Don’t Stop Problem

Last updated: 2019-03-13

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library(susieR)
library(knitr)
library(kableExtra)
R.utils::sourceDirectory("~/Documents/GitHub/susieR/inst/code/susiez_num/")

Data: SuSiE vs DAP: data 31_35 (lower power)

X = readRDS('data/random_data_31.rds')$X
R = cor(X)
data = readRDS('data/random_data_31_sim_gaussian_35.rds')
y = data$Y
beta = data$meta$true_coef
sumstats = readRDS('data/random_data_31_sim_gaussian_35_get_sumstats_1.rds')
zscores = sumstats$sumstats$bhat/sumstats$sumstats$shat

We randomly generated 1200 by 1000 matrix X, each entry is random from N(0,1). The variables are independent. There are 5 signals in the simulated data, total PVE is 0.8. The true signals are 424, 427, 523, 941, 950.

plot(zscores, pch=16, main='z scores')
pos = 1:length(zscores)
points(pos[beta!=0],zscores[beta!=0],col=2,pch=16)

susie_plot(zscores, y = "z", b = beta, main='p values from z scores')

fit_1 = susie_z_general_num(zscores, R, lambda = 1e-6, track_fit = TRUE, verbose = TRUE, max_iter = 100, estimate_prior_method = 'EM')

fit_1 = readRDS('output/random_data_31_35_fit_em.rds')

The algorithm fails to stop.

The objective is -1790.4412135.

susie_plot(fit_1, y='PIP', b=beta)

The estimated prior variance at last 10 iterations are

Vs = matrix(NA, 11, 10)
for(i in 1:10){
  Vs[i,] = fit_1$trace[[90+i]]$V
}
Vs[11,] = fit_1$V
row.names(Vs) = paste0('Iter: ', 91:101)
Vs %>% kable() %>% kable_styling()

Fit model with initial prior variance 50:

fit_2 = susie_z_general_num(zscores, R, lambda = 1e-6, track_fit = TRUE, verbose = TRUE, scaled_prior_variance = 50, estimate_prior_method = 'EM')

[1] "before estimate sigma2 objective:-1816.93777951728"
[1] "after estimate sigma2 objective:-1816.93777951728"
[1] "before estimate sigma2 objective:-1780.84227231863"
[1] "after estimate sigma2 objective:-1780.84227231863"
[1] "before estimate sigma2 objective:-1780.72942172036"
[1] "after estimate sigma2 objective:-1780.72942172036"
[1] "before estimate sigma2 objective:-1780.72794633462"
[1] "after estimate sigma2 objective:-1780.72794633462"
[1] "before estimate sigma2 objective:-1780.72793597231"
[1] "after estimate sigma2 objective:-1780.72793597231"

The algorithm stops. The objective is -1780.727936.

susie_plot(fit_2, y='PIP', b=beta)

The estimated prior variances are

matrix(fit_2$V, 1, 10) %>% kable() %>% kable_styling()

Fit model with initialization at previous one:

fit_3 = susie_z_general_num(zscores, R, lambda = 1e-6, track_fit = TRUE, verbose = TRUE, s_init = fit_2, scaled_prior_variance = fit_2$V)

[1] "before estimate sigma2 objective:-1780.7279359051"
[1] "after estimate sigma2 objective:-1780.7279359051"
[1] "before estimate sigma2 objective:-1780.72793590511"
[1] "after estimate sigma2 objective:-1780.72793590511"

susie_plot(fit_3, y='PIP', b=beta)

Fit model using ‘optim’:

fit_4 = susie_z_general_num(zscores, R, lambda = 1e-6, track_fit = TRUE, verbose = TRUE, estimate_prior_method = 'optim')

[1] "before estimate sigma2 objective:-1786.68857739904"
[1] "after estimate sigma2 objective:-1786.68857739904"
[1] "before estimate sigma2 objective:-1781.50283517316"
[1] "after estimate sigma2 objective:-1781.50283517316"
[1] "before estimate sigma2 objective:-1780.72803928019"
[1] "after estimate sigma2 objective:-1780.72803928019"
[1] "before estimate sigma2 objective:-1780.72793598391"
[1] "after estimate sigma2 objective:-1780.72793598391"

The objective is -1780.727936.

susie_plot(fit_4, y='PIP', b=beta)

The estimated prior variances are

matrix(fit_4$V, 1, 10) %>% kable() %>% kable_styling()

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.3

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] kableExtra_1.0.1  knitr_1.20        susieR_0.7.1.0482

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.0        highr_0.7         compiler_3.5.1   
 [4] pillar_1.3.1      git2r_0.24.0      workflowr_1.1.1  
 [7] R.methodsS3_1.7.1 R.utils_2.7.0     tools_3.5.1      
[10] digest_0.6.18     evaluate_0.12     tibble_2.0.1     
[13] lattice_0.20-38   viridisLite_0.3.0 pkgconfig_2.0.2  
[16] rlang_0.3.1       Matrix_1.2-15     rstudioapi_0.9.0 
[19] yaml_2.2.0        stringr_1.3.1     httr_1.4.0       
[22] xml2_1.2.0        hms_0.4.2         webshot_0.5.1    
[25] rprojroot_1.3-2   grid_3.5.1        glue_1.3.0       
[28] R6_2.3.0          rmarkdown_1.11    readr_1.3.1      
[31] magrittr_1.5      whisker_0.3-2     backports_1.1.3  
[34] scales_1.0.0      htmltools_0.3.6   rvest_0.3.2      
[37] colorspace_1.4-0  stringi_1.2.4     munsell_0.5.0    
[40] crayon_1.3.4      R.oo_1.22.0      

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