CRITERIA {STPGA}

Optimality Criteria

Description

These are some default design criteria to be minimized. There is a table in the details section that gives the formula for each design criterion and describes their usage. Note that the inputs for these functions come in 3 syntax flavors, namely Type-X, Type-D and Type-K. Users can define and use their owm design criteria as long as it has the Type-X syntax as shown with the examples.

Usage

AOPT(Train, Test, P, lambda = 1e-05, C=NULL)
CDMAX(Train, Test, P, lambda = 1e-05, C=NULL)
CDMAX0(Train, Test, P, lambda = 1e-05, C=NULL)
CDMAX2(Train, Test, P, lambda = 1e-05, C=NULL)
CDMEAN(Train, Test, P, lambda = 1e-05, C=NULL)
CDMEAN0(Train, Test, P, lambda = 1e-05, C=NULL)
CDMEAN2(Train, Test, P, lambda = 1e-05, C=NULL)
CDMEANMM(Train, Test, Kinv,K, lambda = 1e-05, C=NULL, Vg=NULL, Ve=NULL)
DOPT(Train, Test, P, lambda = 1e-05, C=NULL)
EOPT(Train, Test, P, lambda = 1e-05, C=NULL)
GAUSSMEANMM(Train, Test, Kinv, K, lambda = 1e-05, C=NULL, Vg=NULL, Ve=NULL)
GOPTPEV(Train, Test, P, lambda = 1e-05, C=NULL)
GOPTPEV2(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMAX(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMAX0(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMAX2(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMEAN(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMEAN0(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMEAN2(Train, Test, P, lambda = 1e-05, C=NULL)
PEVMEANMM(Train, Test, Kinv,K, lambda = 1e-05, C=NULL, Vg=NULL, Ve=NULL)
dist_to_test(Train, Test, Dst, lambda, C)
dist_to_test2(Train, Test, Dst, lambda, C)
neg_dist_in_train(Train, Test, Dst, lambda, C)
neg_dist_in_train2(Train, Test, Dst, lambda, C)

Arguments

Train

vector of identifiers for individuals in the training set

Test

vector of identifiers for individuals in the test set

P

(Only for Type-X) n \times k matrix of the first PCs of the predictor variables. The matrix needs to have union of the identifiers of the candidate and test individuals as rownames.

Dst

(Only for Type-D) n \times n symmetric distance matrix with row and column names.

Kinv

(Only for Type-K) n \times n symmetric matrix (inverse of the relationship matrix K between n individuals) with row and column names.

K

(Only for Type-K) n \times n symmetric matrix (the relationship matrix K between n individuals).

lambda

scalar shrinkage parameter (\lambda>0).

C

Contrast Matrix.

Vg

(Only for PEVMEANMM) covariance matrix between traits generated by the relationship K (multi-trait version).

Ve

(Only for PEVMEANMM) residual covariance matrix for the traits (multi-trait version).

Details

criterion name	formula	Type
AOPT	trace[C(P'_{Train}P_{Train}+lambda*I)^{-1}C']	X
CDMAX	max[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C')/	X
	diag(CP_{Test}P'_{Test}C')]
CDMAX0	max[diag(CP_{Train}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}C')/	X
	diag(CP_{Train}P'_{Train}C')]
CDMAX2	max[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}P_{Train}	X
	(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C')/diag(CP_{Test}P'_{Test}C')]
CDMEAN	mean[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C')/	X
	diag(CP_{Test}P'_{Test}C')]
CDMEAN0	mean[diag(CP_{Train}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}C')/	X
	diag(CP_{Train}P'_{Train}C')]
CDMEAN2	mean[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}P_{Train}	X
	(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C')/diag(CP_{Test}P'_{Test}C')]
CDMEANMM	-mean[diag(CZ_{Test}(K-lambda*(Z_{Train}'MZ_{Train}+\lambda*Kinv)^{-1}Z_{Test}'C')/	K
	(diag(CZ_{Test}KZ_{Test}'C'))]
DOPT	logdet(C(P'_{Train}P_{Train}+lambda*I))^{-1}C'	X
EOPT	max(eigenval(C(P'_{Train}P_{Train}+lambda*I))^{-1}C'))	X
GAUSSMEANMM	-mean(diag(Z_{Test}KZ_{Test}'-	K
	Z_{Test}KZ_{Train}'(Z_{Train}KZ_{Train}'+\lambda*I_{ntrain})^{-1}Z_{Train}KZ_{Test}')
GOPTPEV	max(eigenval(CP_{Test}(P_{Train}'P_{Train}+\lambda*I_{ntrain})^{-1}P_{Test}'C'))	X
GOPTPEV2	mean(eigenval(CP_{Test}(P_{Train}'P_{Train}+\lambda*I_{ntrain})^{-1}P_{Test}'C'))	X
PEVMAX	max(diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C'))	X
PEVMAX0	max(diag(CP_{Train}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}C'))	X
PEVMAX2	max[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}P_{Train}	X
	(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C']
PEVMEAN	mean(diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C'))	X
PEVMEAN0	mean(diag(CP_{Train}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Train}C'))	X
PEVMEAN2	mean[diag(CP_{Test}(P'_{Train}P_{Train}+lambda*I)^{-1}	X
	P'_{Train}P_{Train}(P'_{Train}P_{Train}+lambda*I)^{-1}P'_{Test}C']
PEVMEANMM	mean(diag(CZ_{test}(Ztrain'MZtrain+lambda*Kinv)^{-1}Ztest'C')))	K
dist_to_test	maximum distance from training set to test set based on Dst	D
dist_to_test2	mean distance from training set to test set based on Dst	D
neg_dist_in_train	negative of minimum distance between pairs in the training set based on Dst	D
neg_dist_in_train2	negative of mean distance between distinct pairs in the training set based on Dst	D

Value

value of the criterion.

Author(s)

Deniz Akdemir

Examples

	## Not run: 
#Examples to new criterion:
#1- PEVmax
STPGAUSERFUNC<-function(Train,Test, P, lambda=1e-6, C=NULL){
  PTrain<-P[rownames(P)%in%Train,]
  PTest<-P[rownames(P)%in%Test,]
  if (length(Test)==1){PTest=matrix(PTest, nrow=1)}
  if (!is.null(C)){ PTest<-C%*%PTest}
  PEV<-PTest%*%solve(crossprod(PTrain)+lambda*diag(ncol(PTrain)),t(PTrain))
    PEVmax<-max(diag(tcrossprod(PEV)))
  return(PEVmax)
}




######Here is an example of usage
data(iris)
#We will try to estimate petal width from
#variables sepal length and width and petal length.
X<-as.matrix(iris[,1:4])
distX<-as.matrix(dist(X))
rownames(distX)<-colnames(distX)<-rownames(X)<-paste(iris[,5],rep(1:50,3),sep="_" )
#test data 25 iris plants selected at random from the virginica family,
#candidates are the plants in the  setosa and versicolor families.
candidates<-rownames(X)[1:100]
test<-sample(setdiff(rownames(X),candidates), 25)
#want to select 25 examples using the criterion defined in STPGAUSERFUNC
#Increase niterations and npop substantially for better convergence.
ListTrain<-GenAlgForSubsetSelection(P=distX,Candidates=candidates,
Test=test,ntoselect=25,npop=50,
nelite=5, mutprob=.8, niterations=30,
lambda=1e-5, errorstat="STPGAUSERFUNC", plotiters=TRUE)

## End(Not run)