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Introduction

So in a previous simulation results, the true variances are those learnt from data.

Now I want to see what if true variances are 0? I used the fitted model with relative large variance(init tol 1e-2).

The variances refers to \(var(\epsilon_{ij})\) in

\[\begin{equation} \begin{split} &y_{ij}\sim Poisson(s_i\lambda_{ij}), \\ &\log\lambda_{ij} = f_{j0} + \sum_k l_{ik}f_{jk} + \epsilon_{ij}, \\ &l_{ik}\sim g_{k} ^{(l)},k=1,2,...,K, \\ &f_{jk}\sim g_{k} ^{(f)},k=1,2,...,K. \end{split} \end{equation}\]

library(fastTopics)
library(Matrix)
library(gridExtra)
source('code/poisson_STM/plot_factors.R')
source('code/poisson_STM/plot_factors_general.R')
source('code/poisson_STM/structure_plot.R')
source('code/poisson_STM/get_loadings_order.R')
data("pbmc_facs")
cell_names = pbmc_facs$samples$subpop

small init variance

res = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k_simulation/simu_pbmc_fasttopics_0_var_small_init_var.rds')
K_hat = c()
for(i in c(1,2,3,5)){
  K_hat = rbind(K_hat,c(res$output[[i]]$fitted_model$flash$n.factors,res$output[[i]]$fitted_model$ebpmf$fit_flash$n.factors,ncol(res$sim_data$Factor)))
}
colnames(K_hat) = c('flash','ebpmf','true K')
K_hat
     flash ebpmf true K
[1,]     4     9     10
[2,]     4     9     10
[3,]     4     9     10
[4,]     4     9     10
loadings_order = get_loadings_order(res$sim_data$Loading,res$sim_data$Factor,grouping = cell_names,n_samples = 5000)
Perplexity automatically changed to 53 because the original setting of 100 was too large for the number of samples (163)
plot0=structure_plot_general(res$sim_data$Loading,res$sim_data$Factor,grouping =cell_names,title = 'True',print_plot = F,loadings_order=loadings_order) 
Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"
for(i in c(1,2,3,5)){
  plot1 = structure_plot_general(res$output[[i]]$fitted_model$flash$L.pm,
                                 res$output[[i]]$fitted_model$flash$F.pm
                                 ,grouping=cell_names,
                                 title='flash',
                                 print_plot = F,
                                 loadings_order=loadings_order,
                                 remove_l0f0 = F)
  plot2 = structure_plot_general(res$output[[i]]$fitted_model$ebpmf$fit_flash$L.pm,
                                 res$output[[i]]$fitted_model$ebpmf$fit_flash$F.pm,
                                 grouping =cell_names,
                                 title='ebpmf',
                                 print_plot = F,
                                 loadings_order=loadings_order)
  grid.arrange(plot1, plot0,plot2, nrow=3)
}
Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

for(i in c(1,2,3,5)){
  hist(res$output[[i]]$fitted_model$ebpmf$sigma2,breaks = 100,main='',xlab='var')
}

for(i in c(1,2,3,5)){
  print(res$output[[i]]$fitted_model$ebpmf$run_time)
}
Time difference of 45.35804 mins
Time difference of 45.78565 mins
Time difference of 46.23813 mins
Time difference of 43.47024 mins

large init variance

I used unimodal-nonnegative prior for this simulation because the point-exponential always ran into errors.

res = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k_simulation/simu_pbmc_fasttopics_0_var_large_init_var.rds')
K_hat = c()
for(i in 1:5){
  K_hat = rbind(K_hat,c(res$output[[i]]$fitted_model$flash$n.factors,res$output[[i]]$fitted_model$ebpmf$fit_flash$n.factors,ncol(res$sim_data$Factor)))
}
colnames(K_hat) = c('flash','ebpmf','true K')
K_hat
     flash ebpmf true K
[1,]     4     9     10
[2,]     4     9     10
[3,]     4     9     10
[4,]     7     9     10
[5,]     4     9     10
loadings_order = get_loadings_order(res$sim_data$Loading,res$sim_data$Factor,grouping = cell_names,n_samples = 5000)
Perplexity automatically changed to 53 because the original setting of 100 was too large for the number of samples (163)
plot0=structure_plot_general(res$sim_data$Loading,res$sim_data$Factor,grouping =cell_names,title = 'True',print_plot = F,loadings_order=loadings_order) 
Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"
for(i in 1:5){
  plot1 = structure_plot_general(res$output[[i]]$fitted_model$flash$L.pm,
                                 res$output[[i]]$fitted_model$flash$F.pm
                                 ,grouping=cell_names,
                                 title='flash',
                                 print_plot = F,
                                 loadings_order=loadings_order,
                                 remove_l0f0 = F)
  plot2 = structure_plot_general(res$output[[i]]$fitted_model$ebpmf$fit_flash$L.pm,
                                 res$output[[i]]$fitted_model$ebpmf$fit_flash$F.pm,
                                 grouping =cell_names,
                                 title='ebpmf',
                                 print_plot = F,
                                 loadings_order=loadings_order)
  grid.arrange(plot1, plot0,plot2, nrow=3)
}
Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

Warning in structure_plot(fit_list, grouping = grouping, loadings_order =
loadings_order, : Input argument "n" is ignored when "loadings_order" is not
"embed"

for(i in 1:5){
  hist(res$output[[i]]$fitted_model$ebpmf$sigma2,breaks = 100,main='',xlab='var')
}

for(i in 1:5){
  print(res$output[[i]]$fitted_model$ebpmf$run_time)
}
Time difference of 1.944328 hours
Time difference of 1.835465 hours
Time difference of 1.837452 hours
Time difference of 1.786933 hours
Time difference of 1.664781 hours

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      Matrix_1.5-3       fastTopics_0.6-142
[5] 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   wavethresh_4.7.2   withr_2.5.0       
 [19] tidyselect_1.2.0   prettyunits_1.1.1  ebpm_0.0.1.3      
 [22] compiler_4.1.0     git2r_0.28.0       cli_3.5.0         
 [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] smashrgen_1.1.4    caTools_1.18.2     flashier_0.2.34   
 [34] scales_1.2.1       SQUAREM_2021.1     quadprog_1.5-8    
 [37] pbapply_1.6-0      mixsqp_0.3-48      stringr_1.4.0     
 [40] digest_0.6.30      rmarkdown_2.9      MCMCpack_1.6-3    
 [43] deconvolveR_1.2-1  vebpm_0.4.4        pkgconfig_2.0.3   
 [46] htmltools_0.5.3    ebpmf_2.0.8        highr_0.9         
 [49] fastmap_1.1.0      invgamma_1.1       htmlwidgets_1.5.4 
 [52] rlang_1.0.6        rstudioapi_0.13    farver_2.1.1      
 [55] jquerylib_0.1.4    generics_0.1.3     jsonlite_1.8.3    
 [58] dplyr_1.0.10       magrittr_2.0.3     smashr_1.3-6      
 [61] Rcpp_1.0.9         munsell_0.5.0      fansi_1.0.3       
 [64] RcppZiggurat_0.1.6 lifecycle_1.0.3    stringi_1.6.2     
 [67] whisker_0.4        yaml_2.3.6         MASS_7.3-54       
 [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   glue_1.6.2         evaluate_0.14     
 [85] trust_0.1-8        data.table_1.14.6  RcppParallel_5.1.5
 [88] nloptr_1.2.2.2     vctrs_0.5.1        httpuv_1.6.1      
 [91] MatrixModels_0.5-1 gtable_0.3.1       purrr_0.3.5       
 [94] ebnm_1.0-11        tidyr_1.2.1        assertthat_0.2.1  
 [97] ashr_2.2-54        xfun_0.24          Rfast_2.0.6       
[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