remMap (version 0.2-0)

remMap.BIC: Fit remMap models for a series of tuning parameters and return the corresponding BIC scores.

Description

Fit remMap models for a series of tuning parameters and return the corresponding BIC scores. It is computationally easy. But the BIC procedure assumes orthogonality of the design matrix to estimate the degrees of freedom. Thus it tends to select too small models when the actual design matrix (X.m) is far from orthogonal. In that case, cross validation is recommended (see help(remMap.CV) for more details)

Usage

remMap.BIC(X.m, Y.m, lamL1.v, lamL2.v, C.m=NULL)

Arguments

X.m

numeric matrix (n by p): columns correspond to predictor variables and rows correspond to samples. Missing values are not allowed.

Y.m

numeric matrix (n by q): columns correspond to response variables and rows correspond to samples. Missing values are not allowed.

lamL1.v

numeric vector: a set of $l_1$ norm penalty parameters.

lamL2.v

numeric vector: a set of $l_2$ norm penalty parameters.

C.m

numeric matrix (p by q). $C_m[i,j]=0$ means the corresponding coefficient beta[i,j] is set to be zero in the model; g $C_m[i,j]=1$ means the corresponding beta[i,j] is included in the MAP penalty; $C_m[i,j]=2$ means the corresponding beta[i,j] is not included in the MAP penalty; default(=NULL): $C_m[i,j]$ are all set to be 1.

Value

A list with two components

BIC

a numeric matrix recording the BIC scores of the remMap models. Each element corresponds to one pair of (lamL1, lamL2).

phi

a list recording the fitted remMap coefficients. Each component corresponds to one pair of (lamL1, lamL2) in the grid search.

Details

remMap.BIC is used to perform two-dimensional grid search of the tuning parameters (lamL1.v, lamL2.v) based on the BIC scores. (Peng and et.al., 2008).

References

J. Peng, J. Zhu, A. Bergamaschi, W. Han, D.-Y. Noh, J. R. Pollack, P. Wang, Regularized Multivariate Regression for Identifying Master Predictors with Application to Integrative Genomics Study of Breast Cancer. (http://arxiv.org/abs/0812.3671)

Examples

############################################
############# Generate an example data set
############################################
n=50
p=30
q=30
set.seed(1)

## generate X matrix
X.m<-matrix(rnorm(n*p),n,p)

## generate coefficient
coef.m<-matrix(0,p,q)
hub.n=10
hub.index=sample(1:p, hub.n)
for(i in 1:q){
  cur=sample(1:3,1)
  temp=sample(hub.index, cur)
  coef.m[temp,i]<-runif(length(temp), min=2, max=3)
 }

## generate responses
E.m<-matrix(rnorm(n*q),n,q)
Y.m<-X.m

##############################################
# 1. ## fit model for one pair of (lamL1, lamL2)
##############################################

try1=remMap(X.m, Y.m,lamL1=10, lamL2=5, phi0=NULL, C.m=NULL)

################################################################################################
# 2. ## Select tuning parameters with BIC:
##   ## computationally easy; but the BIC procedure assumes orthogonality of the design matrix
##   ## to estimate the degrees of freedom;
##   ## thus it tends to select too small models when the actual design matrix (X.m) is far
##   ##  from orthogonal
################################################################################################

lamL1.v=exp(seq(log(10),log(20), length=3))
lamL2.v=seq(0,5, length=3)
df.m=remMap.df(X.m, Y.m, lamL1.v, lamL2.v, C.m=NULL)
##  The estimated degrees of freedom can be used to select the ranges of tuning parameters.

try2=remMap.BIC(X.m, Y.m,lamL1.v, lamL2.v, C.m=NULL)
pick=which.min(as.vector(t(try2$BIC)))
result=try2$phi[[pick]]
FP=sum(result$phi!=0 & coef.m==0) ## number of false positives
FN=sum(result$phi==0 & coef.m!=0) ## number of false negatives

#BIC selected tuning parameters
print(paste("lamL1=", round(result$lam1,3), "; lamL2=", round(result$lam2,3), sep=""))
print(paste("FP=", FP, "; FN=", FN, sep=""))

#################################################################################################
# 3. ## Select tuning parameters with v-fold cross-validation;
##   ## computationally demanding;
##   ## but cross-validation assumes less assumptions than BIC and thus is recommended unless
##   ## computation is a concern;
#    ## alos cv based on unshrinked estimator (ols.cv) is recommended over cv based on shrinked
##   ## estimator (rss.cv);
##   ## the latter tends to select too large models.
################################################################################################

lamL1.v=exp(seq(log(10),log(20), length=3))
lamL2.v=seq(0,5, length=3)
try3=remMap.CV(X=X.m, Y=Y.m,lamL1.v, lamL2.v, C.m=NULL, fold=5, seed=1)

############ use CV based on unshrinked estimator (ols.cv)
pick=which.min(as.vector(try3$ols.cv))
#pick=which.min(as.vector(try3$rss.cv))
lamL1.pick=try3$l.index[1,pick]    ##find the optimal (LamL1,LamL2) based on the cv score
lamL2.pick=try3$l.index[2,pick]
##fit the remMap model under the optimal (LamL1,LamL2).
result=remMap(X.m, Y.m,lamL1=lamL1.pick, lamL2=lamL2.pick, phi0=NULL, C.m=NULL)
FP=sum(result$phi!=0 & coef.m==0) ## number of false positives
FN=sum(result$phi==0 & coef.m!=0) ## number of false negatives
##CV (unshrinked) selected tuning parameters
print(paste("lamL1=", round(lamL1.pick,3), "; lamL2=", round(lamL2.pick,3), sep=""))
print(paste("FP=", FP, "; FN=", FN, sep=""))