predictConstraints
Predict coupled constraint violations at a set of points
Syntax
Description
returns the coupled constraint function violations at the points in
ConstraintViolations
= predictConstraints(results
,XTable
)XTable
.
[
also returns the standard deviations of the coupled constraint functions.ConstraintViolations
,sigma
]
= predictConstraints(results
,XTable
)
Examples
Predict Coupled Constraints
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); end 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',... 'BoxConstraint',x.box,... 'KernelScale',x.sigma); 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,... 'NumCoupledConstraints',1,'PlotFcn',... {@plotMinObjective,@plotConstraintModels,@plotObjectiveModel},... 'AcquisitionFunctionName','expected-improvement-plus','Verbose',0);
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); [XTable,table(cons)]
ans = 11x3 table sigma box cons ________ ______ _______ 0.01 1 99.539 0.025119 3.1623 106.74 0.063096 10 94.781 0.15849 31.623 25.242 0.39811 100 -38.79 1 316.23 -56.379 2.5119 1000 -34.247 6.3096 3162.3 4.9263 15.849 10000 39.193 39.811 31623 60.69 100 1e+05 71.82
Input Arguments
results
— Bayesian optimization results
BayesianOptimization
object
Bayesian optimization results, specified as a BayesianOptimization
object.
XTable
— Prediction points
table with D columns
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
ConstraintViolations
— Constraint violations
N
-by-K
matrix
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
.
sigma
— Constraint standard deviations
N
-by-K
matrix
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
See Also
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