Last updated: 2023-01-02

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Introduction

The vga step is an optimization problem. 1 iteration can already increase the elbo. Running till convergence will increase more elbo but is that necessary? does this benefit the overall fit in the long run?

I compare VGA 1 iteration vs convergence

res1000 = readRDS('/project2/mstephens/dongyue/poisson_mf/compare_vga_iterations/pbmc_3cells_vga1000.rds')
res1 = readRDS('/project2/mstephens/dongyue/poisson_mf/compare_vga_iterations/pbmc_3cells_vga1.rds')

compare elbo

plot(res1$fit$elbo_trace,type='l',col=2,lwd=2)
lines(res1000$fit$elbo_trace,col=4,lwd=2)
legend('bottomright',c('vga 1iter','vga converge'),lty=c(1,1),col=c(2,4))

res1$fit$elbo
[1] -4849876
res1000$fit$elbo
[1] -4852412

Not much difference. Running 1 iteration actually results in a slightly larger elbo.

compare run time

res1$fit$run_time
Time difference of 1.158864 hours
res1000$fit$run_time
Time difference of 1.366542 hours
lapply(res1$fit$run_time_break_down,mean)$run_time_vga
[1] 2.162444
lapply(res1000$fit$run_time_break_down,mean)$run_time_vga
[1] 3.618856

1 iteration is much faster.

fitted sturcture

res1$fit$fit_flash$n.factors
[1] 8
res1000$fit$fit_flash$n.factors
[1] 8
library(fastTopics)
data(pbmc_facs)

### use three cells
cells = pbmc_facs$samples$subpop%in%c('B cell', 'NK cell','CD34+')
cell_names =pbmc_facs$samples$subpop[cells]
source('code/poisson_STM/plot_factors.R')
plot.factors(res1$fit$fit_flash,cell_names,title='vga 1 iter')

plot.factors(res1000$fit$fit_flash,cell_names,title='vga converge')

The last 3 factors are slightly different.

Other concerns

The 1 iteration version requires storing the full dense matrix V which can take huge memory space when the dimension is large. For example for a \(10^5\times 10^3\) dense matrix it takes > 16GB RAM.

The converged version can exploit the explicit relationship between optimal M and V so storing V is not required.


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      fastTopics_0.6-142 workflowr_1.6.2   

loaded via a namespace (and not attached):
 [1] mcmc_0.9-7         fs_1.5.0           progress_1.2.2     httr_1.4.4        
 [5] rprojroot_2.0.2    tools_4.1.0        bslib_0.2.5.1      utf8_1.2.2        
 [9] R6_2.5.1           irlba_2.3.5.1      uwot_0.1.14        DBI_1.1.1         
[13] lazyeval_0.2.2     colorspace_2.0-3   withr_2.5.0        tidyselect_1.2.0  
[17] prettyunits_1.1.1  compiler_4.1.0     git2r_0.28.0       cli_3.4.1         
[21] quantreg_5.94      SparseM_1.81       plotly_4.10.1      labeling_0.4.2    
[25] horseshoe_0.2.0    sass_0.4.0         flashier_0.2.34    scales_1.2.1      
[29] SQUAREM_2021.1     quadprog_1.5-8     pbapply_1.6-0      mixsqp_0.3-48     
[33] stringr_1.4.0      digest_0.6.30      rmarkdown_2.9      MCMCpack_1.6-3    
[37] deconvolveR_1.2-1  pkgconfig_2.0.3    htmltools_0.5.3    fastmap_1.1.0     
[41] invgamma_1.1       highr_0.9          htmlwidgets_1.5.4  rlang_1.0.6       
[45] rstudioapi_0.13    farver_2.1.1       jquerylib_0.1.4    generics_0.1.3    
[49] jsonlite_1.8.3     dplyr_1.0.10       magrittr_2.0.3     Matrix_1.5-3      
[53] Rcpp_1.0.9         munsell_0.5.0      fansi_1.0.3        lifecycle_1.0.3   
[57] stringi_1.6.2      whisker_0.4        yaml_2.3.6         MASS_7.3-54       
[61] plyr_1.8.6         Rtsne_0.16         grid_4.1.0         parallel_4.1.0    
[65] promises_1.2.0.1   ggrepel_0.9.2      crayon_1.5.2       lattice_0.20-44   
[69] cowplot_1.1.1      splines_4.1.0      hms_1.1.2          knitr_1.33        
[73] pillar_1.8.1       softImpute_1.4-1   reshape2_1.4.4     glue_1.6.2        
[77] evaluate_0.14      trust_0.1-8        data.table_1.14.6  RcppParallel_5.1.5
[81] vctrs_0.5.1        httpuv_1.6.1       MatrixModels_0.5-1 gtable_0.3.1      
[85] purrr_0.3.5        ebnm_1.0-11        tidyr_1.2.1        assertthat_0.2.1  
[89] ashr_2.2-54        xfun_0.24          coda_0.19-4        later_1.3.0       
[93] survival_3.2-11    viridisLite_0.4.1  truncnorm_1.0-8    tibble_3.1.8      
[97] ellipsis_0.3.2