An attempt to speed up flash add greedy

Last updated: 2022-12-27

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Introduction

In splitting PMF, each iteration needs an add greedy step of flash.

This step involves an initialization step of rank-1 factorization which can be time consuming. On the other hand, the K usually does not change much after certain number of iterations. So I decided to see if I can use the same initialization for the add greedy if the K does not change and set Kmax = 1 in add_greedy in iterations so that at most 1 factor is added each iteration.

IN addition, I set default maxiter of vga to be 1 to speed up iterations.

library(stm)
set.seed(12345)
N = 10000
p = 100
K = 3
Ftrue = matrix(0,nrow=p,ncol=K)
Ftrue[1:20,1] = 5
Ftrue[21:40,2] = 2
Ftrue[41:60,3] = 1
Ltrue = pmax(matrix(rnorm(N*K), ncol=K),0)
Lambda = exp(tcrossprod(Ltrue,Ftrue))
Y = matrix(rpois(N*p,Lambda),nrow=N,ncol=p)
fit1 = splitting_PMF_flashier(Y,verbose=TRUE,
                              ebnm.fn = c(ebnm::ebnm_point_exponential, ebnm::ebnm_point_normal),
                              add_greedy_init = 'new_init',add_greedy_Kmax = 1,
                              printevery = 1,
                              loadings_sign = 1,maxiter = 100,n_cores = 10)

Initializing...Solving VGA for column 1...running initial flash fit
[1] "Running iterations..."
[1] "iter 1, ELBO=-2076127.74564, K=6"
[1] "iter 2, ELBO=-2016816.95943, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 3, ELBO=-1964664.97333, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 4, ELBO=-1928981.79802, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 5, ELBO=-1905978.34881, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 6, ELBO=-1885867.42023, K=5"
[1] "iter 7, ELBO=-1870755.59885, K=5"
[1] "iter 8, ELBO=-1857385.33451, K=5"
[1] "iter 9, ELBO=-1846061.15693, K=5"
[1] "iter 10, ELBO=-1835939.75493, K=5"
[1] "iter 11, ELBO=-1826886.50023, K=5"
[1] "iter 12, ELBO=-1818720.96811, K=5"
[1] "iter 13, ELBO=-1811387.79893, K=5"
[1] "iter 14, ELBO=-1804793.8011, K=5"
[1] "iter 15, ELBO=-1799071.2729, K=5"
  --Estimate of factor 4 is numerically zero!
  --Estimate of factor 4 is numerically zero!
[1] "iter 16, ELBO=-1794105.47488, K=4"
  --Estimate of factor 4 is numerically zero!
  --Estimate of factor 4 is numerically zero!
[1] "iter 17, ELBO=-1789710.97652, K=3"
[1] "iter 18, ELBO=-1785852.46854, K=3"
[1] "iter 19, ELBO=-1782450.01871, K=3"
[1] "iter 20, ELBO=-1779418.59074, K=3"
[1] "iter 21, ELBO=-1776703.46615, K=3"
[1] "iter 22, ELBO=-1774264.08083, K=3"
[1] "iter 23, ELBO=-1772062.12194, K=3"
[1] "iter 24, ELBO=-1770066.58459, K=3"
[1] "iter 25, ELBO=-1768253.40608, K=3"
[1] "iter 26, ELBO=-1766602.01164, K=3"
[1] "iter 27, ELBO=-1765094.70615, K=3"
[1] "iter 28, ELBO=-1763716.15166, K=3"
[1] "iter 29, ELBO=-1762452.98136, K=3"
[1] "iter 30, ELBO=-1761293.4903, K=3"
[1] "iter 31, ELBO=-1760227.38714, K=3"
[1] "iter 32, ELBO=-1759245.59056, K=3"
[1] "iter 33, ELBO=-1758340.0613, K=3"
[1] "iter 34, ELBO=-1757503.66165, K=3"
[1] "iter 35, ELBO=-1756730.03745, K=3"
[1] "iter 36, ELBO=-1756013.51814, K=3"
[1] "iter 37, ELBO=-1755349.0316, K=3"
[1] "iter 38, ELBO=-1754732.03137, K=3"
[1] "iter 39, ELBO=-1754158.43394, K=3"
[1] "iter 40, ELBO=-1753624.56476, K=3"
[1] "iter 41, ELBO=-1753127.11128, K=3"
[1] "iter 42, ELBO=-1752663.08236, K=3"
[1] "iter 43, ELBO=-1752229.77254, K=3"
[1] "iter 44, ELBO=-1751824.73108, K=3"
[1] "iter 45, ELBO=-1751445.7346, K=3"
[1] "iter 46, ELBO=-1751090.76309, K=3"
[1] "iter 47, ELBO=-1750757.97877, K=3"
[1] "iter 48, ELBO=-1750445.70751, K=3"
[1] "iter 49, ELBO=-1750152.42206, K=3"
[1] "iter 50, ELBO=-1749876.72754, K=3"
[1] "iter 51, ELBO=-1749617.34846, K=3"
[1] "iter 52, ELBO=-1749373.11699, K=3"
[1] "iter 53, ELBO=-1749142.96261, K=3"
[1] "iter 54, ELBO=-1748925.90307, K=3"
[1] "iter 55, ELBO=-1748721.03587, K=3"
[1] "iter 56, ELBO=-1748527.53111, K=3"
[1] "iter 57, ELBO=-1748344.62468, K=3"
[1] "iter 58, ELBO=-1748171.61243, K=3"
[1] "iter 59, ELBO=-1748007.84474, K=3"
[1] "iter 60, ELBO=-1747852.72177, K=3"
[1] "iter 61, ELBO=-1747705.68905, K=3"
[1] "iter 62, ELBO=-1747566.23361, K=3"
[1] "iter 63, ELBO=-1747433.88046, K=3"
[1] "iter 64, ELBO=-1747308.18927, K=3"
[1] "iter 65, ELBO=-1747188.75166, K=3"
[1] "iter 66, ELBO=-1747075.1884, K=3"
[1] "iter 67, ELBO=-1746967.14711, K=3"
[1] "iter 68, ELBO=-1746864.30008, K=3"
[1] "iter 69, ELBO=-1746766.34228, K=3"
[1] "iter 70, ELBO=-1746672.98961, K=3"
[1] "iter 71, ELBO=-1746583.97718, K=3"
[1] "iter 72, ELBO=-1746499.05799, K=3"
[1] "iter 73, ELBO=-1746418.00129, K=3"
[1] "iter 74, ELBO=-1746340.59164, K=3"
[1] "iter 75, ELBO=-1746266.62757, K=3"
[1] "iter 76, ELBO=-1746195.92052, K=3"
[1] "iter 77, ELBO=-1746128.2941, K=3"
[1] "iter 78, ELBO=-1746063.58302, K=3"
[1] "iter 79, ELBO=-1746001.63232, K=3"
[1] "iter 80, ELBO=-1745942.29665, K=3"
[1] "iter 81, ELBO=-1745885.43958, K=3"
[1] "iter 82, ELBO=-1745830.93303, K=3"
[1] "iter 83, ELBO=-1745778.65661, K=3"
[1] "iter 84, ELBO=-1745728.49711, K=3"
[1] "iter 85, ELBO=-1745680.34808, K=3"
[1] "iter 86, ELBO=-1745634.10925, K=3"
[1] "iter 87, ELBO=-1745589.68623, K=3"
[1] "iter 88, ELBO=-1745546.99007, K=3"
[1] "iter 89, ELBO=-1745505.93689, K=3"
[1] "iter 90, ELBO=-1745466.44755, K=3"
[1] "iter 91, ELBO=-1745428.44744, K=3"
[1] "iter 92, ELBO=-1745391.866, K=3"
[1] "iter 93, ELBO=-1745356.63663, K=3"
[1] "iter 94, ELBO=-1745322.69639, K=3"
[1] "iter 95, ELBO=-1745289.98574, K=3"
[1] "iter 96, ELBO=-1745258.44834, K=3"
[1] "iter 97, ELBO=-1745228.0309, K=3"
[1] "iter 98, ELBO=-1745198.6829, K=3"
[1] "iter 99, ELBO=-1745170.35657, K=3"
[1] "iter 100, ELBO=-1745143.00657, K=3"

fit2 = splitting_PMF_flashier(Y,verbose=TRUE,
                             ebnm.fn = c(ebnm::ebnm_point_exponential, ebnm::ebnm_point_normal),
                             add_greedy_init = 'previous_init',add_greedy_Kmax = 1,
                             printevery = 1,
                             loadings_sign = 1,maxiter = 100,n_cores = 10)

Initializing...Solving VGA for column 1...running initial flash fit
[1] "Running iterations..."
[1] "iter 1, ELBO=-2076127.74564, K=6"
[1] "iter 2, ELBO=-2016816.95943, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 3, ELBO=-1964664.97333, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 4, ELBO=-1928981.79802, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 5, ELBO=-1905978.34881, K=5"
  --Estimate of factor 6 is numerically zero!
  --Estimate of factor 6 is numerically zero!
[1] "iter 6, ELBO=-1885867.42023, K=5"
[1] "iter 7, ELBO=-1870755.59885, K=5"
[1] "iter 8, ELBO=-1857385.33451, K=5"
[1] "iter 9, ELBO=-1846061.15693, K=5"
[1] "iter 10, ELBO=-1835939.75493, K=5"
[1] "iter 11, ELBO=-1826886.50023, K=5"
[1] "iter 12, ELBO=-1818720.96811, K=5"
[1] "iter 13, ELBO=-1811387.79893, K=5"
[1] "iter 14, ELBO=-1804793.8011, K=5"
[1] "iter 15, ELBO=-1799071.2729, K=5"
  --Estimate of factor 4 is numerically zero!
  --Estimate of factor 4 is numerically zero!
[1] "iter 16, ELBO=-1794105.47488, K=4"
  --Estimate of factor 4 is numerically zero!
  --Estimate of factor 4 is numerically zero!
[1] "iter 17, ELBO=-1789710.97652, K=3"
[1] "iter 18, ELBO=-1785852.46854, K=3"
[1] "iter 19, ELBO=-1782450.01871, K=3"
[1] "iter 20, ELBO=-1779418.59074, K=3"
[1] "iter 21, ELBO=-1776703.46615, K=3"
[1] "iter 22, ELBO=-1774264.08083, K=3"
[1] "iter 23, ELBO=-1772062.12194, K=3"
[1] "iter 24, ELBO=-1770066.58459, K=3"
[1] "iter 25, ELBO=-1768253.40608, K=3"
[1] "iter 26, ELBO=-1766602.01164, K=3"
[1] "iter 27, ELBO=-1765094.70615, K=3"
[1] "iter 28, ELBO=-1763716.15166, K=3"
[1] "iter 29, ELBO=-1762452.98136, K=3"
[1] "iter 30, ELBO=-1761293.4903, K=3"
[1] "iter 31, ELBO=-1760227.38714, K=3"
[1] "iter 32, ELBO=-1759245.59056, K=3"
[1] "iter 33, ELBO=-1758340.0613, K=3"
[1] "iter 34, ELBO=-1757503.66165, K=3"
[1] "iter 35, ELBO=-1756730.03745, K=3"
[1] "iter 36, ELBO=-1756013.51814, K=3"
[1] "iter 37, ELBO=-1755349.0316, K=3"
[1] "iter 38, ELBO=-1754732.03137, K=3"
[1] "iter 39, ELBO=-1754158.43394, K=3"
[1] "iter 40, ELBO=-1753624.56476, K=3"
[1] "iter 41, ELBO=-1753127.11128, K=3"
[1] "iter 42, ELBO=-1752663.08236, K=3"
[1] "iter 43, ELBO=-1752229.77254, K=3"
[1] "iter 44, ELBO=-1751824.73108, K=3"
[1] "iter 45, ELBO=-1751445.7346, K=3"
[1] "iter 46, ELBO=-1751090.76309, K=3"
[1] "iter 47, ELBO=-1750757.97877, K=3"
[1] "iter 48, ELBO=-1750445.70751, K=3"
[1] "iter 49, ELBO=-1750152.42206, K=3"
[1] "iter 50, ELBO=-1749876.72754, K=3"
[1] "iter 51, ELBO=-1749617.34846, K=3"
[1] "iter 52, ELBO=-1749373.11699, K=3"
[1] "iter 53, ELBO=-1749142.96261, K=3"
[1] "iter 54, ELBO=-1748925.90307, K=3"
[1] "iter 55, ELBO=-1748721.03587, K=3"
[1] "iter 56, ELBO=-1748527.53111, K=3"
[1] "iter 57, ELBO=-1748344.62468, K=3"
[1] "iter 58, ELBO=-1748171.61243, K=3"
[1] "iter 59, ELBO=-1748007.84474, K=3"
[1] "iter 60, ELBO=-1747852.72177, K=3"
[1] "iter 61, ELBO=-1747705.68905, K=3"
[1] "iter 62, ELBO=-1747566.23361, K=3"
[1] "iter 63, ELBO=-1747433.88046, K=3"
[1] "iter 64, ELBO=-1747308.18927, K=3"
[1] "iter 65, ELBO=-1747188.75166, K=3"
[1] "iter 66, ELBO=-1747075.1884, K=3"
[1] "iter 67, ELBO=-1746967.14711, K=3"
[1] "iter 68, ELBO=-1746864.30008, K=3"
[1] "iter 69, ELBO=-1746766.34228, K=3"
[1] "iter 70, ELBO=-1746672.98961, K=3"
[1] "iter 71, ELBO=-1746583.97718, K=3"
[1] "iter 72, ELBO=-1746499.05799, K=3"
[1] "iter 73, ELBO=-1746418.00129, K=3"
[1] "iter 74, ELBO=-1746340.59164, K=3"
[1] "iter 75, ELBO=-1746266.62757, K=3"
[1] "iter 76, ELBO=-1746195.92052, K=3"
[1] "iter 77, ELBO=-1746128.2941, K=3"
[1] "iter 78, ELBO=-1746063.58302, K=3"
[1] "iter 79, ELBO=-1746001.63232, K=3"
[1] "iter 80, ELBO=-1745942.29665, K=3"
[1] "iter 81, ELBO=-1745885.43958, K=3"
[1] "iter 82, ELBO=-1745830.93303, K=3"
[1] "iter 83, ELBO=-1745778.65661, K=3"
[1] "iter 84, ELBO=-1745728.49711, K=3"
[1] "iter 85, ELBO=-1745680.34808, K=3"
[1] "iter 86, ELBO=-1745634.10925, K=3"
[1] "iter 87, ELBO=-1745589.68623, K=3"
[1] "iter 88, ELBO=-1745546.99007, K=3"
[1] "iter 89, ELBO=-1745505.93689, K=3"
[1] "iter 90, ELBO=-1745466.44755, K=3"
[1] "iter 91, ELBO=-1745428.44744, K=3"
[1] "iter 92, ELBO=-1745391.866, K=3"
[1] "iter 93, ELBO=-1745356.63663, K=3"
[1] "iter 94, ELBO=-1745322.69639, K=3"
[1] "iter 95, ELBO=-1745289.98574, K=3"
[1] "iter 96, ELBO=-1745258.44834, K=3"
[1] "iter 97, ELBO=-1745228.0309, K=3"
[1] "iter 98, ELBO=-1745198.6829, K=3"
[1] "iter 99, ELBO=-1745170.35657, K=3"
[1] "iter 100, ELBO=-1745143.00657, K=3"

summary_fit = function(fit){
  plot(fit$K_trace,ylab='K',xlab='iteration')
  plot(fit$elbo_trace,ylab='elbo',xlab='iteration')
  
  idx = sample(1:prod(dim(Y)),min(1e5,prod(dim(Y))))
  plot(fitted(fit$fit_flash)[idx],tcrossprod(Ltrue,Ftrue)[idx],col='grey80',xlab='fitted',ylab='true')
  abline(a=0,b=1)
  
  for(k in 1:fit$fit_flash$n.factors){
    plot(fit$fit_flash$F.pm[,k],type='l',xlab='',ylab='',main=paste('factor:',k))
  }
  print(paste('pve=',paste0(round(fit$fit_flash$pve,3),collapse = ',')))
  print(paste('elbo=',round(fit$elbo,3)))
  print(paste('run time: ',round(fit$run_time,3)))
  print(round(unlist(lapply(fit$run_time_break_down,mean)),3))
  
}

new init

summary_fit(fit1)

[1] "pve= 0.838,0.124,0.028"
[1] "elbo= -1745143.007"
[1] "run time:  3.161"
         run_time_vga_init        run_time_flash_init 
                     3.258                      5.012 
              run_time_vga run_time_flash_init_factor 
                     0.130                      0.061 
     run_time_flash_greedy run_time_flash_backfitting 
                     0.709                      0.814 
  run_time_flash_nullcheck 
                     0.034

previous init

summary_fit(fit2)

[1] "pve= 0.838,0.124,0.028"
[1] "elbo= -1745143.007"
[1] "run time:  2.167"
         run_time_vga_init        run_time_flash_init 
                     2.041                      4.536 
              run_time_vga run_time_flash_init_factor 
                     0.131                      0.055 
     run_time_flash_greedy run_time_flash_backfitting 
                     0.174                      0.775 
  run_time_flash_nullcheck 
                     0.032

other thoughts

I have also added add_greedy_every option, such that the flash.add.greedy need not running every iteration.

The acceleration method for EM like daarem, squarem are not very applicable in this setting because (a) K is changing, (b) elbo calculation needs KL term from ebnm, (c) to0 many parameters.

Maybe look at the extrapolation methods.

sessionInfo()

R version 4.2.2 Patched (2022-11-10 r83330)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.1 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so

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

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

other attached packages:
[1] stm_1.1.8       workflowr_1.7.0

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.9         horseshoe_0.2.0    invgamma_1.1       lattice_0.20-45   
 [5] NNLM_0.4.4         getPass_0.2-2      ps_1.7.2           rprojroot_2.0.3   
 [9] digest_0.6.31      utf8_1.2.2         truncnorm_1.0-8    R6_2.5.1          
[13] evaluate_0.19      highr_0.9          httr_1.4.4         ggplot2_3.4.0     
[17] pillar_1.8.1       rlang_1.0.6        wavethresh_4.7.2   data.table_1.14.6 
[21] rstudioapi_0.14    ebnm_1.0-11        irlba_2.3.5.1      nloptr_2.0.3      
[25] whisker_0.4.1      callr_3.7.3        jquerylib_0.1.4    Matrix_1.5-3      
[29] rmarkdown_2.19     splines_4.2.2      smashr_1.3-6       stringr_1.5.0     
[33] munsell_0.5.0      mixsqp_0.3-48      compiler_4.2.2     httpuv_1.6.7      
[37] xfun_0.35          pkgconfig_2.0.3    SQUAREM_2021.1     htmltools_0.5.4   
[41] tidyselect_1.2.0   tibble_3.1.8       matrixStats_0.63.0 fansi_1.0.3       
[45] dplyr_1.0.10       later_1.3.0        MASS_7.3-58.1      bitops_1.0-7      
[49] grid_4.2.2         jsonlite_1.8.4     gtable_0.3.1       lifecycle_1.0.3   
[53] git2r_0.30.1       magrittr_2.0.3     scales_1.2.1       cli_3.4.1         
[57] stringi_1.7.8      cachem_1.0.6       ebpm_0.0.1.3       fs_1.5.2          
[61] promises_1.2.0.1   flashier_0.2.34    bslib_0.4.2        vctrs_0.5.1       
[65] generics_0.1.3     trust_0.1-8        tools_4.2.2        softImpute_1.4-1  
[69] glue_1.6.2         parallel_4.2.2     processx_3.8.0     fastmap_1.1.0     
[73] yaml_2.3.6         vebpm_0.3.7        colorspace_2.0-3   ashr_2.2-54       
[77] caTools_1.18.2     deconvolveR_1.2-1  knitr_1.41         sass_0.4.4

An attempt to speed up flash add greedy

DongyueXie

2022-12-27

Introduction

new init

previous init

other thoughts