M&M RSS V Problem
Yuxin Zou
02/28/2020
Last updated: 2020-03-01
Checks: 7 0
Knit directory: mmbr-rss-dsc/
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library(mmbr)Loading required package: mashrLoading required package: ashrDSC = dscrutils:::load_inputs(c('data/lite_data_6.rds','data/lite_data_6_shared_1.pkl', 'data/lite_data_6_shared_1_get_sumstats_1.rds', 'data/lite_data_6_shared_1_get_sumstats_1_oracle_generator_1_mnm_rss_shared_16.rds'), dscrutils:::read_dsc)
X = DSC$X
meta = DSC$meta
ss = DSC$sumstats
Z = as.matrix(ss$bhat/ss$shat)
r = cor(X)
prior = DSC$prior
Y = DSC$Y_sim
true_pos = as.integer(apply(meta$true_coef, 1, sum) != 0)where \(X\) is column standardized.
We compute z scores from simple linear regression, which has following distribution \[\begin{align} \hat{Z} &\sim MN(RZ, R, V), \\ V &= diag(sd(Y)) \left(\begin{matrix} 0.0366 & 0 & 0 & 0 & 0 \\ 0 & 0.0337 & 0 & 0 & 0 \\ 0 & 0 & 0.0357 & 0 & 0 \\ 0 & 0 & 0 & 0.0351 & 0 \\ 0 & 0 & 0 & 0 & 0.036 \end{matrix}\right) diag(sd(Y)) \\ &= \left( \begin{matrix} 0.8977 & 0 & 0 & 0 & 0 \\ 0 & 0.896 & 0 & 0 & 0 \\ 0 & 0 & 0.9325 & 0 & 0 \\ 0 & 0 & 0 & 0.867 & 0 \\ 0 & 0 & 0 & 0 & 0.8983 \end{matrix} \right) \end{align}\]Oracle residual variance
resid_Z_oracle <- meta$residual_variance/apply(Y, 2, var)
xUlist = lapply(prior$xUlist, function(U) t(t(U*nrow(Y)/apply(Y, 2, sd))/apply(Y, 2, sd)))
# xUlist = lapply(prior$xUlist, function(U) U*nrow(Y))
m_init = mmbr::create_mash_prior(mixture_prior = list(matrices=xUlist, weights=prior$pi), null_weight=prior$null_weight, max_mixture_len=-1)
fit1 = mmbr::msusie_rss(Z, r, L=1, prior_variance=m_init, residual_variance=resid_Z_oracle, compute_objective=TRUE, estimate_residual_variance=F, estimate_prior_variance=T, estimate_prior_method='simple')Warning in mmbr_core(data, s_init, L, residual_variance, prior_variance, :
precompute_covariances option is set to FALSE by default to save memory
usage with MASH prior. The computation will be a lot slower as a result.
It is recommended that you try setting it to TRUE, see if there is a memory
usage issue and only switch back if it is a problem.susieR::susie_plot(fit1,y='PIP', xlab = 'SNP positions', b=true_pos)
The elbo is
fit1$elbo[1] -4294.582 -4294.582Estimate V from Z
resid_Z_all = cor(Z)
round(resid_Z_all, 4) [,1] [,2] [,3] [,4] [,5]
[1,] 1.0000 0.9738 0.9573 0.9411 0.9764
[2,] 0.9738 1.0000 0.9662 0.9688 0.9807
[3,] 0.9573 0.9662 1.0000 0.9596 0.9723
[4,] 0.9411 0.9688 0.9596 1.0000 0.9642
[5,] 0.9764 0.9807 0.9723 0.9642 1.0000m_init = mmbr::create_mash_prior(mixture_prior = list(matrices=xUlist, weights=prior$pi), null_weight=prior$null_weight, max_mixture_len=-1)
fit2 = mmbr::msusie_rss(Z, r, L=1, prior_variance=m_init, residual_variance=resid_Z_all, compute_objective=TRUE, estimate_residual_variance=F, estimate_prior_variance=T, estimate_prior_method='simple')Warning in mmbr_core(data, s_init, L, residual_variance, prior_variance, :
precompute_covariances option is set to FALSE by default to save memory
usage with MASH prior. The computation will be a lot slower as a result.
It is recommended that you try setting it to TRUE, see if there is a memory
usage issue and only switch back if it is a problem.susieR::susie_plot(fit2,y='PIP', xlab = 'SNP positions', b=true_pos)
The elbo is
fit2$elbo[1] -23882.11 -23882.11Estimate V from null Z
max_absz = apply(abs(Z),1, max)
nullish = which(max_absz < 2) # length 17
nullish_z = Z[nullish,]
resid_Z_null <- cor(nullish_z)
resid_Z_null [,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 -0.1328228 -0.1048471 -0.06969663 0.02477598
[2,] -0.13282278 1.0000000 0.5324289 0.36954405 -0.35653624
[3,] -0.10484711 0.5324289 1.0000000 0.50894988 0.35112068
[4,] -0.06969663 0.3695440 0.5089499 1.00000000 -0.10860863
[5,] 0.02477598 -0.3565362 0.3511207 -0.10860863 1.00000000m_init = mmbr::create_mash_prior(mixture_prior = list(matrices=xUlist, weights=prior$pi), null_weight=prior$null_weight, max_mixture_len=-1)
fit3 = mmbr::msusie_rss(Z, r, L=1, prior_variance=m_init, residual_variance=resid_Z_null, compute_objective=TRUE, estimate_residual_variance=F, estimate_prior_variance=T, estimate_prior_method='simple')Warning in mmbr_core(data, s_init, L, residual_variance, prior_variance, :
precompute_covariances option is set to FALSE by default to save memory
usage with MASH prior. The computation will be a lot slower as a result.
It is recommended that you try setting it to TRUE, see if there is a memory
usage issue and only switch back if it is a problem.susieR::susie_plot(fit3,y='PIP', xlab = 'SNP positions', b=true_pos)
The elbo is
fit3$elbo[1] -2996.669 -2996.669Estimate V as identity
resid_Z_identity = diag(ncol(Z))m_init = mmbr::create_mash_prior(mixture_prior = list(matrices=xUlist, weights=prior$pi), null_weight=prior$null_weight, max_mixture_len=-1)
fit4 = mmbr::msusie_rss(Z, r, L=1, prior_variance=m_init, residual_variance=resid_Z_identity, compute_objective=TRUE, estimate_residual_variance=F, estimate_prior_variance=T, estimate_prior_method='simple')Warning in mmbr_core(data, s_init, L, residual_variance, prior_variance, :
precompute_covariances option is set to FALSE by default to save memory
usage with MASH prior. The computation will be a lot slower as a result.
It is recommended that you try setting it to TRUE, see if there is a memory
usage issue and only switch back if it is a problem.susieR::susie_plot(fit4,y='PIP', xlab = 'SNP positions', b=true_pos)
The elbo is
fit4$elbo[1] -3944.114 -3944.114
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] mmbr_0.0.1.0292 mashr_0.2.21.0651 ashr_2.2-47
loaded via a namespace (and not attached):
[1] Rcpp_1.0.3 susieR_0.9.0.0581 compiler_3.5.1
[4] later_0.7.5 git2r_0.26.1 plyr_1.8.5
[7] workflowr_1.6.0 prettyunits_1.1.1 tools_3.5.1
[10] progress_1.2.2 digest_0.6.25 jsonlite_1.6
[13] evaluate_0.12 lattice_0.20-38 pkgconfig_2.0.3
[16] rlang_0.4.4 Matrix_1.2-15 yaml_2.2.0
[19] mvtnorm_1.0-12 invgamma_1.1 stringr_1.4.0
[22] knitr_1.20 dscrutils_0.4.2 vctrs_0.2.3
[25] hms_0.5.3 fs_1.3.1 rprojroot_1.3-2
[28] grid_3.5.1 reticulate_1.10 data.table_1.12.8
[31] glue_1.3.1 R6_2.4.1 rmarkdown_1.10
[34] mixsqp_0.3-20 irlba_2.3.3 rmeta_3.0
[37] magrittr_1.5 whisker_0.3-2 backports_1.1.5
[40] promises_1.0.1 htmltools_0.3.6 matrixStats_0.55.0
[43] abind_1.4-5 assertthat_0.2.1 httpuv_1.4.5
[46] stringi_1.4.3 truncnorm_1.0-8 SQUAREM_2020.2
[49] crayon_1.3.4