Multivariate Elastic Net Regression

box <- function(x,y,w=0.2,h=0.2,labels="",col="black",turn=FALSE,...){
  xs <- x + 0.5*c(-1,-1,1,1)*w
  ys <- y + 0.5*c(-1,1,1,-1)*h
  graphics::polygon(x=xs,y=ys,border=col,col=grey(ifelse(col=="grey",0.99,0.99)),lwd=2,...)
  graphics::text(x=x,y=y,labels=labels,col=col,srt=ifelse(turn,90,0))
}

#grDevices::pdf(file="manuscript/figure_ABS.pdf",width=4,height=2.5)
grDevices::setEPS()
grDevices::postscript(file="manuscript/figure_ABS.eps",width=4,height=2.5)
graphics::par(mar=c(0,0,0,0))
graphics::plot.new()
graphics::plot.window(xlim=c(0,2),ylim=c(-0.1,1.1))

n <- 0.45; p <- 0.4; q <- 0.4
h <- w <- 0.4

y0 <- 0.10; y1 <- 0.50; y2 <- 0.90
x0 <- 0.20; x1 <- 1.00; x2 <- 1.80
y <- seq(from=1,to=0,length.out=5)

w <- 0.15
d <- seq(from=0.06,to=-0.06,length.out=4)[c(1,2,3,Inf,4)]
for(i in 1:5){
  if(i==4){graphics::text(x=c(x1,x2),y=y[4],labels="...",srt=90,font=2,cex=1.2);next}
  graphics::arrows(x0=x0+p/2,x1=x1-q/2-0.02,y0=y1,y1=y[i],lwd=2,length=0.1,col="grey")
  labels <- paste("target",ifelse(i==5,"q",i))
  for(j in 1:5){
    if(j==4){next}
      graphics::arrows(x0=x1+p/2,x1=x2-q/2-0.02,y0=y[i],y1=y[j]+d[i],lwd=2,length=0.1,col=ifelse(i==j,"grey","grey"))
  }
  box(x=x1,y=y[i],h=0.5*h,w=q,labels=labels)
  box(x=x2,y=y[i],h=0.5*h,w=q,labels=labels)
}
box(x=x0,y=y1,h=0.5*h,w=p,labels="features")

grDevices::dev.off()
#grDevices::pdf(file="manuscript/figure_OUT.pdf",width=5,height=3)
grDevices::postscript(file="manuscript/figure_OUT.eps",width=5,height=3)

ellipse <- function(x,y,text=NULL,a=0.5,b=0.5,border="black",col=NULL,txt.col="black",...){
    n <- max(c(length(x),length(y)))
    if(is.null(col)){col <- rep(grey(0.9),times=n)}
    if(length(col)==1){col <- rep(col,times=n)}
    if(length(x)==1){x <- rep(x,times=n)}
    if(length(y)==1){y <- rep(y,times=n)}
    if(length(text)==1){text <- rep(text,times=n)}
    if(length(border)==1){border <- rep(border,times=n)}
    for(i in seq_len(n)){
        angle <- seq(from=0,to=2*pi,length=100)
        xs <- x[i] + a * cos(angle)
        ys <- y[i] + b * sin(angle)
        graphics::polygon(x=xs,y=ys,col=col[i],border=border[i])
        graphics::text(labels=text[i],x=x[i],y=y[i],col=txt.col,...)
    }
}

txt <- list()
txt$x <- expression(x[j])
txt$y <- eval(parse(text=paste0("expression(",paste0("y[",c(1:3,"k","q"),"]",collapse=","),")")))
txt$beta <- eval(parse(text=paste0("expression(",paste0("beta[j",c(1:3,"k","q"),"]",collapse=","),")")))
txt$omega <- eval(parse(text=paste0("expression(",paste0("omega[\"",c(1:3,"k","q"),"k\"]",collapse=","),")")))
txt$dots <- expression(cdots)

pos <- list()
pos$x <- 4
pos$y <- c(1,2,3,5,7)
pos$beta <- median(pos$x)+(pos$y-median(pos$x))/2
pos$omega <- 5+(pos$y-5)/2

a <- b <- 0.3
graphics::plot.new()
graphics::par(mar=c(0,0,0,0))
graphics::plot.window(xlim=c(0.5,7.5),ylim=c(0.5,5.5))

# beta
segments(x0=4,y0=5-a,x1=pos$y,y1=3+a,lwd=2,col="blue")
ellipse(x=pos$beta,y=4,text=txt$beta,a=0.21,b=0.21,cex=1.2,col="white",border="white",txt.col="blue")

# omega
segments(x0=rep(pos$y,each=4),y0=3-a,x1=rep(pos$y,times=4),y1=1+a,lwd=2,col="grey")
segments(x0=pos$y,y0=3-a,y1=1+a,x1=5,lwd=2,col="red")
ellipse(x=pos$omega,y=2,text=txt$omega,a=0.25,b=0.18,cex=1.2,col="white",border="white",txt.col="red")

# x and y
ellipse(x=pos$x,y=5,text=txt$x,a=a,b=b,cex=1.2)
text(x=c(3,5),y=5,labels=txt$dots,cex=1.2)
ellipse(x=pos$y,y=3,text=txt$y,a=a,b=b,cex=1.2)
text(x=c(4,6),y=3,labels=txt$dots,cex=1.2)
ellipse(x=pos$y,y=1,text=txt$y,a=a,b=b,cex=1.2)
text(x=c(4,6),y=1,labels=txt$dots,cex=1.2)

grDevices::dev.off()

Simulation

#<<start>>

grid <- list()
grid$rho_x <- c(0.00,0.10,0.30)
grid$rho_b <- c(0.00,0.50,0.90)
delta <- 0.8
grid <- expand.grid(grid)
grid <- rbind(grid,grid,grid)
grid$p <- rep(c(10,500,500),each=nrow(grid)/3)
grid$nzero <- rep(c(5,5,100),each=nrow(grid)/3)
grid <- grid[rep(1:nrow(grid),times=10),]

n0 <- 100; n1 <- 10000
n <- n0 + n1
q <- 3
foldid.ext <- rep(c(0,1),times=c(n0,n1))

loss <- list(); cor <- numeric()
for(i in seq_len(nrow(grid))){
  p <- grid$p[i]
  set.seed(i)
  cat("i =",i,"\n")
  
  #--- features ---
  mean <- rep(0,times=p)
  sigma <- matrix(grid$rho_x[i],nrow=p,ncol=p)
  diag(sigma) <- 1
  X <- mvtnorm::rmvnorm(n=n,mean=mean,sigma=sigma)
  
  #--- effects --- (multivariate Gaussian)
  mean <- rep(0,times=q)
  sigma <- matrix(data=grid$rho_b[i],nrow=q,ncol=q)
  diag(sigma) <- 1
  beta <- mvtnorm::rmvnorm(n=p,mean=mean,sigma=sigma)
  beta <- 1*apply(beta,2,function(x) x>(sort(x,decreasing=TRUE)[grid$nzero[i]]))
  
  #-- effects --- (multivariate binomial)
  #sigma <- matrix(grid$rho_b[i],nrow=q,ncol=q); diag(sigma) <- 1
  #beta <- bindata::rmvbin(n=p,margprob=rep(grid$prop[i],times=q),bincorr=sigma)
  
  #--- outcomes ---
  signal <- scale(X%*%beta)
  signal[is.na(signal)] <- 0
  noise <- matrix(rnorm(n*q),nrow=n,ncol=q)
  Y <- sqrt(delta)*signal + sqrt(1-delta)*noise
  # binomial: Y <- round(exp(Y)/(1+exp(Y)))
  cors <- stats::cor(Y)
  diag(cors) <- NA
  cor[i] <- mean(cors,na.rm=TRUE)
  
  #--- holdout ---
  alpha.base <- 1*(grid$nzero[i] <= 10) # sparse vs dense
  compare <- TRUE
  loss[[i]] <- tryCatch(expr=cv.joinet(Y=Y,X=X,family="gaussian",compare=compare,foldid.ext=foldid.ext,alpha.base=alpha.base,alpha.meta=1,times=TRUE),error=function(x) NA)
}
save(grid,loss,cor,file="results/simulation.RData")
writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),sessioninfo::session_info()),con="results/info_sim.txt")
#<<start>>
load("results/simulation.RData")

cond <- lapply(loss,length)==2
if(any(!cond)){
  warning("At least one error.",call.=FALSE)
  grid <- grid[cond,]; loss <- loss[cond]
}

#--- computation time ---
time <- sapply(loss,function(x) unlist(x$time))
#round(sort(colMeans(apply(time,1,function(x) x/time["meta",]))),digits=1)
sort(round(rowMeans(time),digits=1))

#--- average ---
loss <- lapply(loss,function(x) x$loss)
prop <- sapply(loss[cond],function(x) rowMeans(100*x/matrix(x["none",],nrow=nrow(x),ncol=ncol(x),byrow=TRUE))[-nrow(x)])
mode <- ifelse(grid$p==10,"ld",ifelse(grid$nzero==5,"hd-s","hd-d"))
set <- as.numeric(sapply(rownames(grid),function(x) strsplit(x,split="\\.")[[1]][[1]]))

#--- mean rank ---
mult <- rownames(prop)!="base"
sort(round(rowMeans(apply(prop[mult,mode=="ld"],2,rank)),digits=1))
sort(round(rowMeans(apply(prop[mult,mode=="hd-s"],2,rank)),digits=1))
sort(round(rowMeans(apply(prop[mult,mode=="hd-d"],2,rank)),digits=1))

#--- testing ---
apply(prop[mult,],1,function(x) sum(tapply(X=x-prop["base",],INDEX=set,FUN=function(x) wilcox.test(x,alternative="less")$p.value<0.05),na.rm=TRUE))

colSums(tapply(X=prop["meta",]-prop["base",],INDEX=list(set=set,mode=mode),FUN=function(x) wilcox.test(x,alternative="less")$p.value<0.05),na.rm=TRUE)
colSums(tapply(X=prop["spls",]-prop["base",],INDEX=list(set=set,mode=mode),FUN=function(x) wilcox.test(x,alternative="less")$p.value<0.05),na.rm=TRUE)
beta <- sapply(unique(set),function(i) rowMeans(prop[,set==i]))
cor <- sapply(unique(set),function(i) mean(cor[set==i]))

rownames(beta)[rownames(beta)=="mnorm"] <- "mvn"
sign <- apply(beta,2,function(x) sign(x["base"]-x))
#min <- apply(beta,2,function(x) which.min(x)) # incorrect (old)
min <- apply(beta,2,function(x) which(x==min(x))) # correct (new)
beta <- format(round(beta,digits=1),trim=TRUE)
beta[sign<=0] <- paste0("\\textcolor{gray}{",beta[sign<=0],"}")
index <- cbind(min,1:ncol(beta))
beta[index] <- paste0("\\underline{",beta[index],"}")
unique <- unique(grid)
info <- format(round(cbind("$\\rho_x$"=unique$rho_x,"$\\rho_b$"=unique$rho_b,"$\\rho_y$"=cor),digits=1))
temp <- paste0("\\cran{",sapply(rownames(beta),function(x) switch(x,base="glmnet",meta="joinet",mvn="glmnet",mars="earth",spls="spls",mrce="MRCE",map="remMap",mrf="MultivariateRandomForest",sier="SiER",mcen="mcen",gpm="GPM",rmtl="RMTL",mtps="MTPS",NULL)),"}")
temp[1] <- paste0(temp[1],"$^1$")
temp[3] <- paste0(temp[3],"$^2$")
temp[8] <- "\\href{https://CRAN.R-project.org/package=MultivariateRandomForest}{\\texttt{MRF}}$^3$"
rownames(beta) <- paste0("\\begin{sideways}",temp,"\\end{sideways}")
xtable <- xtable::xtable(cbind(info,t(beta)),align=paste0("rccc",paste0(rep("c",times=nrow(beta)),collapse=""),collapse=""),caption="Mean loss of different models (as percentage of empty model) in low-dimensional (top), sparse high-dimensional (centre), and dense high-dimensional (bottom) settings. The first three columns indicate the correlation between inputs ($\\rho_x$), the correlation between effects ($\\rho_b$), and the resulting mean correlation between outputs ($\\rho_y$). For each setting, the colour black indicates which models are more predictive than univariate regression, and the underline indicates the most predictive model. $\\hfill$ \\footnotesize$^1$univariate and $^2$multivariate linear regression with \\cran{glmnet}, $^3$\\cran{MultivariateRandomForest}\\normalsize\\label{table_SIM}")
xtable::print.xtable(xtable,comment=FALSE,floating=TRUE,sanitize.text.function=identity,hline.after=c(0,9,18,ncol(beta)),include.rownames=FALSE,size="\\footnotesize",caption.placement="top")

Application

# clinical features
X <- read.csv("data/PPMI_Baseline_Data_02Jul2018.csv",row.names="PATNO",na.strings=c(".",""))
colnames(X) <- tolower(colnames(X))
X <- X[X$apprdx==1,] # Parkinson's disease
X[c("site","apprdx","event_id","symptom5_comment")] <- NULL
for(i in seq_len(ncol(X))){
  if(is.factor(X[[i]])){levels(X[[i]]) <- paste0("-",levels(X[[i]]))}
}
100*mean(is.na(X)) # proportion missingness
x <- lapply(seq_len(1),function(x) missRanger::missRanger(data=X,pmm.k=3,
        num.trees=100,verbose=0,seed=1))
x <- lapply(x,function(x) model.matrix(~.-1,data=x))

# genomic features
load("data/ppmi_rnaseq_bl_pd_hc-2019-01-11.Rdata",verbose=TRUE)
counts <- t(ppmi_rnaseq_bl_pdhc)
mean(grepl(pattern="ENSG0000|ENSGR0000",x=colnames(counts)))
cond <- apply(counts,2,function(x) sd(x)>0) & !grepl(pattern="ENSG0000|ENSGR0000",x=colnames(counts))
Z <- palasso:::.prepare(counts[,cond],filter=10,cutoff="knee")$X

# outcome
Y <- read.csv("data/PPMI_Year_1-3_Data_02Jul2018.csv",na.strings=".")
Y <- Y[Y$APPRDX==1 & Y$EVENT_ID %in% c("V04","V06","V08"),]
colnames(Y)[colnames(Y)=="updrs_totscore"] <- "updrs"
vars <- c("moca","quip","updrs","gds","scopa","ess","bjlot","rem")
# too few levels: "NP1HALL","NP1DPRS"
Y <- Y[,c("EVENT_ID","PATNO",vars)]
Y <- reshape(Y,idvar="PATNO",timevar="EVENT_ID",direction="wide")
rownames(Y) <- Y$PATNO; Y$PATNO <- NULL

# overlap
names <- Reduce(intersect,list(rownames(X),rownames(Y),rownames(Z)))
Z <- Z[names,]
Y <- Y[names,]
Y <- sapply(vars,function(x) Y[,grepl(pattern=x,x=colnames(Y))],simplify=FALSE)
for(i in seq_along(Y)){
  colnames(Y[[i]]) <- c("V04","V06","V08")
}
x <- lapply(x,function(x) x[names,]); rm(names)
X <- x[[1]]; rm(x) # impute multiple times!

# inversion for positive correlation
Y$moca <- -Y$moca # "wrong" sign
Y$bjlot <- -Y$bjlot # "wrong" sign
sapply(Y,function(x) range(unlist(x),na.rm=TRUE))

save(Y,X,Z,file="results/data.RData")
writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),sessioninfo::session_info()),con="results/info_dat.txt")
load("results/data.RData",verbose=TRUE)

#grDevices::pdf(file="manuscript/figure_COR.pdf",width=6,height=3)
grDevices::postscript(file="manuscript/figure_COR.eps",width=6,height=3)
graphics::par(mar=c(0.5,3,2,0.5))
graphics::layout(mat=matrix(c(1,2),nrow=1,ncol=2),width=c(0.2,0.8))

# correlation between years
cor <- cbind(sapply(Y,function(x) cor(x[,1],x[,2],use="complete.obs",method="spearman")),
sapply(Y,function(x) cor(x[,2],x[,3],use="complete.obs",method="spearman")),
sapply(Y,function(x) cor(x[,1],x[,3],use="complete.obs",method="spearman")))
colnames(cor) <- c("1-2","2-3","1-3")
cor <- rowMeans(cor)
joinet:::plot.matrix(cor,range=c(-3,3),margin=1,cex=0.7)

# correlation between variables
cor <- 1/3*cor(sapply(Y,function(x) x[,1]),use="complete.obs",method="spearman")+
1/3*cor(sapply(Y,function(x) x[,2]),use="complete.obs",method="spearman")+
1/3*cor(sapply(Y,function(x) x[,3]),use="complete.obs",method="spearman")
joinet:::plot.matrix(cor,range=c(-3,3),margin=c(1,2),cex=0.7)
grDevices::dev.off()

# other information
sapply(Y,colMeans,na.rm=TRUE) # increasing values
sapply(Y,function(x) apply(x,2,sd,na.rm=TRUE)) # increasing variance
sapply(Y,function(x) colSums(is.na(x))) # increasing numbers of NAs
#<<start>>

set.seed(1)
load("results/data.RData",verbose=TRUE)

set.seed(1)
foldid.ext <- rep(1:5,length.out=nrow(Y$moca))
foldid.int <- rep(rep(1:10,each=5),length.out=nrow(Y$moca))
table(foldid.ext,foldid.int)

#- - - - - - - - - - - - -
#- - internal coaching - -
#- - - - - - - - - - - - -

table <- list()
table$alpha <- c("lasso","ridge")
table$data <- c("clinic","omics","both")
table$var <- names(Y)
table <- rev(expand.grid(table,stringsAsFactors=FALSE))

loss <- fit <- list()
for(i in seq_len(nrow(table))){
  cat(rep("*",times=5),"setting",i,rep("*",times=5),"\n")
  y <- Y[[table$var[i]]]
  x <- list(clinic=X,omics=Z,both=cbind(X,Z))[[table$data[i]]]
  alpha <- 1*(table$alpha[i]=="lasso")
  loss[[i]] <- cv.joinet(Y=y,X=x,alpha.base=alpha,foldid.ext=foldid.ext,
          foldid.int=foldid.int) # add joinet::
  #fit[[i]] <- joinet(Y=y,X=x,alpha.base=alpha,foldid=foldid.int)
}

save(table,loss,file="results/internal.RData")

#- - - - - - - - - - - - -
#- - external coaching - -
#- - - - - - - - - - - - -

table <- list()
temp <- utils::combn(x=names(Y),m=2)
table$comb <- paste0(temp[1,],"-",temp[2,])
table$step <-  c("V04","V06","V08")
table$alpha <- c("lasso","ridge")
table$data <- c("clinic","omics","both")
table <- rev(expand.grid(table,stringsAsFactors=FALSE))
temp <- strsplit(table$comb,split="-"); table$comb <- NULL
table$var1 <- sapply(temp,function(x) x[[1]])
table$var2 <- sapply(temp,function(x) x[[2]])

loss <- fit <- list()
for(i in seq_len(nrow(table))){
  cat(rep("*",times=5),"setting",i,rep("*",times=5),"\n")
  y <- cbind(Y[[table$var1[i]]][,table$step[i]],
             Y[[table$var2[i]]][,table$step[i]])
  x <- list(clinic=X,omics=Z,both=cbind(X,Z))[[table$data[i]]]
  alpha <- 1*(table$alpha[i]=="lasso")
  loss[[i]] <- cv.joinet(Y=y,X=x,alpha.base=alpha,
                foldid.ext=foldid.ext,foldid.int=foldid.int) # add joinet::
  #fit[[i]] <- joinet(Y=y,X=x,alpha.base=alpha,foldid=foldid.int)
}

save(table,loss,file="results/external.RData")
writeLines(text=capture.output(utils::sessionInfo(),cat("\n"),sessioninfo::session_info()),con="results/info_app.txt")
load("results/internal.RData")

# standardised loss
vars <- unique(table$var)
former <- t(sapply(loss,function(x) x["base",]))
min <- sapply(vars,function(x) min(former[table$var==x,]))
max <- sapply(vars,function(x) max(former[table$var==x,]))
index <- match(x=table$var,table=vars)
former <- (former-min[index])/(max[index]-min[index])
dimnames(former) <- list(table$var,seq_len(3))

# percentage change
change <- t(sapply(loss,function(x) 100*(x["meta",]-x["base",])/x["base",]))
dimnames(change) <- list(table$var,c("1st","2nd","3rd"))

# overview
#grDevices::pdf(file="manuscript/figure_INT.pdf",width=6,height=3,pointsize=12)
grDevices::postscript(file="manuscript/figure_INT.eps",width=6,height=3,pointsize=12)
graphics::par(mfrow=c(2,3),mar=c(0.1,3,2,0.1),oma=c(0,1.1,1,0))
for(alpha in c("lasso","ridge")){
  for(data in c("clinic","omics","both")){
    cond <- table$alpha==alpha & table$data==data
    joinet:::plot.matrix(X=change[cond,],range=c(-50,50),cex=0.7)
    #graphics::title(main=paste0(alpha,"-",data),col.main="red",line=0) # check
    if(alpha=="lasso"){graphics::mtext(text=data,side=3,line=1.5,cex=0.8)}
    if(data=="clinic"){graphics::mtext(text=alpha,side=2,line=3,cex=0.8)}
  }
}
grDevices::dev.off()

TEMP <- tapply(X=rowMeans(change),INDEX=table$var,FUN=mean)[vars]
mean(change<0)
round(tapply(X=rowMeans(change),INDEX=table$data,FUN=mean),digits=2)
round(tapply(X=rowMeans(change),INDEX=table$alpha,FUN=mean),digits=2)
round(colMeans(change),digits=2)
load("results/external.RData")

data <- c("clinic","omics","both")
alpha <- c("lasso","ridge")
step <- c("V04","V06","V08")

# percentage change
change <- t(sapply(loss,function(x) 100*(x["meta",]-x["base",])/x["base",]))

# overview
vars <- unique(c(table$var1,table$var2))
temp <- matrix(NA,nrow=length(vars),ncol=length(vars),dimnames=list(vars,vars))
array <- array(data=list(temp),dim=c(3,2,3),dimnames=list(data,alpha,step))
#grDevices::pdf(file="manuscript/figure_EXT.pdf",width=7.5,height=10,pointsize=14)
grDevices::postscript(file="manuscript/figure_EXT.eps",width=7.5,height=10,pointsize=14)
graphics::par(mfrow=c(6,3),mar=c(0.1,2.5,2.5,0.1),oma=c(0,1,2,0))
for(i in data){
  for(j in alpha){
    for(k in step){
      cond <- table$data==i & table$alpha==j & table$step==k
      array[i,j,k][[1]][cbind(table$var1,table$var2)[cond,]] <- change[cond,1]
      array[i,j,k][[1]][cbind(table$var2,table$var1)[cond,]] <- change[cond,2]
      joinet:::plot.matrix(array[i,j,k][[1]],margin=0,las=2,range=c(-20,20),cex=0.6)
      #graphics::title(main=paste0(i,"-",j,"-",k),col.main="red",line=0) # check
      if(i=="clinic" & j=="lasso"){graphics::mtext(text=ifelse(k=="V04","1st",ifelse(k=="V06","2nd","3rd")),side=3,line=2.5,cex=0.8)}
      if(k=="V04"){graphics::mtext(text=paste0(i,"-",j),side=2,line=2.5,cex=0.8)}
    }
  }
}
grDevices::dev.off()

# check
i <- sample(seq_len(nrow(table)),size=1)
table[i,]
x <- loss[[i]]
100*(x["meta",]-x["base",])/x["base",]
#grDevices::pdf(file="manuscript/figure_ALL.pdf",height=3,width=6)
grDevices::postscript(file="manuscript/figure_ALL.eps",height=3,width=6)

graphics::par(mar=c(0.5,3,2,0.5))
graphics::layout(mat=matrix(c(1,2),nrow=1,ncol=2),width=c(0.2,0.8))
joinet:::plot.matrix(as.matrix(TEMP),margin=1,las=1,range=c(-20,20),cex=0.7)

sum(unlist(array)<0,na.rm=TRUE)/sum(!is.na(unlist(array)))
means <- apply(array,c(1,2,3),function(x) mean(x[[1]],na.rm=TRUE))
lapply(seq_len(3),function(x) apply(means,x,mean))
mean <- 1/length(array)*Reduce(f="+",x=array)
joinet:::plot.matrix(mean,margin=1,las=1,range=c(-20,20),cex=0.7)
# rows: target variable, columns: coaching variable

grDevices::dev.off()
#grDevices::pdf(file="manuscript/figure_DIF.pdf",height=1.2,width=5)
grDevices::postscript(file="manuscript/figure_DIF.eps",height=1.2,width=5)

load("results/internal.RData")
vars <- unique(table$var)
base <- t(sapply(loss,function(x) 100*(x["base",]-x["none",])/x["none",]))
meta <- t(sapply(loss,function(x) 100*(x["meta",]-x["none",])/x["none",]))
dimnames(meta) <- dimnames(base) <- list(table$var,c("1st","2nd","3rd"))
standard <- tapply(X=rowMeans(base),INDEX=table$var,FUN=mean)[vars]
internal <- tapply(X=rowMeans(meta),INDEX=table$var,FUN=mean)[vars]

load("results/external.RData")
vars <- unique(c(table$var1,table$var2))
base <- meta <- list()
for(i in seq_len(2)){
  base[[i]] <- sapply(loss,function(x) 100*(x["base",i]-x["none",i])/x["none",i])
  meta[[i]] <- sapply(loss,function(x) 100*(x["meta",i]-x["none",i])/x["none",i])
}
index <- c(table$var1,table$var2)
base <- unlist(base); meta <- unlist(meta)
#standard <- tapply(X=base,INDEX=index,FUN=mean)[vars]
external <- tapply(X=meta,INDEX=index,FUN=mean)[vars]

matrix <- round(rbind(standard,internal,external),digits=2)
rownames(matrix) <- c("","","")
graphics::par(mfrow=c(1,1),mar=c(0.5,3,1.5,1))
joinet:::plot.matrix(matrix,margin=c(1,2),las=1,range=c(-100,0),cex=0.7,digits=3)

grDevices::dev.off()