trained models, each corresponding to a regularization strength.

Estimate the test-sample misclassification rates for each regularized model.

ce = loss(Mdl,X(:,idxTest),Y(idxTest),'ObservationsIn','columns');

Plot the misclassification rates with respect to regularization strength on the log scale.

figure
plot(log10(Lambda),log10(ce),'-o')
ylabel('log_{10} misclassification rates')
xlabel('log_{10} Lambda')
[~,minCEIdx] = min(ce);
minLambda = Lambda(minCEIdx);
hold on
plot(log10(minLambda),log10(ce(minCEIdx)),'ro');
hold off

Several values of Lambda yield similarly small classification error values. Consider choosing greater values of Lambda (that still yield good classification rates) because they lead to predictor variable sparsity.

Select the four models with regularization strengths that occur around the point at which the classification error starts increasing.

idx = 7:10;
MdlFinal = selectModels(Mdl,idx)

MdlFinal = 
  CompactClassificationECOC
      ResponseName: 'Y'
        ClassNames: [comm    dsp    ecoder    fixedpoint    hdlcoder    phased    physmod    simulink    stats    supportpkg    symbolic    vision    xpc]
    ScoreTransform: 'none'
    BinaryLearners: {78×1 cell}
      CodingMatrix: [13×78 double]


  Properties, Methods

LambdaFinal = MdlFinal.BinaryLearners{1}.Lambda

LambdaFinal = 1×4

    0.0002    0.0008    0.0040    0.0200

MdlFinal is a CompactClassificationECOC model object. You can think of it as four models trained using the four regularization strengths in LambdaFinal.

Input Arguments

Mdl — Multiclass ECOC model composed of binary linear classifiers

CompactClassificationECOC model object

Multiclass ECOC model composed of binary linear classifiers, trained using various regularization strengths, specified as a CompactClassificationECOC model object.

When creating Mdl, you must:

• Use fitcecoc.

• Specify ClassificationLinear binary learners (see Learners).

• Specify the same regularization strengths for each linear binary learner.

Although Mdl is one model object, if numel(Mdl.BinaryLearners{1}.Lambda) = L ≥ 2, then you can think of Mdl as L trained models.

idx — Indices corresponding to regularization strengths

positive integer vector

Indices corresponding to regularization strengths, specified as a positive integer vector. Values of idx must be in the interval [1,L], where L = numel(Mdl.BinaryLearners{1}.Lambda).

Data Types: double | single

Tips

• One way to build several predictive ECOC models composed of binary linear classification models is:

  1. Create a linear classification model template using templateLinear and specify a grid of regularization strengths using the 'Lambda' name-value pair argument.

  2. Hold out a portion of the data for testing.

  3. Train an ECOC model using fitcecoc. Specify the template using the 'Learners' name-value pair argument and supply the training data. fitcecoc returns one CompactClassificationECOC model object containing ClassificationLinear binary learners, but all binary learners contain a model for each regularization strength.

  4. To determine the quality of each regularized model, pass the returned model object and the held-out data to, for example, loss.

  5. Identify the indices (idx) of a satisfactory subset of regularized models, and then pass the returned model and the indices to selectModels. The function selectModels returns one CompactClassificationECOC model object, but it contains numel(idx) regularized models.

  6. To predict class labels for new data, pass the data and the subset of regularized models to predict.