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  • Introduction
    • Design setting
    • Signal setting
    • PVE
    • Packages / Libraries
  • Results
  • Source code
  • System Configuration

Last updated: 2019-10-22

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Introduction

The experiment is based on the following simulation setting.

Design setting

We sample the equicorrelated Gaussian measurement XijN(0,Σ) where Σ has diagonal entries 1 and off-diagonal entries ρ.

The we construct XRp with n=500 and p=2000.

Signal setting

We sample the i.i.d. normal coefficients βjN(0,σ2β) for jJ and βj=0 otherwise, where J is a set of randomly s indices in {1,,p}c hosen uniformly at random.

This signal will be called pointnormal. We fix s=20.

PVE

We fix PVE = 0.5.

Packages / Libraries

A list of packages we have loaded is collapsed. Please click “code” to see the list.

library(Matrix); library(ggplot2); library(cowplot); library(susieR); library(BGLR);
library(glmnet); library(mr.ash); library(ncvreg); library(L0Learn); library(varbvs);
standardize = FALSE
source('code/method_wrapper.R')
source('code/sim_wrapper.R')

Results

The result is summarized below.

res_df       = readRDS("results/equicorr.RDS")
method_list  = c("Mr.ASH","VarBVS","BayesB","Blasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn",
                 "Mr.ASH.order","Mr.ASH.init")
method_level = c("Mr.ASH","Mr.ASH.order","Mr.ASH.init","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "VarBVS","BayesB","Blasso","SuSiE")
col          = gg_color_hue(13)[c(1,12,13,2:11)]
rho_list     = c(0.3,0.6,0.9,0.95)
for (i in 1:4) {
res_df[[i+1]]$fit   = rep(method_list, each = 20)
res_df[[i+1]]$fit   = factor(res_df[[i+1]]$fit, levels =  method_level)
}
pp = list()
for (i in 1:4) {
  d       = res_df[[i+1]]
  pp[[i]] = my.box2(d, "fit", "pred", cols = col) +
  theme(axis.line    = element_blank(),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        legend.position = "none") +
  geom_hline(yintercept = mean(d$pred[d$fit == "Mr.ASH.init"]), col = col[3],
             linetype = "dotted", size = 1.5) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.2,1.4,1.6,1.8,2.0)) +
  coord_cartesian(ylim = c(1,1.6))
  subtitle  = ggdraw() + draw_label(paste(paste("rho = ",rho_list[i], sep = ""),"", sep = ""),
                                    fontface  = 'bold', size = 18)
  pp[[i]]   = plot_grid(subtitle, pp[[i]], ncol = 1, rel_heights = c(0.06,0.95))
}
fig_main  = plot_grid(pp[[1]],pp[[2]],pp[[3]],pp[[4]], nrow = 2, rel_widths = c(0.3,0.3,0.3,0.3))
title     = ggdraw() + draw_label("Prediction Error (log-scale)", fontface = 'bold', size = 20) 
subtitle  = ggdraw() + draw_label("Scenario: EquiCorrGauss + SparseNormal, n = 500, p = 2000, pve = 0.5", fontface = 'bold', size = 18)
fig       = plot_grid(title,subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.06,0.95))
fig

Version Author Date
79e1aab Youngseok 2019-10-17

Source code

The source code will be popped up when you click code on the right side.

tdat1        = list()
n            = 500
p            = 2000
s            = 20
rho_list     = c(0.3,0.6,0.9,0.95)
method_list  = c("varbvs","bayesb","blasso","susie","enet","lasso","ridge","scad2","mcp2","l0learn")
method_list2 = c("mr.ash", method_list, "mr.ash.order", "mr.ash.init")
method_num   = length(method_list2)
iter_num     = 20
pred         = matrix(0, iter_num, method_num); colnames(pred) = method_list2
time         = matrix(0, iter_num, method_num); colnames(time) = method_list2


for (iter in 1:4) {
rho        = rho_list[iter]
for (i in 1:20) {
  data          = simulate_data(n, p, s = s, seed = i, signal = "normal", rho = rho,
                                design = "equicorrgauss", pve = 0.5)
 
  for (j in 1:length(method_list)) {
    fit.method    = get(paste("fit.",method_list[j],sep = ""))
    fit           = fit.method(data$X, data$y, data$X.test, data$y.test, seed = i)
    pred[i,j+1]   = fit$rsse / data$sigma / sqrt(n)
    time[i,j+1]   = fit$t
    
    if (method_list[j] == "lasso") {
      lasso.path.order = mr.ash:::path.order(fit$fit$glmnet.fit)
      lasso.beta       = as.vector(coef(fit$fit))[-1]
      lasso.time       = c(fit$t, fit$t2)
    }
  }
 
  fit         = fit.mr.ash(data$X, data$y, data$X.test, data$y.test, seed = i,
                           sa2 = (2^((0:19) / 20) - 1)^2)
  pred[i,1]   = fit$rsse / data$sigma / sqrt(n)
  time[i,1]   = fit$t
  
  fit         = fit.mr.ash2(data$X, data$y, data$X.test, data$y.test, seed = i,
                            update.order = lasso.path.order,
                            sa2 = (2^((0:19) / 5) - 1)^2)
  pred[i,j+2] = fit$rsse / data$sigma / sqrt(n)
  time[i,j+2] = fit$t + lasso.time[2]
  
  fit         = fit.mr.ash2(data$X, data$y, data$X.test, data$y.test, seed = i,
                            beta.init = lasso.beta,
                            sa2 = (2^((0:19) / 5) - 1)^2)
  pred[i,j+3] = fit$rsse / data$sigma / sqrt(n)
  time[i,j+3] = fit$t + lasso.time[1]
  
  print(c(pred[i,]))
}
tdat1[[iter]] = data.frame(pred = c(pred), time = c(time), fit = rep(method_list2, each = 20))
}

System Configuration

Click the below Session Info.


sessionInfo()
R version 3.5.3 (2019-03-11)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.3

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] varbvs_2.6-5  L0Learn_1.1.0 ncvreg_3.11-1 mr.ash_0.1-2  glmnet_2.0-16
 [6] foreach_1.4.4 BGLR_1.0.8    susieR_0.7.1  cowplot_0.9.4 ggplot2_3.2.1
[11] Matrix_1.2-17

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2          RColorBrewer_1.1-2  plyr_1.8.4         
 [4] compiler_3.5.3      pillar_1.3.1        git2r_0.25.2       
 [7] workflowr_1.3.0     iterators_1.0.10    tools_3.5.3        
[10] digest_0.6.18       evaluate_0.13       tibble_2.1.1       
[13] gtable_0.3.0        lattice_0.20-38     pkgconfig_2.0.2    
[16] rlang_0.4.0         yaml_2.2.0          xfun_0.6           
[19] withr_2.1.2         stringr_1.4.0       dplyr_0.8.3        
[22] knitr_1.22          fs_1.3.0            rprojroot_1.3-2    
[25] grid_3.5.3          tidyselect_0.2.5    glue_1.3.1         
[28] R6_2.4.0            rmarkdown_1.12      latticeExtra_0.6-28
[31] reshape2_1.4.3      purrr_0.3.2         magrittr_1.5       
[34] whisker_0.3-2       codetools_0.2-16    backports_1.1.4    
[37] scales_1.0.0        htmltools_0.4.0     assertthat_0.2.1   
[40] colorspace_1.4-1    labeling_0.3        nor1mix_1.2-3      
[43] stringi_1.4.3       lazyeval_0.2.2      munsell_0.5.0      
[46] truncnorm_1.0-8     crayon_1.3.4