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###Set options
options(stringsAsFactors=FALSE)

###Load libraries
library(dscrutils)
library(ggplot2)
library(cowplot)
library(scales)

###Function to convert dscquery output from list to data.frame suitable for plotting
convert_dsc_to_dataframe <- function(dsc){
  ###Data.frame to store the results after convertion
  dsc_df <- data.frame()
  
  ###Get length of list elements 
  n_elem <- length(dsc$DSC)
  
  ###Loop through the dsc list
  for(i in 1:n_elem){
    ##Prepare vectors making up the final data frame
    r_scalar <- dsc$simulate.r[i]
    repp <- rep(dsc$DSC[i], times=r_scalar)
    n <- rep(dsc$simulate.n[i], times=r_scalar)
    p <- rep(dsc$simulate.p[i], times=r_scalar)
    p_causal <- rep(dsc$simulate.p_causal[i], times=r_scalar)
    r <- rep(dsc$simulate.r[i], times=r_scalar)
    response <- 1:r_scalar
    pve <- rep(dsc$simulate.pve[i], times=r_scalar)
    simulate <- rep(dsc$simulate[i], times=r_scalar)
    fit <- rep(dsc$fit[i], times=r_scalar)
    score <- rep(dsc$score[i], times=r_scalar)
    score.err <- dsc$score.err[[i]]
    timing <- rep(dsc$fit.time[i], times=r_scalar)
    
    ##Build the data frame
    df <- data.frame(rep=repp, n=n, p=p, p_num_caus=p_causal, r=r, response=response, pve=pve,  
                     scenario=simulate, method=fit, score_metric=score, score_value=score.err, time=timing)
    dsc_df <- rbind(dsc_df, df)
  }
  
  return(dsc_df)
}

###Function to compute rmse (relative to mr_mash_consec_em)
compute_rmse <- function(dsc_plot, log10_scale=FALSE){
  dsc_plot <- transform(dsc_plot, experiment=paste(rep, response, scenario, sep="-"))
  t <- 0
  for (i in unique(dsc_plot$experiment)) {
    t <- t+1
    rmse_data  <- dsc_plot[which(dsc_plot$experiment == i & dsc_plot$score_metric=="mse"), ]
    mse_mr_mash_consec_em <- rmse_data[which(rmse_data$method=="mr_mash_consec_em"), "score_value"]
    if(!log10_scale)
      rmse_data$score_value <- rmse_data$score_value/mse_mr_mash_consec_em
    else
      rmse_data$score_value <- log10(rmse_data$score_value/mse_mr_mash_consec_em)
    rmse_data$score_metric <- "rmse"
    if(t>1){
      rmse_data_tot <- rbind(rmse_data_tot, rmse_data)
    } else if(t==1){
      rmse_data_tot <- rmse_data
    }
  }
  
  rmse_data_tot$experiment <- NULL
  
  return(rmse_data_tot)
}

###Function to shift legend in the empty facet
shift_legend <- function(p) {
  library(gtable)
  library(lemon)
  # check if p is a valid object
  if(!(inherits(p, "gtable"))){
    if(inherits(p, "ggplot")){
      gp <- ggplotGrob(p) # convert to grob
    } else {
      message("This is neither a ggplot object nor a grob generated from ggplotGrob. Returning original plot.")
      return(p)
    }
  } else {
    gp <- p
  }
  
  # check for unfilled facet panels
  facet.panels <- grep("^panel", gp[["layout"]][["name"]])
  empty.facet.panels <- sapply(facet.panels, function(i) "zeroGrob" %in% class(gp[["grobs"]][[i]]), 
                               USE.NAMES = F)
  empty.facet.panels <- facet.panels[empty.facet.panels]
  
  if(length(empty.facet.panels) == 0){
    message("There are no unfilled facet panels to shift legend into. Returning original plot.")
    return(p)
  }
  
  # establish name of empty panels
  empty.facet.panels <- gp[["layout"]][empty.facet.panels, ]
  names <- empty.facet.panels$name
  
  # return repositioned legend
  reposition_legend(p, 'center', panel=names)
}

###Set some quantities used in the following plots
colors <- c("skyblue", "dodgerblue", "limegreen", "green", "gold", "orange", "red", "firebrick", "darkmagenta", "mediumpurple")
facet_labels <- c(r2 = "r2", bias = "bias", rmse="MSE (relative to consec_em)")
###Load the dsc results
dsc_out <- dscquery("output/dsc_05_18_20", c("simulate.n", "simulate.p", "simulate.p_causal", "simulate.r",   
                                 "simulate.pve", "simulate.B_cor", "simulate.B_scale",
                                 "simulate.X_cor", "simulate.X_scale",
                                 "simulate.V_cor", "simulate.prop_testset",
                                 "simulate", "fit", "score", "score.err", "fit.time"), 
                    conditions = "$(simulate) == 'indepX_lowcorrV_sharedB' & $(simulate.p_causal) == 50", verbose=FALSE,
                    ignore.missing.files = TRUE )

###Obtain simulation parameters
n <- unique(dsc_out$simulate.n)
p <- unique(dsc_out$simulate.p)
p_causal <- unique(dsc_out$simulate.p_causal)
r <- unique(dsc_out$simulate.r)
k <- 166
pve <- unique(dsc_out$simulate.pve)
prop_testset <- unique(dsc_out$simulate.prop_testset)
B_cor <- unique(dsc_out$simulate.B_cor)
B_scale <- unique(dsc_out$simulate.B_scale)
X_cor <- unique(dsc_out$simulate.X_cor)
X_scale <- unique(dsc_out$simulate.X_scale)
V_cor <- unique(dsc_out$simulate.V_cor)

###Remove list elements that are not useful anymore
dsc_out$simulate.prop_testset <- NULL
dsc_out$simulate.B_cor <- NULL
dsc_out$simulate.B_scale <- NULL
dsc_out$simulate.X_cor <- NULL
dsc_out$simulate.X_scale <- NULL
dsc_out$simulate.V_cor <- NULL

50 causal variables

Standard vs DAAREM

The results below are based on 20 simulations with 600 samples, 1000 variables of which 50 were causal, 10 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), where Gamma is such that it achieves a correlation between variables of 0 and a scale of 0.8. Causal effects, B, were drawn from MVN(0, Sigma), where Sigma is such that it achieves a correlation between responses of 1 and a scale of 0.8. The responses, Y, were drawn from MN(XB, I, V), where V is such that it achieves a correlation between responses of 0.15 and a scale defined py PVE.

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using EM updates. We investigate a few combinations of orderings of the coordinate ascent updates (i.e., consecutive and decreasing logBF from a multivariate simple linear regression with MASH prior), and initialization of the posterior means of the regression coefficients (i.e., 0, from mr.ash assuming shared effects across tissues, from two passes of mr.ash – first assuming shared effects across tissues, then using the estimated coefficients as initial values assuming independent effects across tissues –, the true coefficients). The mixture prior consisted of 166 components defined by a few canonical matrices correpsonding to different settings of effect sharing/specificity (i.e., zero, singletons, independent, low heterogeneity, medium heterogeneity, high heterogeneity, shared) scaled by a grid of values (i.e., from 0.1 to 2.1 in steps of 0.2). The same grid was used in mr.ash with the addition of 0. Convergence was declared when the maximum difference in the posterior mean of the regression coefficients between two successive iterations was smaller than 1e-4. Standard mr.mash is compared to an accelerated version that uses DAAREM.

Then, responses were predicted on the test data (20% of the data).

Here, we evaluate the accuracy of prediction assessed by \(r^2\) and bias (slope) from the regression of the true response on the predicted response, and the relative mean square error (rMSE) in the test data. The boxplots are across simulations and responses.

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rmse_dat <- compute_rmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="mse" & dsc_plots$method %in% c("mr_mash_consec_em", "mr_mash_declogBF_em", 
                                                          "mr_mash_consec_em_init_shared", "mr_mash_consec_em_init_2pass",
                                                          "mr_mash_consec_em_init_trueB",
                                                          "mr_mash_consec_em_daarem", "mr_mash_declogBF_em_daarem", 
                                                          "mr_mash_consec_em_daarem_init_shared", "mr_mash_consec_em_daarem_init_2pass",
                                                          "mr_mash_consec_em_daarem_init_trueB")), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_consec_em", "mr_mash_declogBF_em", 
                                                          "mr_mash_consec_em_init_shared", "mr_mash_consec_em_init_2pass",
                                                          "mr_mash_consec_em_init_trueB",
                                                          "mr_mash_consec_em_daarem", "mr_mash_declogBF_em_daarem", 
                                                          "mr_mash_consec_em_daarem_init_shared", "mr_mash_consec_em_daarem_init_2pass",
                                                          "mr_mash_consec_em_daarem_init_trueB"),
                                                labels=c("consec_em", "decrease_logBF_em", "consec_em_mrash_shared", 
                                                         "consec_em_init_2pass", "consec_em_init_trueB",
                                                         "consec_em_daarem", "decrease_logBF_em_daarem", "consec_em_daarem_mrash_shared",
                                                         "consec_em_daarem_init_2pass", "consec_em_daarem_init_trueB"))

###Build data.frame with best accuracy achievable
hlines <- data.frame(score_metric=c("r2", "bias"), max_val=c(unique(dsc_plots$pve), 1))

###Create plots
p <- ggplot(dsc_plots, aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
    geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
    facet_wrap(vars(score_metric), scales="free_y", ncol=2, labeller=labeller(score_metric=facet_labels)) +
    scale_fill_manual(values = colors) +
    labs(x = "", y = "Accuracy/Error", title = "Prediction performance", fill="Method") +
    geom_hline(data=hlines, aes(yintercept = max_val), linetype="dashed", size=1) +
    theme_cowplot(font_size = 20) +
    theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
          plot.title = element_text(hjust = 0.5))

shift_legend(p)

Version Author Date
4263395 fmorgante 2020-05-20

Let’s now remove outliers from the rMSE plot to make things a little clearer.

p_rmse_nooutliers <- ggplot(dsc_plots[which(dsc_plots$score_metric=="rmse"), ], aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black", outlier.size = 1, width = 0.85, width.errorbar = 0) +
  scale_fill_manual(values = colors) +
  labs(x = "", y = "Relative error", title = "rMSE (relative to consec_em)", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_rmse_nooutliers)

Version Author Date
4263395 fmorgante 2020-05-20

Here, we look at the elapsed time (\(log_{10}\) seconds) of mr.mash. Note that this time does not include the run time of mr.ash in the cases where we used it to initialize the posterior means of the regression coefficients.

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="r2"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log10", breaks = trans_breaks("log10", function(x) 10^x),
                      labels = trans_format("log10", math_format(10^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log10 scale",title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
4263395 fmorgante 2020-05-20

mr.mash vs other methods

Here, we compare mr.mash to the multivariate versions of LASSO, Elastic Net (\(\alpha = 0.5\)), and Ridge Regression as implemented in glmnet. The form of the penalty id the following: \(\lambda[(1-\alpha)/2 ||\mathbf{\beta}_j||^2_2 + \alpha ||\mathbf{\beta}_j||_2]\). \(\lambda\) is chosen by cross-validation in the training set.

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rmse_dat <- compute_rmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="mse" & dsc_plots$method %in% c("mr_mash_consec_em", "mr_mash_consec_em_init_mlasso",
                                                          "mr_mash_consec_em_init_trueB", "mlasso", "menet", "mridge")), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_consec_em", "mr_mash_consec_em_init_mlasso",
                                                          "mr_mash_consec_em_init_trueB", "mlasso", "menet", "mridge"),
                                                labels=c("consec_em", "consec_em_init_mlasso", "consec_em_init_trueB",
                                                         "mlasso", "menet", "mridge"))

###Build data.frame with best accuracy achievable
hlines <- data.frame(score_metric=c("r2", "bias"), max_val=c(unique(dsc_plots$pve), 1))

###Create plots
p <- ggplot(dsc_plots, aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
    geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
    facet_wrap(vars(score_metric), scales="free_y", ncol=2, labeller=labeller(score_metric=facet_labels)) +
    scale_fill_manual(values = colors) +
    labs(x = "", y = "Accuracy/Error", title = "Prediction performance", fill="Method") +
    geom_hline(data=hlines, aes(yintercept = max_val), linetype="dashed", size=1) +
    theme_cowplot(font_size = 20) +
    theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
          plot.title = element_text(hjust = 0.5))

shift_legend(p)

Version Author Date
9f85985 fmorgante 2020-05-25

Let’s now remove outliers from the rMSE plot to make things a little clearer.

p_rmse_nooutliers <- ggplot(dsc_plots[which(dsc_plots$score_metric=="rmse"), ], aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black", outlier.size = 1, width = 0.85, width.errorbar = 0) +
  scale_fill_manual(values = colors) +
  labs(x = "", y = "Relative error", title = "rMSE (relative to consec_em)", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_rmse_nooutliers)

Version Author Date
9f85985 fmorgante 2020-05-25

Here, we look at the elapsed time (\(log_{10}\) seconds) of mr.mash. Note that this time does not include the run time of glmnet in the cases where we used it to initialize the posterior means of the regression coefficients.

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="r2"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log10", breaks = trans_breaks("log10", function(x) 10^x),
                      labels = trans_format("log10", math_format(10^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log10 scale",title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
9f85985 fmorgante 2020-05-25 
###Load the dsc results
dsc_out <- dscquery("output/dsc_05_18_20", c("simulate.n", "simulate.p", "simulate.p_causal", "simulate.r",   
                                 "simulate.pve", "simulate.B_cor", "simulate.B_scale",
                                 "simulate.X_cor", "simulate.X_scale",
                                 "simulate.V_cor", "simulate.prop_testset",
                                 "simulate", "fit", "score", "score.err", "fit.time"), 
                    conditions = "$(simulate) == 'indepX_lowcorrV_sharedB' & $(simulate.p_causal) == 500", verbose=FALSE,
                    ignore.missing.files = TRUE )

###Obtain simulation parameters
n <- unique(dsc_out$simulate.n)
p <- unique(dsc_out$simulate.p)
p_causal <- unique(dsc_out$simulate.p_causal)
r <- unique(dsc_out$simulate.r)
k <- 166
pve <- unique(dsc_out$simulate.pve)
prop_testset <- unique(dsc_out$simulate.prop_testset)
B_cor <- unique(dsc_out$simulate.B_cor)
B_scale <- unique(dsc_out$simulate.B_scale)
X_cor <- unique(dsc_out$simulate.X_cor)
X_scale <- unique(dsc_out$simulate.X_scale)
V_cor <- unique(dsc_out$simulate.V_cor)

###Remove list elements that are not useful anymore
dsc_out$simulate.prop_testset <- NULL
dsc_out$simulate.B_cor <- NULL
dsc_out$simulate.B_scale <- NULL
dsc_out$simulate.X_cor <- NULL
dsc_out$simulate.X_scale <- NULL
dsc_out$simulate.V_cor <- NULL

500 causal variables

The results below are based on the same simulation/analysis scheme as above but with 500 causal variables.

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rmse_dat <- compute_rmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="mse" & dsc_plots$method %in% c("mr_mash_consec_em", "mr_mash_declogBF_em", 
                                                          "mr_mash_consec_em_init_shared", "mr_mash_consec_em_init_2pass",
                                                          "mr_mash_consec_em_init_trueB",
                                                          "mr_mash_consec_em_daarem", "mr_mash_declogBF_em_daarem", 
                                                          "mr_mash_consec_em_daarem_init_shared", "mr_mash_consec_em_daarem_init_2pass",
                                                          "mr_mash_consec_em_daarem_init_trueB")), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_consec_em", "mr_mash_declogBF_em", 
                                                          "mr_mash_consec_em_init_shared", "mr_mash_consec_em_init_2pass",
                                                          "mr_mash_consec_em_init_trueB",
                                                          "mr_mash_consec_em_daarem", "mr_mash_declogBF_em_daarem", 
                                                          "mr_mash_consec_em_daarem_init_shared", "mr_mash_consec_em_daarem_init_2pass",
                                                          "mr_mash_consec_em_daarem_init_trueB"),
                                                labels=c("consec_em", "decrease_logBF_em", "consec_em_mrash_shared", 
                                                         "consec_em_init_2pass", "consec_em_init_trueB",
                                                         "consec_em_daarem", "decrease_logBF_em_daarem", "consec_em_daarem_mrash_shared",
                                                         "consec_em_daarem_init_2pass", "consec_em_daarem_init_trueB"))

###Build data.frame with best accuracy achievable
hlines <- data.frame(score_metric=c("r2", "bias"), max_val=c(unique(dsc_plots$pve), 1))

###Create plots
p <- ggplot(dsc_plots, aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
    geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
    facet_wrap(vars(score_metric), scales="free_y", ncol=2, labeller=labeller(score_metric=facet_labels)) +
    scale_fill_manual(values = colors) +
    labs(x = "", y = "Accuracy/Error", title = "Prediction performance", fill="Method") +
    geom_hline(data=hlines, aes(yintercept = max_val), linetype="dashed", size=1) +
    theme_cowplot(font_size = 20) +
    theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
          plot.title = element_text(hjust = 0.5))

shift_legend(p)

Version Author Date
4263395 fmorgante 2020-05-20

Let’s now remove outliers from the rMSE plot to make things a little clearer.

p_rmse_nooutliers <- ggplot(dsc_plots[which(dsc_plots$score_metric=="rmse"), ], aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black", outlier.size = 1, width = 0.85, width.errorbar = 0) +
  scale_fill_manual(values = colors) +
  labs(x = "", y = "Relative error", title = "rMSE (relative to consec_em)", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_rmse_nooutliers)

Version Author Date
4263395 fmorgante 2020-05-20

Here, we look at the elapsed time (\(log_{10}\) seconds) of mr.mash. Note that this time does not include the run time of mr.ash in the cases where we used it to initialize the posterior means of the regression coefficients.

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="r2"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log10", breaks = trans_breaks("log10", function(x) 10^x),
                      labels = trans_format("log10", math_format(10^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log10 scale",title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
4263395 fmorgante 2020-05-20

mr.mash vs other methods

Here, we compare mr.mash to the multivariate versions of LASSO, Elastic Net (\(\alpha = 0.5\)), and Ridge Regression as implemented in glmnet. The form of the penalty id the following: \(\lambda[(1-\alpha)/2 ||\mathbf{\beta}_j||^2_2 + \alpha ||\mathbf{\beta}_j||_2]\). \(\lambda\) is chosen by cross-validation in the training set.

###Convert from list to data.frame for plotting
dsc_plots <- convert_dsc_to_dataframe(dsc_out)

###Compute rmse score (relative to mr_mash_consec_em) and add it to the data
rmse_dat <- compute_rmse(dsc_plots)
dsc_plots <- rbind(dsc_plots, rmse_dat)

###Remove mse from scores and keep only methods wanted
dsc_plots <- dsc_plots[which(dsc_plots$score_metric!="mse" & dsc_plots$method %in% c("mr_mash_consec_em", "mr_mash_consec_em_init_mlasso",
                                                          "mr_mash_consec_em_init_trueB", "mlasso", "menet", "mridge")), ]

###Create factor version of method
dsc_plots$method_fac <- factor(dsc_plots$method, levels=c("mr_mash_consec_em", "mr_mash_consec_em_init_mlasso",
                                                          "mr_mash_consec_em_init_trueB", "mlasso", "menet", "mridge"),
                                                labels=c("consec_em", "consec_em_init_mlasso", "consec_em_init_trueB",
                                                         "mlasso", "menet", "mridge"))

###Build data.frame with best accuracy achievable
hlines <- data.frame(score_metric=c("r2", "bias"), max_val=c(unique(dsc_plots$pve), 1))

###Create plots
p <- ggplot(dsc_plots, aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
    geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
    facet_wrap(vars(score_metric), scales="free_y", ncol=2, labeller=labeller(score_metric=facet_labels)) +
    scale_fill_manual(values = colors) +
    labs(x = "", y = "Accuracy/Error", title = "Prediction performance", fill="Method") +
    geom_hline(data=hlines, aes(yintercept = max_val), linetype="dashed", size=1) +
    theme_cowplot(font_size = 20) +
    theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
          plot.title = element_text(hjust = 0.5))

shift_legend(p)

Version Author Date
9f85985 fmorgante 2020-05-25

Let’s now remove outliers from the rMSE plot to make things a little clearer.

p_rmse_nooutliers <- ggplot(dsc_plots[which(dsc_plots$score_metric=="rmse"), ], aes_string(x = "method_fac", y = "score_value", fill = "method_fac")) +
  Ipaper::geom_boxplot2(color = "black", outlier.size = 1, width = 0.85, width.errorbar = 0) +
  scale_fill_manual(values = colors) +
  labs(x = "", y = "Relative error", title = "rMSE (relative to consec_em)", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_rmse_nooutliers)

Version Author Date
9f85985 fmorgante 2020-05-25

Here, we look at the elapsed time (\(log_{10}\) seconds) of mr.mash. Note that this time does not include the run time of glmnet in the cases where we used it to initialize the posterior means of the regression coefficients.

dsc_plots_time <- dsc_plots[which(dsc_plots$response==1 & dsc_plots$score_metric=="r2"), 
                          -which(colnames(dsc_plots) %in% c("score_metric", "score_value", "response"))]

p_time <- ggplot(dsc_plots_time, aes_string(x = "method_fac", y = "time", fill = "method_fac")) +
  geom_boxplot(color = "black", outlier.size = 1, width = 0.85) +
  scale_fill_manual(values = colors) +
  scale_y_continuous(trans="log10", breaks = trans_breaks("log10", function(x) 10^x),
                      labels = trans_format("log10", math_format(10^.x))) +
  labs(x = "", y = "Elapsed time (seconds) in log10 scale",title = "Run time", fill="Method") +
  theme_cowplot(font_size = 20) +
  theme(axis.line.x = element_blank(), axis.text.x = element_blank(), axis.ticks.x = element_blank(),
        plot.title = element_text(hjust = 0.5))

print(p_time)

Version Author Date
9f85985 fmorgante 2020-05-25 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
[1] devtools_2.1.0  usethis_1.5.1   magrittr_1.5    lemon_0.4.3    
[5] gtable_0.3.0    scales_1.1.0    cowplot_1.0.0   ggplot2_3.2.0  
[9] dscrutils_0.4.2

loaded via a namespace (and not attached):
 [1] pkgload_1.0.2      jsonlite_1.6       foreach_1.4.4     
 [4] Ipaper_0.1.5       assertthat_0.2.1   sp_1.3-1          
 [7] cellranger_1.1.0   yaml_2.2.1         remotes_2.1.0     
[10] progress_1.2.2     sessioninfo_1.1.1  pillar_1.4.1      
[13] backports_1.1.5    lattice_0.20-38    glue_1.4.0        
[16] digest_0.6.25      RColorBrewer_1.1-2 promises_1.0.1    
[19] colorspace_1.4-1   htmltools_0.3.6    httpuv_1.4.5      
[22] plyr_1.8.5         clipr_0.4.1        pkgconfig_2.0.3   
[25] purrr_0.3.3        processx_3.4.0     whisker_0.3-2     
[28] openxlsx_4.1.0     later_0.7.5        git2r_0.26.1      
[31] tibble_2.1.3       farver_2.0.3       withr_2.1.2       
[34] repr_0.17          lazyeval_0.2.2     cli_1.1.0         
[37] crayon_1.3.4       readxl_1.1.0       memoise_1.1.0     
[40] evaluate_0.12      ps_1.2.1           fs_1.3.1          
[43] doParallel_1.0.14  xml2_1.2.0         pkgbuild_1.0.3    
[46] tools_3.5.1        data.table_1.12.8  prettyunits_1.1.1 
[49] hms_0.5.3          matrixStats_0.55.0 lifecycle_0.2.0   
[52] stringr_1.4.0      munsell_0.5.0      zip_1.0.0         
[55] callr_3.3.2        compiler_3.5.1     rlang_0.4.5       
[58] grid_3.5.1         rstudioapi_0.10    iterators_1.0.10  
[61] base64enc_0.1-3    labeling_0.3       rmarkdown_1.10    
[64] boot_1.3-20        testthat_2.1.1     codetools_0.2-15  
[67] reshape2_1.4.3     R6_2.4.1           lubridate_1.7.4   
[70] gridExtra_2.3      knitr_1.20         dplyr_0.8.0.1     
[73] workflowr_1.6.1    rprojroot_1.3-2    desc_1.2.0        
[76] stringi_1.4.3      parallel_3.5.1     IRdisplay_0.6.1   
[79] Rcpp_1.0.4.6       vctrs_0.2.4        tidyselect_0.2.5