Objective Function: ebnm_pn vs. ebnm_ash

Introduction

Here I use ebnm_ash to see if I obtain similar decreases in the objective function as were obtained in the previous investigation.

Fits

I use the same dataset as in the previous investigation.

# 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

gtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE")))
strong <- gtex$strong.z

I fit four factors greedily using both ebnm_pn and ebnm_ash.

pn_res <- flash_add_greedy(strong, Kmax=4, verbose=FALSE)

fitting factor/loading 1

fitting factor/loading 2

fitting factor/loading 3

fitting factor/loading 4

ash_res <- flash_add_greedy(strong, Kmax=4, ebnm_fn = "ebnm_ash", 
                            verbose=FALSE)

fitting factor/loading 1

fitting factor/loading 2

fitting factor/loading 3

fitting factor/loading 4

plot_obj <- function(res, k, niters) {
  obj_data <- as.vector(rbind(res$obj[[k]]$after_tau,
                              res$obj[[k]]$after_f,
                              res$obj[[k]]$after_l))
  max_obj <- max(obj_data)
  obj_data <- obj_data - max_obj
  iter <- 1:length(obj_data) / 3
  
  if (length(obj_data) > niters*3) {
    idx <- (length(obj_data) - niters*3 + 1):length(obj_data)
    obj_data <- obj_data[idx]
    iter <- iter[idx]
  }
  
  plt_xlab = "Iteration"
  plt_ylab = "Diff. from maximum obj."
  plt_colors <- c("indianred1", "indianred3", "indianred4")
  plt_pch <- c(16, 17, 15)
  
  plot(iter, obj_data, col=plt_colors, pch=plt_pch,
       xlab=plt_xlab, ylab=plt_ylab)
  legend("bottomright", c("after tau", "after f", "after l"),
         col=plt_colors, pch=plt_pch)
}

Results: ebnm_pn

The problem discussed in the previous investigation occurs every time.

plot_obj(pn_res, 1, niters=3)

plot_obj(pn_res, 2, niters=5)

plot_obj(pn_res, 3, niters=20)

plot_obj(pn_res, 4, niters=10)

Results: ebnm_ash

But no obvious problems occur when using ebnm_ash.

plot_obj(ash_res, 1, niters=3)

plot_obj(ash_res, 2, niters=5)

plot_obj(ash_res, 3, niters=10)

plot_obj(ash_res, 4, niters=20)

Conclusions

When using ebnm_ash, the objective does not suffer from the same erratic behavior as when using ebnm_pn. Is there a weird bug somewhere in the computation of the likelihood function for ebnm_pn?

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          REBayes_1.2         devtools_1.13.4    
[31] rprojroot_1.3-2     grid_3.4.3          R6_2.2.2           
[34] rmarkdown_1.8       ggplot2_2.2.1       ashr_2.2-10        
[37] magrittr_1.5        whisker_0.3-2       backports_1.1.2    
[40] scales_0.5.0        codetools_0.2-15    htmltools_0.3.6    
[43] MASS_7.3-48         assertthat_0.2.0    softImpute_1.4     
[46] colorspace_1.3-2    stringi_1.1.6       Rmosek_7.1.3       
[49] lazyeval_0.2.1      munsell_0.4.3       doParallel_1.0.11  
[52] pscl_1.5.2          truncnorm_1.0-8     SQUAREM_2017.10-1  
[55] R.oo_1.21.0