Bad loadings updates

Introduction

Convergence of objective

Convergence of prior

Session information

Last updated: 2018-07-20

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Rmd	2761284	Jason Willwerscheid	2018-07-20	wflow_publish(c(“analysis/objective3.Rmd”,
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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.

# devtools::install_github("stephenslab/flashr", ref="trackObj")
devtools::load_all("/Users/willwerscheid/GitHub/flashr")

Loading flashr

# devtools::install_github("stephenslab/ebnm")
devtools::load_all("/Users/willwerscheid/GitHub/ebnm")

Loading ebnm

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
}

Convergence of 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

This reproducible R Markdown analysis was created with workflowr 1.0.1

Bad loadings updates

Jason Willwerscheid

7/16/2018

Introduction

Convergence of objective

Convergence of prior

Session information