MSGLasso {MSGLasso} | R Documentation |
A function to fit the Multivariate Sparse Group Lasso with an arbitrary group structure using the mixed coordinate descent algorithm.
MSGLasso(X.m, Y.m, grp.WTs, Pen.L, Pen.G, PQ.grps, GR.grps, grp_Norm0, lam1, lam.G, Beta0 = NULL)
X.m |
numeric predictor matrix (n by p): columns correspond to predictor variables and rows correspond to samples. Missing values are not allowed. |
Y.m |
numeric predictor matrix (n by q): columns correspond to response variables and rows correspond to samples. Missing values are not allowed. |
grp.WTs |
user specified adaptive group weighting matrix of g by r, for putting different penalization levels on different groups. Missing values are not allowed. |
Pen.L |
user specified single-entry level penalization indictor mateix of p by q. 1 for being penalized and 0 for not. Missing values are not allowed. |
Pen.G |
user specified group level penalization indictor mateix of g by r. 1 for being penalized and 0 for not. Missing values are not allowed. |
PQ.grps |
the group attributing matrix of (p+q) by (gmax+1), where gmax is max number of different groups a single variable belongs to. Each row corresponds to a (predictor or response) varaible, and starts with group indexes the variable belongs to and followed by 999. |
GR.grps |
the variable attributing matrix of (g+r)*(cmax+1), where cmax is max number of variables a single group contains. Each row corresponds to a (predictor or response) group, and starts with variable indexes the group contains to and followed by 999. |
grp_Norm0 |
a numeric matrix (g by r) containing starting L2 group norm values. Should be calculated from the Beta starting value matrix Beta0. |
lam1 |
lasso panelty parameter scaler. |
lam.G |
group penalty parameter matrix (g by r). |
Beta0 |
numeric matrix (p by q) containing starting beta values. By defalt use a zero matrix. |
Uses the mixed coordinate descent algorithm for fitting the multivariate sparse group lasso in a multivariate-response-multiple-predictor linear regression setting, with an arbitrary group structure on the regression coefficient matrix (Li, Nan and Zhu 2014).
A list with five components:
Beta |
the estimated regression coefficient matrix (p by q). |
grpNorm |
the L2 group norm matrix (g by r) of the estimated regression coefficient matrix. |
E |
residual matrix (n by q). |
rss.v |
a vector of length q recording the resisual sum square for each of the q responses. |
rss |
a scaler of overall residual sum of square. |
iter |
a positive interger recording the number of iterations till convergence. |
Yanming Li, Bin Nan, Ji Zhu
Y. Li, B. Nan and J. Zhu (2015) Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure. Biometrics. DOI: 10.1111/biom.12292
##################################################### # Simulate data ##################################################### set.seed(sample(1:100,1)) G.arr <- c(0,20,20,20,20,20,20,20,20,20,20) data("Beta.m") ######## generate data set for model fitting simDataGen<-function(N, Beta, rho, s, G.arr, seed=1){ P<-nrow(Beta) Q<-ncol(Beta) gsum<-0 X.m<-NULL set.seed(seed) Sig<-matrix(0,P,P) jstart <-1 for(g in 1:length(G.arr)-1){ X.m<-cbind(X.m, matrix(rnorm(N*G.arr[g+1]),N,G.arr[g+1], byrow=TRUE)) for(i in 2:P){ for(j in jstart: (i-1)){ Sig[i,j]<-rho^(abs(i-j)) Sig[j,i]<-Sig[i,j] }} jstart <- jstart + G.arr[g+1] } diag(Sig)<-1 R<-chol(Sig) X.m<-X.m%*%R SVsum <-0 for (q in 1:Q){SVsum <-SVsum+var(X.m %*% Beta[,q])} sdr =sqrt(s*SVsum/Q) E.m <- matrix(rnorm(N*Q,0,sdr),N, Q, byrow=TRUE) Y.m<-X.m%*%Beta+E.m return(list(X=X.m, Y=Y.m, E=E.m)) } N <-150 rho=0.5; s=4; Data <- simDataGen(N, Beta.m,rho, s, G.arr, seed=sample(1:100,1)) X.m<-Data$X Y.m<-Data$Y ############################################################ ## fit model for one set of (lam1, lam.G) using example data ############################################################ P <- dim(Beta.m)[1] Q <- dim(Beta.m)[2] G <- 10 R <- 10 gmax <- 1 cmax <- 20 GarrStarts <- c(0,20,40,60,80,100,120,140,160,180) GarrEnds <- c(19,39,59,79,99,119,139,159,179,199) RarrStarts <- c(0,20,40,60,80,100,120,140,160,180) RarrEnds <- c(19,39,59,79,99,119,139,159,179,199) tmp <- FindingPQGrps(P, Q, G, R, gmax, GarrStarts, GarrEnds, RarrStarts, RarrEnds) PQgrps <- tmp$PQgrps tmp1 <- Cal_grpWTs(P, Q, G, R, gmax, PQgrps) grpWTs <- tmp1$grpWTs tmp2 <- FindingGRGrps(P, Q, G, R, cmax, GarrStarts, GarrEnds, RarrStarts, RarrEnds) GRgrps <- tmp2$GRgrps Pen_L <- matrix(rep(1,P*Q),P,Q, byrow=TRUE) Pen_G <- matrix(rep(1,G*R),G,R, byrow=TRUE) grp_Norm0 <- matrix(rep(0, G*R), nrow=G, byrow=TRUE) MSGLassolam1 <- 1.6 MSGLassolamG <- 0.26 MSGLassolamG.m <- matrix(rep(MSGLassolamG, G*R),G,R,byrow=TRUE) system.time(try <-MSGLasso(X.m, Y.m, grpWTs, Pen_L, Pen_G, PQgrps, GRgrps, grp_Norm0, MSGLassolam1, MSGLassolamG.m, Beta0=NULL)) ## Not run: ################################################ ## visulizing model fitting results ################################################ ########visulizing selection effect using heatmaps MYplotBW <- function(Beta){ colorNP <- ceiling(abs(max(Beta)))+2 ColorValueP <- colorRampPalette(c("gray50", "black"))(colorNP) colorNN <- ceiling(abs(min(Beta)))+2 ColorValueN <- colorRampPalette(c("gray50", "white"))(colorNN) P <-nrow(Beta) Q <-ncol(Beta) Xlim <- c(0,2*(P+1)) Ylim <- c(0,2*(Q+1)) plot(0, type="n", xlab="", ylab="", xlim=Xlim, ylim=Ylim, cex.lab=1.0, bty="n", axes=FALSE) for (p in 1:P){ for (q in 1:Q){ k0 <- Beta[p,q] if(k0==0){ rect(2*(P-p+1)-1,2*(Q-q+1)-1, 2*(P-p+1)+1, 2*(Q-q+1)+1, col="white", border=NA) } if(k0>0){ k <- ceiling(k0)+1 if(k>2) {k <- k+1} rect(2*(P-p+1)-1,2*(Q-q+1)-1, 2*(P-p+1)+1, 2*(Q-q+1)+1, col="black", border=NA) } if(k0<0){ k <- ceiling(abs(k0))+1 if(k>2) {k <- k+1} rect(2*(P-p+1)-1,2*(Q-q+1)-1, 2*(P-p+1)+1, 2*(Q-q+1)+1, col="black", border=NA) } } } rect(1,1,2*P, 2*Q, lty=2) } MYplotBW(try$Beta) rect(1,1,40,40, lty=2) rect(41,41,80,80, lty=2) rect(81,81,120,120, lty=2) rect(121,121,160,160, lty=2) rect(161,161,200,200, lty=2) rect(201,201,240,240, lty=2) rect(241,241,280,280, lty=2) rect(281,281,320,320, lty=2) rect(361,1,400,400, lty=2) ######## visulizing the true Beta matrix #X11() MYplotBW(Beta.m) rect(1,1,40,40, lty=2) rect(41,41,80,80, lty=2) rect(81,81,120,120, lty=2) rect(121,121,160,160, lty=2) rect(161,161,200,200, lty=2) rect(201,201,240,240, lty=2) rect(241,241,280,280, lty=2) rect(281,281,320,320, lty=2) rect(361,1,400,400, lty=2) ## End(Not run)