Last updated: 2018-07-16

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    Rmd e11ca44 Jason Willwerscheid 2018-07-16 wflow_publish(“analysis/objective3.Rmd”)

Introduction

Here I look into the bad loadings updates some more.

First I load the flash object from just before the “bad” update discussed in the first investigation. Next, I alternately update the precision and the loadings (I do not update the factors). I do so for 20 iterations.

load("data/before_bad.Rdata")

init_fl <- res2$f
data <- flash_set_data(strong)
k <- 4

fl = init_fl
all_fls = list()
niters = 20
for (i in 1:niters) {
  # update precision
  R2 = flashr:::flash_get_R2(data, fl)
  fl$tau = flashr:::compute_precision(R2, data$missing,
                                      "by_column", data$S)
  # update loadings
  s2 = 1/(fl$EF2[, k] %*% t(fl$tau))
  s = sqrt(s2)
  Rk = flashr:::flash_get_Rk(data, fl, k)
  x = fl$EF[, k] %*% t(Rk * fl$tau) * s2
  ebnm_l = flashr:::ebnm_pn(x, s, list())
  KL_l = (ebnm_l$penloglik
          - flashr:::NM_posterior_e_loglik(x, s, ebnm_l$postmean,
                                           ebnm_l$postmean2))
  fl$EL[, k] = ebnm_l$postmean
  fl$EL2[, k] = ebnm_l$postmean2
  fl$gl[[k]] = ebnm_l$fitted_g
  fl$KL_l[[k]] = KL_l

  all_fls[[i]] = fl
}

Objective

Interestingly, the objective function gets worse every iteration. Nonetheless, it is apparently converging to something.

for (i in 1:niters) {
  message(flash_get_objective(data, all_fls[[i]])
          - flash_get_objective(data, init_fl))
}
-0.115442661102861
-0.215697337407619
-0.294866794254631
-0.35520419664681
-0.400229783495888
-0.43337183073163
-0.457542995689437
-0.475060580996796
-0.487700638826936
-0.496793346246704
-0.503320154268295
-0.507998006418347
-0.511347066378221
-0.51374295167625
-0.51545600919053
-0.516680368920788
-0.517555203288794
-0.518180169630796
-0.518626571865752
-0.518945396877825

Convergence of prior

To confirm that convergence is taking place, I check the estimated prior \(g_l\) after each iteration (the first list gives the values of \(\pi_0\); the second, the values of \(a\)):

for (i in 1:niters) {
  message(all_fls[[i]]$gl[[4]]$pi0)
}
0.725369968917067
0.725667291395093
0.725879906389941
0.726031747043764
0.726140171228166
0.726217591908512
0.726272874154216
0.726312348284179
0.726340534554095
0.726360660713668
0.726375031572563
0.726385292894894
0.726392619840946
0.726397851530249
0.726401587130227
0.726404254470323
0.72640615903681
0.726407518957799
0.726408489984264
0.726409183327606
for (i in 1:niters) {
  message(all_fls[[i]]$gl[[4]]$a)
}
0.0516088117170904
0.0515789373518519
0.05155757657634
0.0515423298574009
0.0515314481621149
0.0515236810522557
0.0515181364728055
0.0515141781288619
0.0515113520575102
0.0515093343000696
0.0515078936274401
0.051506864975469
0.051506130502068
0.0515056060731487
0.051505231618544
0.0515049642483025
0.0515047733386485
0.0515046370237395
0.0515045396909259
0.0515044701924125

Session information

sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/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] ebnm_0.1-12   flashr_0.5-12

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.17        pillar_1.2.1        plyr_1.8.4         
 [4] compiler_3.4.3      git2r_0.21.0        workflowr_1.0.1    
 [7] R.methodsS3_1.7.1   R.utils_2.6.0       iterators_1.0.9    
[10] tools_3.4.3         testthat_2.0.0      digest_0.6.15      
[13] tibble_1.4.2        evaluate_0.10.1     memoise_1.1.0      
[16] gtable_0.2.0        lattice_0.20-35     rlang_0.2.0        
[19] Matrix_1.2-12       foreach_1.4.4       commonmark_1.4     
[22] yaml_2.1.17         parallel_3.4.3      withr_2.1.1.9000   
[25] stringr_1.3.0       roxygen2_6.0.1.9000 xml2_1.2.0         
[28] knitr_1.20          devtools_1.13.4     rprojroot_1.3-2    
[31] grid_3.4.3          R6_2.2.2            rmarkdown_1.8      
[34] ggplot2_2.2.1       ashr_2.2-10         magrittr_1.5       
[37] whisker_0.3-2       backports_1.1.2     scales_0.5.0       
[40] codetools_0.2-15    htmltools_0.3.6     MASS_7.3-48        
[43] assertthat_0.2.0    softImpute_1.4      colorspace_1.3-2   
[46] stringi_1.1.6       lazyeval_0.2.1      munsell_0.4.3      
[49] doParallel_1.0.11   pscl_1.5.2          truncnorm_1.0-8    
[52] SQUAREM_2017.10-1   R.oo_1.21.0

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