Result3_SignalShape

Introduction

Signal setting
PVE
Packages / Libraries

Results

Source code

System Configuration

Last updated: 2019-10-21

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Introduction

Signal setting

We will use the following 6 different signal settings with the same sparsity $s = 20$ .

SparseLaplace: $\beta_j \sim \textrm{Laplace}(1)$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.
SparseT2: $\beta_j \sim \textrm{t}_2$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.
SparseT5: $\beta_j \sim \textrm{t}_5$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.
SparseNormal: $\beta_j \sim N(0,\sigma_\beta^2)$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.
SparseUniform: $\beta_j \sim \textrm{Unif}(0,1)$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.
SparseConstant: $\beta_j = 1$ for $j \in J$ and $\beta_j = 0$ otherwise, where $J$ is a set of randomly $s$ indices in $\{1,\cdots,p\}$ , chosen uniformly at random.

The following is the tail behaviors of the above signal generating probability distributions.

library(ggplot2); library(cowplot)
x = seq(-100,100,0.01)
dat = rbind(data.frame(x = x, y = dexp(abs(x), 1, log = TRUE) / 2, signal = "SparseLaplace"),
            data.frame(x = x, y = dt(x, df = 2, log = TRUE), signal = "SparseT2"),
            data.frame(x = x, y = dt(x, df = 5, log = TRUE), signal = "SparseT5"),
            data.frame(x = x, y = dnorm(x, log = TRUE), signal = "SparseNormal"))
ggplot(dat) + geom_line(aes(x = x, y = y, color = signal)) + 
  coord_cartesian(ylim = c(-50,0)) + theme_cowplot(font_size = 14) +
  theme(axis.line    = element_blank()) +
  labs(x = "x", y = "logpdf(x)")

Version	Author	Date
3bab6f7	Youngseok Kim	2019-10-20
bd36a79	Youngseok	2019-10-14

PVE

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

res_df       = readRDS("results/signalshape_pve0.99.RDS")
method_list  = c("Mr.ASH","VarBVS","BayesB","Blasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "VarBVS","BayesB","Blasso","SuSiE")
col          = gg_color_hue(11)
for (i in 1:6) {
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels =  c("Mr.ASH","E-NET","Lasso","Ridge",
                                            "SCAD","MCP","L0Learn",
                                            "VarBVS","BayesB","Blasso","SuSiE"))
some              = c(1,2,3,5,6,7)
res_df[[i]] = res_df[[i]][res_df[[i]]$fit %in% method_level[some],]
}
pp = list()
signal_name = c("SparseLaplace","SparseT2","SparseT5","SparseNormal","SparseUnif","SparseConst")
for (i in 1:6) {
  d       = res_df[[i]]
  pp[[i]] = my.box(d, "fit", "pred", values = col[some]) +
  theme(axis.line    = element_blank(),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        legend.position = "none") +
  geom_hline(yintercept = median(d$pred[d$fit == "Mr.ASH"]), col = col[1],
             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(0.95,1.8))
  subtitle  = ggdraw() + draw_label(paste(paste("Signal: ",signal_name[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]],pp[[5]],pp[[6]], 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: LowdimIndepGauss, n = 500, p = 2000, s = 20, pve = 0.99", 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
3bab6f7	Youngseok Kim	2019-10-20
bd36a79	Youngseok	2019-10-14

sdat = rbind(res_df[[1]], res_df[[2]], res_df[[3]], res_df[[4]], res_df[[5]], res_df[[6]])
p1       = my.box(res_df[[1]], "fit", "time", values = gg_color_hue(11)[c(1,3,7,6,9,11,2,4,5,8)]) +
  theme(axis.line    = element_blank(),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        legend.position = "none") +
  scale_y_continuous(trans = "log10")
p0        = ggplot() + geom_blank() + theme_cowplot() + theme(axis.line = element_blank())
fig_main  = plot_grid(p0,p1,p0, nrow = 1, rel_widths = c(0.6,0.6,0.6))
title     = ggdraw() + draw_label("Computation time (log-scale)", fontface = 'bold', size = 20) 
subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + SparseSignals, n = 500, p = 2000, s = 20, pve = 0.99", fontface  = 'bold', size = 18) 
fig       = plot_grid(title,subtitle,fig_main, ncol = 1, rel_heights = c(0.1,0.06,0.95))
fig

Version	Author	Date
3bab6f7	Youngseok Kim	2019-10-20
bd36a79	Youngseok	2019-10-14

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
signal_list  = c("lap","t2","t5","normal","unif","const")
method_list  = c("enet","lasso","scad","mcp","l0learn")
method_num   = length(method_list) + 1
iter_num     = 20
pred         = matrix(0, iter_num, method_num); colnames(pred) = c("mr.ash", method_list)
time         = matrix(0, iter_num, method_num); colnames(time) = c("mr.ash", method_list)

for (iter in 1:6) {
for (i in 1:20) {
  data          = simulate_data(n, p, s = s, seed = i, signal = signal_list[iter], pve = 0.99)


 
  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
  }
 
  fit         = fit.mr.ash(data$X, data$y, data$X.test, data$y.test, seed = i,
                           sa2 = (2^((0:19) / 5) - 1)^2)
  pred[i,1]   = fit$rsse / data$sigma / sqrt(n)
  time[i,1]   = fit$t
}
}
tdat1[[iter]] = data.frame(pred = c(pred), time = c(time), fit = rep(c("mr.ash", method_list), each = 20))

# cross validation is fairly accurate
data          = simulate_data(n, p, s = s, seed = 1, signal = signal_list[1], pve = 0.99)
fit1          = fit.scad(data$X, data$y, data$X.test, data$y.test, seed = i)
res1          = c(data$y.test) - predict(fit1$fit, X = data$X.test, lambda = fit1$fit$lambda)
pred1         = sqrt(colMeans(res1^2)) / data$sigma

fit2          = fit.mcp(data$X, data$y, data$X.test, data$y.test, seed = i)
res2          = c(data$y.test) - predict(fit2$fit, X = data$X.test, lambda = fit2$fit$lambda)
pred2         = sqrt(colMeans(res2^2)) / data$sigma

fit3          = fit.enet(data$X, data$y, data$X.test, data$y.test, seed = i)
res3          = c(data$y.test) - predict(fit3$fit, newx = data$X.test, s = fit3$fit$lambda)
pred3         = sqrt(colMeans(res3^2))/ data$sigma

# compare with mr.ash
fit0          = fit.mr.ash(data$X, data$y, data$X.test, data$y.test, seed = i,
                           sa2 = (2^((0:19) / 10) - 1)^2)
pred0         = fit0$rsse / data$sigma / sqrt(n)

## thus mr.ash is better than the best
print(c(mr.ash = pred0,
        scad.best = as.numeric(pred1[which.min(pred1)]),
        scad.cv = as.numeric(pred1[which.min(fit1$fit$cve)]),
        mcp.best = as.numeric(pred2[which.min(pred2)]),
        mcp.cv = as.numeric(pred2[which.min(fit2$fit$cve)]),
        enet.best = as.numeric(pred3[which.min(pred3)]),
        enet.cv = as.numeric(pred3[which.min(fit3$fit$cvm)])))

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 Mojave 10.14

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_2.5-16 L0Learn_1.2.0 ncvreg_3.11-1 mr.ash_0.1-2  glmnet_2.0-18
 [6] foreach_1.4.7 BGLR_1.0.8    susieR_0.8.0  Matrix_1.2-17 cowplot_1.0.0
[11] ggplot2_3.2.1

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_1.4.2        git2r_0.26.1       
 [7] workflowr_1.4.0     iterators_1.0.12    tools_3.5.3        
[10] digest_0.6.21       evaluate_0.14       tibble_2.1.3       
[13] gtable_0.3.0        lattice_0.20-38     pkgconfig_2.0.3    
[16] rlang_0.4.0         yaml_2.2.0          xfun_0.9           
[19] withr_2.1.2         stringr_1.4.0       dplyr_0.8.3        
[22] knitr_1.25          fs_1.3.1            rprojroot_1.3-2    
[25] grid_3.5.3          tidyselect_0.2.5    glue_1.3.1         
[28] R6_2.4.0            rmarkdown_1.15      latticeExtra_0.6-28
[31] reshape2_1.4.3      purrr_0.3.2         magrittr_1.5       
[34] whisker_0.4         codetools_0.2-16    backports_1.1.4    
[37] scales_1.0.0        htmltools_0.3.6     assertthat_0.2.1   
[40] colorspace_1.4-1    labeling_0.3        nor1mix_1.3-0      
[43] stringi_1.4.3       lazyeval_0.2.2      munsell_0.5.0      
[46] truncnorm_1.0-8     crayon_1.3.4