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Predict coupled constraint violations at a set of points



ConstraintViolations = predictConstraints(results,XTable) returns the coupled constraint function violations at the points in XTable.

[ConstraintViolations,sigma] = predictConstraints(results,XTable) also returns the standard deviations of the coupled constraint functions.


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This example shows how to predict the coupled constraints of an optimized SVM model. For details of this model, see Optimize Cross-Validated Classifier Using bayesopt.

rng default
grnpop = mvnrnd([1,0],eye(2),10);
redpop = mvnrnd([0,1],eye(2),10);
redpts = zeros(100,2);
grnpts = redpts;
for i = 1:100
    grnpts(i,:) = mvnrnd(grnpop(randi(10),:),eye(2)*0.02);
    redpts(i,:) = mvnrnd(redpop(randi(10),:),eye(2)*0.02);
cdata = [grnpts;redpts];
grp = ones(200,1);
grp(101:200) = -1;
c = cvpartition(200,'KFold',10);
sigma = optimizableVariable('sigma',[1e-5,1e5],'Transform','log');
box = optimizableVariable('box',[1e-5,1e5],'Transform','log');

The objective function is the cross-validation loss of the SVM model for the partition c. The coupled constraint is the number of support vectors in the model minus 100. The model has 200 data points, so the coupled constraint values range from -100 to 100. Positive values mean the constraint is not satisfied.

function [objective,constraint] = mysvmfun(x,cdata,grp,c)
SVMModel = fitcsvm(cdata,grp,'KernelFunction','rbf',...
cvModel = crossval(SVMModel,'CVPartition',c);
objective = kfoldLoss(cvModel);
constraint = sum(SVMModel.IsSupportVector)-100.5;

Call the optimizer using this function and its one coupled constraint.

fun = @(x)mysvmfun(x,cdata,grp,c);
results = bayesopt(fun,[sigma,box],'IsObjectiveDeterministic',true,...

The constraint model plot shows that most parameters in the range are infeasible, and are feasible only for relatively high values of the box parameter and a small range of the sigma parameter. Predict the coupled constraint values for several values of the control variables box and sigma.

sigma = logspace(-2,2,11)';
box = logspace(0,5,11)';
XTable = table(sigma,box);
cons = predictConstraints(results,XTable);
ans =

  11x3 table

     sigma       box       cons  
    ________    ______    _______

        0.01         1     99.443
    0.025119    3.1623     106.49
    0.063096        10     94.468
     0.15849    31.623     25.134
     0.39811       100    -38.732
           1    316.23    -55.156
      2.5119      1000    -34.181
      6.3096    3162.3     5.0153
      15.849     10000     39.465
      39.811     31623       60.9
         100     1e+05     71.906

Input Arguments

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Bayesian optimization results, specified as a BayesianOptimization object.

Prediction points, specified as a table with D columns, where D is the number of variables in the problem. The function performs its predictions on these points.

Data Types: table

Output Arguments

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Constraint violations, returned as an N-by-K matrix, where there are N rows in XTable and K coupled constraints. The constraint violations are the posterior means of the Gaussian process model of the coupled constraints at the points in XTable.

Constraint standard deviations, returned as an N-by-K matrix, where there are N rows in XTable and K coupled constraints. The standard deviations represent those of the posterior distribution at the points in XTable.

Version History

Introduced in R2016b