Convergence
Fabio Morgante
30 March, 2020
Last updated: 2020-03-30
Checks: 7 0
Knit directory: mr_mash_test/
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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$inputs$GammaThe 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 0.8cat("Sigma")SigmaSigma1 [,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 0.8cat("V")VV1 [,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 25.55836mr.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.
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 |
|---|---|---|
| 40cd0cf | fmorgante | 2020-03-30 |
plot(progress_dat1$iter, progress_dat1$mu1_max.diff, xlab="Iteration", ylab="log Difference in max(mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
| Version | Author | Date |
|---|---|---|
| 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$inputs$GammaThe 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 0.8cat("Sigma")SigmaSigma2 [,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 0.8cat("V")VV2 [,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 29.00472mr.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.
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 |
|---|---|---|
| 40cd0cf | fmorgante | 2020-03-30 |
plot(progress_dat2$iter, progress_dat2$mu1_max.diff, xlab="Iteration", ylab="log Difference in max(mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
| Version | Author | Date |
|---|---|---|
| 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$inputs$GammaThe 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 0.8cat("Sigma")SigmaSigma3 [,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 0.8cat("V")VV3 [,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 13.98625mr.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.
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 |
|---|---|---|
| 40cd0cf | fmorgante | 2020-03-30 |
plot(progress_dat3$iter, progress_dat3$mu1_max.diff, xlab="Iteration", ylab="log Difference in max(mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
| Version | Author | Date |
|---|---|---|
| 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$inputs$GammaThe 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 0.8cat("Sigma")SigmaSigma4 [,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 0.8cat("V")VV4 [,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 15.37456mr.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.
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")
plot(progress_dat4$iter, progress_dat4$mu1_max.diff, xlab="Iteration", ylab="log Difference in max(mu1)", main="mu1 vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
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_1.0.3 digest_0.6.23 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_1.3.1 httpuv_1.4.5 yaml_2.2.0
[21] compiler_3.5.1 htmltools_0.3.6 knitr_1.20