Name

findTheta — Optimizes over kriging hyper-parameters (corelation scale parameters (theta) and/or process variance (sigma) or proporionality coefficent between process variance and noise (alfa)), by minimizing negative Likelihood or minimizing Leave One Out Cross validation.

Calling Sequence

   [kmodel, perf]=findTheta(model,lob,upb,crit,method,maxiter,params);
   
   

Parameters

model:

mlist of type kmodel created previously using function km.

lob:

row vector (1*model.n). Lower boundaries for optimization over theta.

upb:

row vector (1*model.n). Upper boundaries for optimization over theta.

crit:

criterion for optimization.

if =='MLL' optimization uses Likelihood;

if == 'CV' optimization uses Leave-One-Out Cross-validation;

method:

optimization method;

if == 'CMA' optimization is based on CMA-ES.

if == 'NM' optimization is based on Nelder-Mead method with restarts.

if == 'RS' optimization is based on random search.

if == 'RLHS' optimization is based on random Latin Hypercubes.

maxiter:

maximum number of criterion evaluations.

params:

additional parameters for optimizer; If not given maxiter for number of maximum objective evaluations and for other default parameters are used.

if method == 'CMA', params may specify CMA-ES input structure.

if method == 'NM', params may specify parameters for Nelder-Mead method with restarts.

kmodel:

mlist of type kmodel, that contains updated kriging model with optimal parameters.

perf:

mlist structure of type perf containing data of performance of optimization.

iter - total number of criterion evaluations.

imprIter - number of iterations, where criterion value was improved.

models - list of kmodel objects for each iteration.

imprModels - list of kmodel objects for iterations, where criterion value was improved.

crit - column vector (perf.iter*1) containing criterion values for each iteration.

imprCrit - column vector (perf.imprIter*1) containing criterion values for iterations, where criterion value was improved.

Description

Optimizes over correlation function's hyper-parameters of previously created kriging model by km(.). Determines corelation scale parameters (theta) and/or process variance (sigma) or proporionality coefficent between process variance and noise (alfa), by minimizing negative Likelihood or minimizing LOO Cross validation.

This function sets and uses global variables R_kriging T_kriging Ty_kriging Tyfb_kriging M_kriging Y_kriging frf_kriging Beta_kriging.

Examples

See demos directory for more examples.
   

See also

km, predict, LL_driver_optim, simGaussian, SimCondGaussian

Authors

Janis Janusevskis, 3MI/EMSE

Bibliography