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Introduction

I have a previous result run the very initial version of the splitting PMF. Now I revise the code and re-run the model. THe main diff is a. run vga 1 iter every big iteration; b. 1000 iterations; c. add 1 dimension each add_greedy attempt.

I set the scaling factors as \(s_{ij} = \frac{y_{i+}y_{+j}}{y_{++}}\). For comparison, I also fit flash on transformed count data, as \(\tilde{y}_{ij} = \log(1+\frac{y_{ij}}{s_{i}}\frac{a}{0.5})\) where \(s_i=\sum_j y_{ij}\), \(a = median(s_{i})\).

library(fastTopics)
library(Matrix)
library(stm)
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 
fit = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/pbmc_splitting_point_normal_vga1.rds')
plot(fit$K_trace, ylab='K',xlab='iterations')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
plot(fit$elbo_trace,ylab='elbo',xlab='iterations',type='l')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
plot(colSums(counts/c(rowSums(counts)))/dim(counts)[1],fit$sigma2,xlab='gene mean count(after library size adjustment)')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
plot(colSums(counts==0)/dim(counts)[1],fit$sigma2,xlab='sparsity')

Version Author Date
42f0de4 DongyueXie 2023-01-05

Visualize loadings

source('code/poisson_STM/plot_factors.R')
cell_names = as.character(pbmc_facs$samples$subpop)
plot.factors(fit$fit_flash,cell_names,title='splitting PMF')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
fit_flashier = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/flash_pbmc3k.rds')
plot.factors(fit_flashier,cell_names,title='flashier')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
source('code/poisson_STM/plot_factors_general.R')
fit_glmpca_poi = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/glmpca_pbmc3k_poi.rds')
plot.factors.general(fit_glmpca_poi$loadings,cell_names,title='glmpca poi')

Version Author Date
42f0de4 DongyueXie 2023-01-05 
fit_glmpca_nb = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/glmpca_pbmc3k_nb.rds')
plot.factors.general(fit_glmpca_nb$loadings,cell_names,title='glmpca nb')

Version Author Date
42f0de4 DongyueXie 2023-01-05

run time analysis

fit$run_time
Time difference of 10.15867 hours
lapply(fit$run_time_break_down,mean)
$run_time_vga_init
Time difference of 28.89131 secs

$run_time_flash_init
Time difference of 71.49468 secs

$run_time_vga
[1] 11.04436

$run_time_flash_init_factor
[1] 4.846896

$run_time_flash_greedy
[1] 0.4588499

$run_time_flash_backfitting
[1] 13.73861

$run_time_flash_nullcheck
[1] 1.401617

Latent variable

Take a look at the latent M in splitting PMF model. M is the posterior mean of \(q_\mu = N(\mu;m,v)\).

  1. What are M’s corresponds to zero Ys? Large Ys?

  2. How does the M compared to GLMPCA’s latent representation?

Histogram of latent variable corresponding to y = 0.

hist(fit$fit_flash$flash.fit$Y[as.vector(counts==0)],breaks=100,xlab='splitting PMF latent var size for those Y=0',main='')

summary(fit$fit_flash$flash.fit$Y[as.vector(counts==0)])
      Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
-17.532822  -0.000597  -0.000043  -0.021565  -0.000001   3.997050

It seems that most of them are very close to 0? Let’s set probability = TRUE and restrict ylim to (0,0.2).

hist(fit$fit_flash$flash.fit$Y[as.vector(counts==0)],breaks=200,xlab='splitting PMF latent var size for those Y=0',main='',probability = T,ylim=c(0,0.2))

Look at GLMPCA:

hist(tcrossprod(as.matrix(fit_glmpca_poi$loadings),as.matrix(fit_glmpca_poi$factors))[as.vector(counts==0)],breaks=100,xlab='GLMPCA latent var size for those Y=0',main='')

summary(tcrossprod(as.matrix(fit_glmpca_poi$loadings),as.matrix(fit_glmpca_poi$factors))[as.vector(counts==0)])
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-32.12124  -0.99826   0.63654  -0.05514   1.36053   9.60655

The GLMPCA latent vraibles are less concentrated around 0. Maybe this is because it does not induce sparsity on L and F.

Histogram of latent variable corresponding to y > 0.

hist(fit$fit_flash$flash.fit$Y[as.vector(counts>0)],breaks=100,xlab='splitting PMF latent var size for those Y>0',main='')

summary(fit$fit_flash$flash.fit$Y[as.vector(counts>0)])
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-8.96516  0.01205  0.04553  0.08838  0.11864  7.19377

Let’s limit ylim to (0,1), and set probability = TRUE.

hist(fit$fit_flash$flash.fit$Y[as.vector(counts>0)],breaks=200,xlab='splitting PMF latent var size for those Y>0',main='',ylim=c(0,1),probability = T,col=rgb(1,0,0,1/4))
abline(v = 0,lty=2)

hist(tcrossprod(as.matrix(fit_glmpca_poi$loadings),as.matrix(fit_glmpca_poi$factors))[as.vector(counts>0)],breaks=100,xlab='GLMPCA latent var size for those Y>0',main='')

summary(tcrossprod(as.matrix(fit_glmpca_poi$loadings),as.matrix(fit_glmpca_poi$factors))[as.vector(counts>0)])
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-8.2505  0.7475  1.1542  1.2377  1.6455 11.1552

Look at how many non-zeros are there in the Y:

hist(log(counts[counts>0]),breaks = 100)
<sparse>[ <logic> ]: .M.sub.i.logical() maybe inefficient

# The latent variable from splitting PMF seems to be very symmetric for those corresponding to $Y>0$. 
h_smaller = hist(log(counts[(fit$fit_flash$flash.fit$Y[as.vector(counts>0)])<0]),breaks = 100,main='',xlab='')
h_larger = hist(log(counts[(fit$fit_flash$flash.fit$Y[as.vector(counts>0)])>0]),breaks = 100,main='',xlab='')

plot( h_larger, col=rgb(0,0,1,1/4), xlim=c(0,5)) 
plot( h_smaller, col=rgb(1,0,0,1/4), xlim=c(0,5),add=T) 
legend('topright',c('>0','<0'),fill=c(rgb(0,0,1,1/4),rgb(1,0,0,1/4)),)

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      stm_1.2.8          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   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_3.5.0         
 [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_1.1.1    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      deconvolveR_1.2-1 
 [43] MCMCpack_1.6-3     vebpm_0.3.8        pkgconfig_2.0.3   
 [46] htmltools_0.5.3    highr_0.9          fastmap_1.1.0     
 [49] invgamma_1.1       htmlwidgets_1.5.4  rlang_1.0.6       
 [52] rstudioapi_0.13    farver_2.1.1       jquerylib_0.1.4   
 [55] generics_0.1.3     jsonlite_1.8.3     dplyr_1.0.10      
 [58] magrittr_2.0.3     smashr_1.3-6       Rcpp_1.0.9        
 [61] munsell_0.5.0      fansi_1.0.3        RcppZiggurat_0.1.6
 [64] lifecycle_1.0.3    stringi_1.6.2      whisker_0.4       
 [67] yaml_2.3.6         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] Rfast_2.0.6        NNLM_0.4.4         coda_0.19-4       
[103] later_1.3.0        survival_3.2-11    viridisLite_0.4.1 
[106] glmpca_0.2.0       truncnorm_1.0-8    tibble_3.1.8      
[109] ellipsis_0.3.2