data-raw/ridge_linear.R

In Elsa-Yang98/ConformalSmallest: Efficient Tuning-Free Conformal Prediction

#This file explains how we obtained 4 .rData files in the data folder with the prefix ridge_linear_

library(glmnet)
library(MASS)
library(mvtnorm)
source("ridge_funs.R")
name=paste("linear_fm_t3",sep="")


df <- 3  #degrees of freedom
#l <- 60    #number of dimensions
l=2
l.lambda <- 100
lambda_seq <- seq(0,200,l=l.lambda)
dim <- round(seq(5,300,l=l))
alpha <- 0.1
n <- 200   #number of training samples
n0 <- 100  #number of prediction points
nrep <- 100 #number of independent trials
rho <- 0.5

cov.efcp <- len.efcp <- matrix(0,nrep,l)
cov.vfcp <- len.vfcp <- matrix(0,nrep,l)
cov.naive <- len.naive <- matrix(0,nrep,l)
cov.param <- len.param <- matrix(0,nrep,l)
cov.star <- len.star <- matrix(0,nrep,l)
cov.cv10 <- len.cv10 <- matrix(0,nrep,l)
cov.cv5 <- len.cv5 <- matrix(0,nrep,l)
cov.cvloo <- len.cvloo <- matrix(0,nrep,l)


out.efcp.up <- out.efcp.lo <- matrix(0,n0,l)
out.vfcp.up <- out.vfcp.lo <- matrix(0,n0,l)
out.naive.up <- out.naive.lo <- matrix(0,n0,l)
out.param.up <- out.param.lo <- matrix(0,n0,l)
out.star.up <- out.star.lo <- matrix(0,n0,l)
out.cv10.up <- out.cv10.lo <- matrix(0,n0,l)
out.cv5.up <- out.cv5.lo <- matrix(0,n0,l)
out.cvloo.up <- out.cvloo.lo <- matrix(0,n0,l)


for(i in 1:nrep){
  cat(i,"\n")
  for (r in 1:l){
    d <- dim[r]
    set.seed(i)

    Sigma <- matrix(rho,d,d)
    diag(Sigma) <- rep(1,d)
    X <- rmvt(n,Sigma,df)	#multivariate t distribution
    beta <- rep(1:5,d/5)
    eps <- rt(n,df)*(1+sqrt(X[,1]^2+X[,2]^2))
    Y <- X%*%beta+eps


    X0 <- rmvt(n0,Sigma,df)
    eps0 <- rt(n0,df)*(1+sqrt(X0[,1]^2+X0[,2]^2))
    Y0 <- X0%*%beta+eps0


    out.param <- ginverse.fun(X,Y,X0,alpha=alpha)
    out.param.lo[,r] <- out.param$lo
    out.param.up[,r] <- out.param$up
    cov.param[i,r] <- mean(out.param.lo[,r] <= Y0 & Y0 <= out.param.up[,r])
    len.param[i,r] <- mean(out.param.up[,r]-out.param.lo[,r])


    out.efcp <- efcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
    out.efcp.up[,r] <- out.efcp$up
    out.efcp.lo[,r] <- out.efcp$lo
    cov.efcp[i,r] <- mean(out.efcp.lo[,r] <= Y0 & Y0 <= out.efcp.up[,r])
    len.efcp[i,r] <- mean(out.efcp.up[,r]-out.efcp.lo[,r])


    out.vfcp <- vfcp_ridge(X,Y,X0,lambda=lambda_seq,alpha=alpha)
    out.vfcp.up[,r] <- out.vfcp$up
    out.vfcp.lo[,r] <- out.vfcp$lo
    cov.vfcp[i,r] <- mean(out.vfcp.lo[,r] <= Y0 & Y0 <= out.vfcp.up[,r])
    len.vfcp[i,r] <- mean(out.vfcp.up[,r]-out.vfcp.lo[,r])

    out.naive <- naive.fun(X,Y,X0,alpha=alpha)
    out.naive.up[,r] <- out.naive$up
    out.naive.lo[,r] <- out.naive$lo
    cov.naive[i,r] <- mean(out.naive.lo[,r] <= Y0 & Y0 <= out.naive.up[,r])
    len.naive[i,r] <- mean(out.naive.up[,r]-out.naive.lo[,r])


    out.star <- star.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha)
    out.star.up[,r] <- out.star$up
    out.star.lo[,r] <- out.star$lo
    cov.star[i,r] <- mean(out.star.lo[,r] <= Y0 & Y0 <= out.star.up[,r])
    len.star[i,r] <- mean(out.star.up[,r] - out.star.lo[,r])


    out.cv5 <- cv.fun(X,Y,X0,lambda=lambda_seq,alpha=alpha,nfolds=5)
    out.cv5.up[,r] <- out.cv5$up
    out.cv5.lo[,r] <- out.cv5$lo
    cov.cv5[i,r] <- mean(out.cv5.lo[,r] <= Y0 & Y0 <= out.cv5.up[,r])
    len.cv5[i,r] <- mean(out.cv5.up[,r] - out.cv5.lo[,r])

  }
}

df.cov <- data.frame(dim,apply(cov.param,2,mean),apply(cov.naive,2,mean),apply(cov.vfcp,2,mean),apply(cov.star,2,mean),apply(cov.cv5,2,mean), apply(cov.efcp,2,mean))

df.len <- data.frame(dim,apply(len.param,2,mean),apply(len.naive,2,mean),apply(len.vfcp,2,mean),apply(len.star,2,mean),apply(len.cv5,2,mean), apply(len.efcp,2,mean))

save(dim,cov.param, cov.naive, cov.vfcp, cov.star, cov.cv5, cov.efcp, file = "ridge_linear_cov100_t3.RData" )
save(dim,len.param, len.naive, len.vfcp, len.star, len.cv5, len.efcp, file = "ridge_linear_len100_t3.RData" )