remMap.cv: Fit remMap models for a series of tuning parameters and...
In remMap: Regularized Multivariate Regression for Identifying Master Predictors

Description Usage Arguments Details Value Author(s) References Examples

Fit remMap models for a series of tuning parameters and return the corresponding v-fold cross-validation scores. Two types of cross-validation scores are computed: cv based on unshrinked estimator (ols.cv); and cv based on shrinked estimator (rss.cv); ols.cv is recommended. rss.cv tends to select very large models and thus is not recommended in general (especially for very sparse models). v-fold CV is computationally demanding. But it assumes less assumptions than BIC and thus ols.cv is recommended over BIC unless computation is a concern.

1	remMap.CV(X, Y,lamL1.v, lamL2.v, C.m=NULL, fold=10, seed=1)

`X`	numeric matrix (n by p): columns correspond to predictor variables and rows correspond to samples. Missing values are not allowed.
`Y`	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; 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.
`fold`	positive integer. It specifies the cross validation fold number; default=10.
`seed`	numeric scalar. It specifies the seed of the random number generator in R for generating cross validation subsets; default=1.

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

A list with four components

`ols.cv`	a numeric matrix recording the cross validation scores based on unshrinked OLS estimators for each pair of (lamL1, lamL2).
`rss.cv`	a numeric matrix recording the cross validation scores based on shrinked remMap estimators for each pair of (lamL1, lamL2).
`phi.cv`	a list recording the fitted remMap coefficients on cross validation training subsets. Each component corresponds to one cv fold and it is again a list with each component corresponding to the estimated remMap coefficients for one pair of (lamL1, lamL2) on that training subset.
`l.index`	numeric matrix with two rows: each column is a pair of (lamL1, lamL2) and the kth column corresponds to the kth cv score in as.vector(ols.cv) and as.vector(rss.cv).

Jie Peng, Pei Wang, Ji Zhu

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)

############################################
############# 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=""))