Last updated: 2020-04-08

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library(ggplot2); library(cowplot);
## function for color
gg_color_hue <- function(n) {
  hues = seq(15, 375, length = n + 1)
  hcl(h = hues, l = 65, c = 100)[1:n]
}

Figure

Varying-n

res_df = readRDS("./results/scenario7.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
df           = data.frame()
n_range      = c(200,500,1000,2000,5000)
for (i in 1:5) {
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_list)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         time2 = apply(matrix(res_df[[i]]$time, 20, 11), 2, median),
                                         time = c(colMeans(matrix(res_df[[i]]$time, 20, 11))),
                                         n    = n_range[i],
                                         fit  = method_list))
}
df$fit = factor(df$fit, levels = method_list)
df = df[df$fit %in% c("Mr.ASH","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn"),]
df$size = 0.5
df$size[1:5] = 1.2
col   = gg_color_hue(13)[1:7]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1,2,6)[1:7]
df$Method = df$fit
p1    = ggplot(df) + geom_line(aes(x = n, y = pred, color = Method), size = df$size) +
  geom_point(aes(x = n, y = pred, color = Method, shape = Method), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = n_range) +
  labs(y = "predictior error (rmse / sigma)", x = "sample size (n)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank()) +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.4))
fig_dummy1 = p1
fig_main  = p1 + theme(legend.position = "none")
#suptitle  = ggdraw() + draw_label("Varying n", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + PointNormal, n = 200-5000, p = 2000, s = 20, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_7     = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
#subtitle   = ggdraw() + draw_label("Varying n (Scenario 7)", fontface  = 'bold', size = 22)  
subtitle  = ggdraw() + draw_label("Varying n", fontface  = 'bold.italic', size = 22) 
fig1_7    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying PVE

res_df = readRDS("./results/scenario8.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
col          = gg_color_hue(13)[1:11]
shape        = c(19,17,24,25,9,3,11,4,5,7,8)
pve_list     = seq(0,0.9,0.1)
sdat         = data.frame()
for (i in 1:10) {
  sdat = rbind(sdat, data.frame(pred = colMeans(matrix(res_df[[i]]$pred, 20, 11)),
                                time = colMeans(matrix(res_df[[i]]$time, 20, 11)),
                                fit  = method_list,
                                pve  = pve_list[i]))
}
sdat$fit = factor(sdat$fit, levels = method_level)
sdat     = sdat[sdat$fit %in% c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn"),]
sdat$size = 0.5
sdat$size[1:10] = 1.2

p1 = ggplot(sdat) + geom_line(aes(x = pve, y = pred, color = fit), size = sdat$size) +
  geom_point(aes(x = pve, y = pred, color = fit, shape = fit), size = 2.5) +
  scale_x_continuous(breaks = pve_list) +
  theme_cowplot(font_size = 22) +
  labs(y = "predictior error (rmse / sigma)", x = "signal strength (PVE)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.35))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying PVE (or SNR, Noise Variance)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + PointNormal, n = 500, p = 2000, s = 20, pve = 0-0.9", fontface  = 'bold', size = 22) 
#fig1_8    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
# subtitle   = ggdraw() + draw_label("Varying PVE / Signal-to-Noise Ratio (Scenario 8)", fontface  = 'bold', size = 22)  
subtitle  = ggdraw() + draw_label("Varying PVE", fontface  = 'bold.italic', size = 22) 
fig1_8    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying h (dense)

res_df = readRDS("./results/scenario9.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
x_range      = 2^(c(1,2,3,4,5,6,7,8) - 1)
df           = data.frame()
for (i in 1:8) {
res_df[[i]]       = res_df[[i]][1:220,]
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_level)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         df   = x_range[i],
                                         fit  = method_list))
}
df = df[df$fit %in% c("Mr.ASH","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn"),]
df$fit = factor(df$fit, levels = method_level)
df$size = 0.5
df$size[1:8] = 1.2
col   = gg_color_hue(13)[1:7]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1)[1:7]
p1    = ggplot(df) + geom_line(aes(x = df, y = pred, color = fit), size = df$size) +
  geom_point(aes(x = df, y = pred, color = fit, shape = fit), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = c(1,2,4,8,16,32,64,128),
                     labels = c("t (df=1)","t (df=2)","t (df=4)","t (df=8)","Laplace",
                                "Normal","Uniform","Constant")) +
  labs(y = "predictior error (rmse / sigma)", x = "signal shape (h)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.5))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying Signal Shape (p = 200, s = 200)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + Spike-and-Slab, n = 500, p = 200, s = 200, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_9    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
# subtitle   = ggdraw() + draw_label("Varying Signal Shape, Dense Signal (Scenario 9)", fontface  = 'bold', size = 22)
subtitle  = ggdraw() + draw_label("Varying h (dense)", fontface  = 'bold.italic', size = 22) 
fig1_9    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying h

res_df = readRDS("./results/scenario10.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
x_range      = 2^(c(1,2,3,4,5,6,7,8) - 1)
df           = data.frame()
for (i in 1:8) {
res_df[[i]]       = res_df[[i]][1:220,]
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_level)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         df   = x_range[i],
                                         fit  = method_list))
}
df = df[df$fit %in% c("Mr.ASH","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn"),]
df$fit = factor(df$fit, levels = method_level)
df$size = 0.5
df$size[1:8] = 1.2
col   = gg_color_hue(13)[1:7]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1)[1:7]
p1    = ggplot(df) + geom_line(aes(x = df, y = pred, color = fit), size = df$size) +
  geom_point(aes(x = df, y = pred, color = fit, shape = fit), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = c(1,2,4,8,16,32,64,128),
                     labels = c("t (df=1)","t (df=2)","t (df=4)","t (df=8)","Laplace",
                                "Normal","Uniform","Constant")) +
  labs(y = "predictior error (rmse / sigma)", x = "signal shape (h)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.4))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying Signal Shape (p = 2000, s = 20)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + Spike-and-Slab, n = 500, p = 2000, s = 20, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_10    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
# subtitle   = ggdraw() + draw_label("Varying Signal Shape, Sparse Signal (Scenario 10)", fontface  = 'bold', size = 22)  
subtitle  = ggdraw() + draw_label("Varying h", fontface  = 'bold.italic', size = 22) 
fig1_10    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying-n

res_df = readRDS("./results/scenario7.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
df           = data.frame()
n_range      = c(200,500,1000,2000,5000)
for (i in 1:5) {
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_list)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         time2 = apply(matrix(res_df[[i]]$time, 20, 11), 2, median),
                                         time = c(colMeans(matrix(res_df[[i]]$time, 20, 11))),
                                         n    = n_range[i],
                                         fit  = method_list))
}
df$fit = factor(df$fit, levels = method_list)
df = df[df$fit %in% c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE"),]
df$size = 0.5
df$size[1:5] = 1.2
col   = gg_color_hue(13)[c(1,8:11)]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1)[c(1,8:11)]
df$Method = df$fit
p1    = ggplot(df) + geom_line(aes(x = n, y = pred, color = Method), size = df$size) +
  geom_point(aes(x = n, y = pred, color = Method, shape = Method), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = n_range) +
  labs(y = "predictior error (rmse / sigma)", x = "sample size (n)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank()) +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.4))
fig_dummy2 = p1
fig_main  = p1 + theme(legend.position = "none")
#suptitle  = ggdraw() + draw_label("Varying n", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + PointNormal, n = 200-5000, p = 2000, s = 20, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_7     = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
subtitle   = ggdraw() + draw_label("Varying n", fontface  = 'bold.italic', size = 22)  
fig2_7    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying PVE

res_df = readRDS("./results/scenario8.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
col          = gg_color_hue(13)[c(1,8:11)]
shape        = c(19,17,24,25,9,3,11,4,5,7,8,1)[c(1,8:11)]
pve_list     = seq(0,0.9,0.1)
sdat         = data.frame()
for (i in 1:10) {
  sdat = rbind(sdat, data.frame(pred = colMeans(matrix(res_df[[i]]$pred, 20, 11)),
                                time = colMeans(matrix(res_df[[i]]$time, 20, 11)),
                                fit  = method_list,
                                pve  = pve_list[i]))
}
sdat$fit = factor(sdat$fit, levels = method_level)
sdat     = sdat[sdat$fit %in% c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE"),]
sdat$size = 0.5
sdat$size[1:10] = 1.2

p1 = ggplot(sdat) + geom_line(aes(x = pve, y = pred, color = fit), size = sdat$size) +
  geom_point(aes(x = pve, y = pred, color = fit, shape = fit), size = 2.5) +
  scale_x_continuous(breaks = pve_list) +
  theme_cowplot(font_size = 22) +
  labs(y = "predictior error (rmse / sigma)", x = "signal strength (PVE)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.35))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying PVE (or SNR, Noise Variance)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + PointNormal, n = 500, p = 2000, s = 20, pve = 0-0.9", fontface  = 'bold', size = 22) 
#fig1_8    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
subtitle   = ggdraw() + draw_label("Varying PVE", fontface  = 'bold.italic', size = 22)  
fig2_8    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying h (dense)

res_df = readRDS("./results/scenario9.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
x_range      = 2^(c(1,2,3,4,5,6,7,8) - 1)
df           = data.frame()
for (i in 1:8) {
res_df[[i]]       = res_df[[i]][1:220,]
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_level)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         df   = x_range[i],
                                         fit  = method_list))
}
df = df[df$fit %in% c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE"),]
df$fit = factor(df$fit, levels = method_level)
df$size = 0.5
df$size[1:8] = 1.2
col   = gg_color_hue(13)[c(1,8:11)]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1)[c(1,8:11)]
p1    = ggplot(df) + geom_line(aes(x = df, y = pred, color = fit), size = df$size) +
  geom_point(aes(x = df, y = pred, color = fit, shape = fit), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = c(1,2,4,8,16,32,64,128),
                     labels = c("t (df=1)","t (df=2)","t (df=4)","t (df=8)","Laplace",
                                "Normal","Uniform","Constant")) +
  labs(y = "predictior error (rmse / sigma)", x = "signal shape (h)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,sqrt(2)))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying Signal Shape (p = 200, s = 200)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + Spike-and-Slab, n = 500, p = 200, s = 200, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_9    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
subtitle   = ggdraw() + draw_label("Varying h (dense)", fontface  = 'bold.italic', size = 22)  
fig2_9    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Varying h

res_df = readRDS("./results/scenario10.RDS")
method_list  = c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE","E-NET","Lasso","Ridge","SCAD","MCP","L0Learn")
method_level = c("Mr.ASH","E-NET","Lasso","Ridge",
                 "SCAD","MCP","L0Learn",
                 "varbvs","BayesB","B-Lasso","SuSiE")
x_range      = 2^(c(1,2,3,4,5,6,7,8) - 1)
df           = data.frame()
for (i in 1:8) {
res_df[[i]]       = res_df[[i]][1:220,]
res_df[[i]]$fit   = rep(method_list, each = 20)
res_df[[i]]$fit   = factor(res_df[[i]]$fit, levels = method_level)
df                = rbind(df, data.frame(pred = c(colMeans(matrix(res_df[[i]]$pred, 20, 11))),
                                         df   = x_range[i],
                                         fit  = method_list))
}
df = df[df$fit %in% c("Mr.ASH","varbvs","BayesB","B-Lasso","SuSiE"),]
df$fit = factor(df$fit, levels = method_level)
df$size = 0.5
df$size[1:8] = 1.2
col   = gg_color_hue(13)[c(1,8:11)]
shape = c(19,17,24,25,9,3,11,4,5,7,8,1)[c(1,8:11)]
p1    = ggplot(df) + geom_line(aes(x = df, y = pred, color = fit), size = df$size) +
  geom_point(aes(x = df, y = pred, color = fit, shape = fit), size = 2.5) +
  theme_cowplot(font_size = 22) +
  scale_x_continuous(trans = "log10", breaks = c(1,2,4,8,16,32,64,128),
                     labels = c("t (df=1)","t (df=2)","t (df=4)","t (df=8)","Laplace",
                                "Normal","Uniform","Constant")) +
  labs(y = "predictior error (rmse / sigma)", x = "signal shape (h)") +
  theme(axis.line = element_blank(),
        plot.title = element_text(hjust = 0.5),
        axis.text.x  = element_text(angle = 45,hjust = 1),
        axis.title.y = element_blank(),
        legend.position = "none") +
  scale_color_manual(values = col) +
  scale_shape_manual(values = shape) +
  scale_y_continuous(trans = "log10", breaks = c(1,1.1,1.2,1.3,1.4)) +
  coord_cartesian(ylim = c(1,1.4))
fig_main = p1
#suptitle  = ggdraw() + draw_label("Varying Signal Shape (p = 2000, s = 20)", fontface  = 'bold', size = 22) 
#subtitle  = ggdraw() + draw_label("Scenario: IndepGauss + Spike-and-Slab, n = 500, p = 2000, s = 20, pve = 0.5", fontface  = 'bold', size = 22) 
#fig1_10    = plot_grid(suptitle, subtitle,fig_main, ncol = 1, rel_heights = c(0.04,0.04,0.95))
subtitle   = ggdraw() + draw_label("Varying h", fontface  = 'bold.italic', size = 22)  
fig2_10    = plot_grid(subtitle, fig_main, ncol = 1, rel_heights = c(0.08,0.92))

Draw Figure

figure4  = plot_grid(fig1_7, fig1_8, fig1_9, fig1_10, ncol = 2, rel_heights = c(0.5,0.53))
legend   <- get_legend(fig_dummy1 +
                         theme_cowplot(font_size = 22) +
                         theme(legend.box.margin = margin(0, 0, 0, 12),
                               legend.key.size = unit(0.8, "cm")))
yaxis    = ggdraw() + draw_label("predictior error (rmse / sigma)", size = 25, angle = 90)
figure4  = plot_grid(plot_grid(plot_grid(yaxis,
                                                figure4, rel_widths = c(0.03,0.97), nrow = 1),
                               ncol = 1, rel_heights = c(0.05,0.95)),
                     legend, nrow = 1, rel_widths = c(0.9,0.1))
ggsave("figure4_for_paper.pdf", figure4, width = 18, height = 15.5)
figure5  = plot_grid(fig2_7, fig2_8, fig2_9, fig2_10, ncol = 2, rel_widths = c(0.5,0.53))
title    = ggdraw() + draw_label("Adaptation to Dimension, Signal Shape and PVE (Penalized Linear Regression)", fontface = 'bold', size = 22)
legend   <- get_legend(fig_dummy2 +
                         theme_cowplot(font_size = 22) +
                         theme(legend.box.margin = margin(0, 0, 0, 12),
                               legend.key.size = unit(0.8, "cm")))
yaxis    = ggdraw() + draw_label("predictior error (rmse / sigma)", size = 25, angle = 90)
figure5  = plot_grid(plot_grid(plot_grid(yaxis,
                                                figure5, rel_widths = c(0.03,0.97), nrow = 1),
                               ncol = 1, rel_heights = c(0.05,0.95)),
                     legend, nrow = 1, rel_widths = c(0.9,0.1))
ggsave("figure5_for_paper.pdf", figure5, width = 18, height = 15.5)
figure45  = plot_grid(figure4, figure5, ncol = 1)
ggsave("figure4and5_for_paper.pdf", figure45, width = 18, height = 24)

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] cowplot_1.0.0 ggplot2_3.2.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.3       compiler_3.5.3   pillar_1.4.3     git2r_0.26.1    
 [5] workflowr_1.4.0  tools_3.5.3      digest_0.6.23    evaluate_0.14   
 [9] lifecycle_0.1.0  tibble_2.1.3     gtable_0.3.0     pkgconfig_2.0.3 
[13] rlang_0.4.2      yaml_2.2.0       xfun_0.9         withr_2.1.2     
[17] stringr_1.4.0    dplyr_0.8.3      knitr_1.25       fs_1.3.1        
[21] rprojroot_1.3-2  grid_3.5.3       tidyselect_0.2.5 glue_1.3.1      
[25] R6_2.4.1         rmarkdown_1.15   purrr_0.3.2      farver_2.0.3    
[29] magrittr_1.5     whisker_0.4      backports_1.1.5  scales_1.1.0    
[33] htmltools_0.3.6  assertthat_0.2.1 colorspace_1.4-1 stringi_1.4.5   
[37] lazyeval_0.2.2   munsell_0.5.0    crayon_1.3.4