predictError
Predict error value at a set of points
Description
Examples
Error Prediction
This example shows optimizing a function that throws an error when the evaluation point has norm larger than 2
. The error model for the objective function learns this behavior.
Create variables named x1
and x2
that range from -5
to 5
.
var1 = optimizableVariable('x1',[-5,5]); var2 = optimizableVariable('x2',[-5,5]); vars = [var1,var2];
The following objective function throws an error when the norm of x = [x1,x2]
exceeds 2:
function f = makeanerror(x)
f = x.x1 - x.x2 - sqrt(4-x.x1^2-x.x2^2);
fun = @makeanerror;
Plot the error model and minimum objective as the optimization proceeds. Optimize for 60 iterations so the error model becomes well-trained. For reproducibility, set the random seed and use the 'expected-improvement-plus'
acquisition function.
rng default results = bayesopt(fun,vars,'Verbose',0,'MaxObjectiveEvaluations',60,... 'AcquisitionFunctionName','expected-improvement-plus',... 'PlotFcn',{@plotMinObjective,@plotConstraintModels});
Predict the error at points on the line x1 = x2
. If the error model were perfect, it would have value -1
at every point where the norm of x
is no more than 2
, and value 1
at all other points.
x1 = (-5:0.5:5)'; x2 = x1; XTable = table(x1,x2); error = predictError(results,XTable); normx = sqrt(x1.^2 + x2.^2); [XTable,table(normx,error)]
ans = 21x4 table x1 x2 normx error ____ ____ _______ _________ -5 -5 7.0711 0.94663 -4.5 -4.5 6.364 0.97396 -4 -4 5.6569 0.99125 -3.5 -3.5 4.9497 1.0033 -3 -3 4.2426 1.0018 -2.5 -2.5 3.5355 0.99627 -2 -2 2.8284 1.0043 -1.5 -1.5 2.1213 0.89886 -1 -1 1.4142 0.4746 -0.5 -0.5 0.70711 0.0042389 0 0 0 -0.16004 0.5 0.5 0.70711 -0.012397 1 1 1.4142 0.30187 1.5 1.5 2.1213 0.88588 2 2 2.8284 1.0872 2.5 2.5 3.5355 0.997 3 3 4.2426 0.99861 3.5 3.5 4.9497 0.98894 4 4 5.6569 0.98941 4.5 4.5 6.364 0.98956 5 5 7.0711 0.95549
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
error
— Mean of error coupled constraint
N
-by-1
vector
Mean of error coupled constraint, returned as an
N
-by-1
vector, where
N
is the number of rows of
XTable
. The mean is the posterior mean of the error
coupled constraint at the points in XTable
.
bayesopt
deems your objective function to return an
error if it returns anything other than a finite real scalar. See Objective Function Errors.
sigma
— Standard deviation of error coupled constraint
N
-by-1
vector
Standard deviation of error coupled constraint, returned as an
N
-by-1
vector, where
N
is the number of rows of
XTable
.
Version History
Introduced in R2016b
See Also
MATLAB-Befehl
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