Last updated: 2022-12-17

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Introduction

The results here show that using 1 back-fitting in flash initialization does not affect the final results.

rmse = function(x,y){return(sqrt(mean((x-y)^2)))}
res = readRDS('/project2/mstephens/dongyue/poisson_mf/PMF10_K3simu_pbmc_3cells_1backinit.rds')

We first look at the number factors recovered from both methods. The true \(K\) is 3.

K_hat = c()
for(i in 1:length(res$output)){
  K_hat = rbind(K_hat,c(res$output[[i]]$fitted_model$flash$n.factors,res$output[[i]]$fitted_model$splitting$fit_flash$n.factors))
}
colnames(K_hat) = c('flash','splittingPMF')
K_hat
      flash splittingPMF
 [1,]     8            3
 [2,]    12            3
 [3,]     6            3
 [4,]     7            3
 [5,]     6            3
 [6,]     8            3
 [7,]     8            3
 [8,]    10            3
 [9,]    13            3
[10,]     5            3

Next we compare \(\hat L\hat F'\) and true \(LF'\).

fit = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc_3cells_Sij.rds')
kset = order(fit$fit$fit_flash$pve,decreasing = TRUE)[1:3]
Ltrue = fit$fit$fit_flash$L.pm[,kset]
Ftrue = fit$fit$fit_flash$F.pm[,kset]
Mu_true = tcrossprod(Ltrue,Ftrue)
rmses= c()
for(i in 1:length(res$output)){
  rmses = rbind(rmses,c(rmse(Mu_true,fitted(res$output[[i]]$fitted_model$flash)),rmse(Mu_true,fitted(res$output[[i]]$fitted_model$splitting$fit_flash))))
}
colnames(rmses) = c('flash','splittingPMF')
rmses
          flash splittingPMF
 [1,] 0.5819739    0.1742745
 [2,] 0.5819058    0.1763028
 [3,] 0.5815135    0.1732575
 [4,] 0.5817050    0.1724475
 [5,] 0.5823862    0.1709836
 [6,] 0.5809864    0.1773127
 [7,] 0.5816003    0.1786152
 [8,] 0.5814658    0.1785925
 [9,] 0.5821286    0.1762915
[10,] 0.5815670    0.1660298
par(mfrow=c(2,1))
for(i in 1:length(res$output)){
  plot(fitted(res$output[[i]]$fitted_model$flash),Mu_true,col='grey80',xlab='fitted',ylab='LF',main='flash')
  abline(a=0,b=1)
  plot(fitted(res$output[[i]]$fitted_model$splitting$fit_flash),Mu_true,col='grey80',xlab='fitted',ylab='LF',main='splitting')
  abline(a=0,b=1)
}
par(mfrow=c(1,1))

Next we look at how the structures of L and F are recovered by both methods.

We first plot loadings.

library(fastTopics)
library(Matrix)
library(stm)
require(gridExtra)
Loading required package: gridExtra
data(pbmc_facs)
counts <- pbmc_facs$counts
table(pbmc_facs$samples$subpop)

 B cell   CD14+   CD34+ NK cell  T cell 
    767     163     687     673    1484 
## use only B cell and NK cell and CD34+
cells = pbmc_facs$samples$subpop%in%c('B cell', 'NK cell','CD34+')
counts = counts[cells,]
# filter out genes that has few expressions(3% cells)
genes = (colSums(counts>0) > 0.03*dim(counts)[1])
cell_names = pbmc_facs$samples$subpop[cells]
source('code/poisson_STM/plot_factors.R')
plot0=plot.factors(fit$fit$fit_flash,cell.types=cell_names,kset=kset,title='True Loadings')
for(i in 1:length(res$output)){
  plot1 = plot.factors(res$output[[i]]$fitted_model$flash,cell.types=cell_names,title='flash')
  plot2 = plot.factors(res$output[[i]]$fitted_model$splitting$fit_flash,cell.types=cell_names,title='splittingPMF')
  grid.arrange(plot1, plot0,plot2, ncol=3)
}

misc

number of iterations until convergence

for(i in 1:length(res$output)){
   print(length(res$output[[i]]$fitted_model$splitting$eblo_trace))
}
[1] 88
[1] 90
[1] 92
[1] 90
[1] 88
[1] 87
[1] 88
[1] 85
[1] 86
[1] 90

run time analysis

for(i in 1:length(res$output)){
   print((res$output[[i]]$fitted_model$splitting$run_time))
}
Time difference of 15.33213 mins
Time difference of 16.28081 mins
Time difference of 16.98529 mins
Time difference of 16.27841 mins
Time difference of 16.96993 mins
Time difference of 14.47638 mins
Time difference of 16.00253 mins
Time difference of 15.43373 mins
Time difference of 15.69402 mins
Time difference of 16.36275 mins

run time break down

tt = c()
for(i in 1:length(res$output)){
   tt = rbind(tt,unlist(lapply(res$output[[i]]$fitted_model$splitting$run_time_break_down,mean)))
}
apply(tt,2,mean)
         run_time_vga_init               run_time_vga 
               187.4276577                  4.0366805 
       run_time_flash_init run_time_flash_init_factor 
                 0.2409684                  0.3362548 
     run_time_flash_greedy run_time_flash_backfitting 
                 1.5484761                  1.4630587 
  run_time_flash_nullcheck 
                 0.1801452

Plot K trace

plot(res$output[[i]]$fitted_model$splitting$K_trace,ylab='K',xlab='iterations',type='l',col='grey80')
for(i in 1:length(res$output)){
   lines(res$output[[i]]$fitted_model$splitting$K_trace,col=i)
}

Maybe omit greedy step after the K is stabilized? to reduce computation time.


sessionInfo()
R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS:   /software/R-4.1.0-no-openblas-el7-x86_64/lib64/R/lib/libRblas.so
LAPACK: /software/R-4.1.0-no-openblas-el7-x86_64/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C         LC_TIME=C           
 [4] LC_COLLATE=C         LC_MONETARY=C        LC_MESSAGES=C       
 [7] LC_PAPER=C           LC_NAME=C            LC_ADDRESS=C        
[10] LC_TELEPHONE=C       LC_MEASUREMENT=C     LC_IDENTIFICATION=C 

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.4.0      gridExtra_2.3      stm_1.1.6          Matrix_1.5-3      
[5] fastTopics_0.6-142 workflowr_1.6.2   

loaded via a namespace (and not attached):
  [1] mcmc_0.9-7         bitops_1.0-7       matrixStats_0.59.0
  [4] fs_1.5.0           progress_1.2.2     httr_1.4.4        
  [7] rprojroot_2.0.2    tools_4.1.0        bslib_0.2.5.1     
 [10] utf8_1.2.2         R6_2.5.1           irlba_2.3.5.1     
 [13] uwot_0.1.14        DBI_1.1.1          lazyeval_0.2.2    
 [16] colorspace_2.0-3   withr_2.5.0        wavethresh_4.7.2  
 [19] tidyselect_1.2.0   prettyunits_1.1.1  ebpm_0.0.1.3      
 [22] compiler_4.1.0     git2r_0.28.0       cli_3.4.1         
 [25] quantreg_5.94      SparseM_1.81       plotly_4.10.1     
 [28] labeling_0.4.2     horseshoe_0.2.0    sass_0.4.0        
 [31] caTools_1.18.2     flashier_0.2.34    scales_1.2.1      
 [34] SQUAREM_2021.1     quadprog_1.5-8     pbapply_1.6-0     
 [37] mixsqp_0.3-48      stringr_1.4.0      digest_0.6.30     
 [40] rmarkdown_2.9      MCMCpack_1.6-3     deconvolveR_1.2-1 
 [43] vebpm_0.3.3        pkgconfig_2.0.3    htmltools_0.5.3   
 [46] highr_0.9          fastmap_1.1.0      invgamma_1.1      
 [49] htmlwidgets_1.5.4  rlang_1.0.6        rstudioapi_0.13   
 [52] farver_2.1.1       jquerylib_0.1.4    generics_0.1.3    
 [55] jsonlite_1.8.3     dplyr_1.0.10       magrittr_2.0.3    
 [58] smashr_1.3-6       Rcpp_1.0.9         munsell_0.5.0     
 [61] fansi_1.0.3        lifecycle_1.0.3    stringi_1.6.2     
 [64] whisker_0.4        yaml_2.3.6         nleqslv_3.3.3     
 [67] rootSolve_1.8.2.3  MASS_7.3-54        plyr_1.8.6        
 [70] Rtsne_0.16         grid_4.1.0         parallel_4.1.0    
 [73] promises_1.2.0.1   ggrepel_0.9.2      crayon_1.5.2      
 [76] lattice_0.20-44    cowplot_1.1.1      splines_4.1.0     
 [79] hms_1.1.2          knitr_1.33         pillar_1.8.1      
 [82] softImpute_1.4-1   reshape2_1.4.4     glue_1.6.2        
 [85] evaluate_0.14      trust_0.1-8        data.table_1.14.6 
 [88] RcppParallel_5.1.5 nloptr_1.2.2.2     vctrs_0.5.1       
 [91] httpuv_1.6.1       MatrixModels_0.5-1 gtable_0.3.1      
 [94] purrr_0.3.5        ebnm_1.0-11        tidyr_1.2.1       
 [97] assertthat_0.2.1   ashr_2.2-54        xfun_0.24         
[100] NNLM_0.4.4         coda_0.19-4        later_1.3.0       
[103] survival_3.2-11    viridisLite_0.4.1  truncnorm_1.0-8   
[106] tibble_3.1.8       ellipsis_0.3.2