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options(stringsAsFactors = FALSE)

Simulation 1 – Shared effects, independent variables

dat1 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag1_sigmascale0.8_gammaoffdiag0_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n1 <- dat1$params$n
p1 <- dat1$params$p
p_causal1 <- dat1$params$p_causal
r1 <- dat1$params$r
k1 <- length(dat1$fit$w0)
pve1 <- dat1$params$pve
prop_testset1 <- dat1$params$prop_testset
progress_dat1 <- dat1$fit$progress
V1 <- dat1$inputs$V
Sigma1 <- dat1$inputs$Sigma
Gamma1 <- dat1$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma1[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("Sigma")
Sigma
Sigma1
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.8  0.8  0.8  0.8
[2,]  0.8  0.8  0.8  0.8  0.8
[3,]  0.8  0.8  0.8  0.8  0.8
[4,]  0.8  0.8  0.8  0.8  0.8
[5,]  0.8  0.8  0.8  0.8  0.8
cat("V")
V
V1
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 25.55836  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 25.55836  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 25.55836  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 25.55836  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 25.55836

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP. The mixture prior consisted of 101 components.

Here, we investigate convergence. Convergence was reached when max(\(mu1_{t}\) - \(mu1_{t-1}\)) was less than 1e-8.

plot(progress_dat1$iter, progress_dat1$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 7 y values <= 0 omitted
from logarithmic plot

Version Author Date
422658e fmorgante 2020-04-16
40cd0cf fmorgante 2020-03-30 
plot(progress_dat1$iter, progress_dat1$mu1_max.diff, xlab="Iteration", ylab="log max(Difference in mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")

Version Author Date
422658e fmorgante 2020-04-16
04f5485 fmorgante 2020-03-30
40cd0cf fmorgante 2020-03-30

Simulation 2 – Independent effects, independent variables

dat2 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag0_sigmascale0.8_gammaoffdiag0_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n2 <- dat2$params$n
p2 <- dat2$params$p
p_causal2 <- dat2$params$p_causal
r2 <- dat2$params$r
k2 <- length(dat2$fit$w0)
pve2 <- dat2$params$pve
prop_testset2 <- dat2$params$prop_testset
progress_dat2 <- dat2$fit$progress
V2 <- dat2$inputs$V
Sigma2 <- dat2$inputs$Sigma
Gamma2 <- dat2$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma2[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("Sigma")
Sigma
Sigma2
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("V")
V
V2
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 39.87305  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 24.41042  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 27.69452  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 25.53166  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 29.00472

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP. The mixture prior consisted of 101 components.

Here, we investigate convergence. Convergence was reached when max(\(mu1_{t}\) - \(mu1_{t-1}\)) was less than 1e-8.

plot(progress_dat2$iter, progress_dat2$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 13 y values <= 0 omitted
from logarithmic plot

Version Author Date
422658e fmorgante 2020-04-16
40cd0cf fmorgante 2020-03-30 
plot(progress_dat2$iter, progress_dat2$mu1_max.diff, xlab="Iteration", ylab="log max(Difference in mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")

Version Author Date
422658e fmorgante 2020-04-16
04f5485 fmorgante 2020-03-30
40cd0cf fmorgante 2020-03-30

Simulation 3 – Shared effects, correlated variables

dat3 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag1_sigmascale0.8_gammaoffdiag0.5_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n3 <- dat3$params$n
p3 <- dat3$params$p
p_causal3 <- dat3$params$p_causal
r3 <- dat3$params$r
k3 <- length(dat3$fit$w0)
pve3 <- dat3$params$pve
prop_testset3 <- dat3$params$prop_testset
progress_dat3 <- dat3$fit$progress
V3 <- dat3$inputs$V
Sigma3 <- dat3$inputs$Sigma
Gamma3 <- dat3$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma3[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.4  0.4  0.4  0.4
[2,]  0.4  0.8  0.4  0.4  0.4
[3,]  0.4  0.4  0.8  0.4  0.4
[4,]  0.4  0.4  0.4  0.8  0.4
[5,]  0.4  0.4  0.4  0.4  0.8
cat("Sigma")
Sigma
Sigma3
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.8  0.8  0.8  0.8
[2,]  0.8  0.8  0.8  0.8  0.8
[3,]  0.8  0.8  0.8  0.8  0.8
[4,]  0.8  0.8  0.8  0.8  0.8
[5,]  0.8  0.8  0.8  0.8  0.8
cat("V")
V
V3
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 13.98626  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 13.98625  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 13.98625  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 13.98625  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 13.98625

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP. The mixture prior consisted of 101 components.

Here, we investigate convergence. Convergence was reached when max(\(mu1_{t}\) - \(mu1_{t-1}\)) was less than 1e-8.

plot(progress_dat3$iter, progress_dat3$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 18 y values <= 0 omitted
from logarithmic plot

Version Author Date
422658e fmorgante 2020-04-16
378e278 fmorgante 2020-03-30
40cd0cf fmorgante 2020-03-30 
plot(progress_dat3$iter, progress_dat3$mu1_max.diff, xlab="Iteration", ylab="log max(Difference in mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")

Version Author Date
422658e fmorgante 2020-04-16
04f5485 fmorgante 2020-03-30
378e278 fmorgante 2020-03-30
40cd0cf fmorgante 2020-03-30

Simulation 4 – Independent effects, correlated variables

dat4 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag0_sigmascale0.8_gammaoffdiag0.5_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n4 <- dat4$params$n
p4 <- dat4$params$p
p_causal4 <- dat4$params$p_causal
r4 <- dat4$params$r
k4 <- length(dat4$fit$w0)
pve4 <- dat4$params$pve
prop_testset4 <- dat4$params$prop_testset
progress_dat4 <- dat4$fit$progress
V4 <- dat4$inputs$V
Sigma4 <- dat4$inputs$Sigma
Gamma4 <- dat4$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma4[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.4  0.4  0.4  0.4
[2,]  0.4  0.8  0.4  0.4  0.4
[3,]  0.4  0.4  0.8  0.4  0.4
[4,]  0.4  0.4  0.4  0.8  0.4
[5,]  0.4  0.4  0.4  0.4  0.8
cat("Sigma")
Sigma
Sigma4
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("V")
V
V4
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 31.75545  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 31.47091  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 14.55202  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 42.12604  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 15.37456

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP. The mixture prior consisted of 101 components.

Here, we investigate convergence. Convergence was reached when max(\(mu1_{t}\) - \(mu1_{t-1}\)) was less than 1e-8.

plot(progress_dat4$iter, progress_dat4$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")

Version Author Date
422658e fmorgante 2020-04-16
378e278 fmorgante 2020-03-30 
plot(progress_dat4$iter, progress_dat4$mu1_max.diff, xlab="Iteration", ylab="log max(Difference in mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")

Version Author Date
422658e fmorgante 2020-04-16
04f5485 fmorgante 2020-03-30
378e278 fmorgante 2020-03-30 

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     

loaded via a namespace (and not attached):
 [1] workflowr_1.6.1 Rcpp_1.0.4.6    digest_0.6.25   later_0.7.5    
 [5] rprojroot_1.3-2 R6_2.4.1        backports_1.1.5 git2r_0.26.1   
 [9] magrittr_1.5    evaluate_0.12   stringi_1.4.3   fs_1.3.1       
[13] promises_1.0.1  whisker_0.3-2   rmarkdown_1.10  tools_3.5.1    
[17] stringr_1.4.0   glue_1.4.0      httpuv_1.4.5    yaml_2.2.1     
[21] compiler_3.5.1  htmltools_0.3.6 knitr_1.20