Last updated: 2023-02-09

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Rmd 3638ec1 DongyueXie 2023-02-09 wflow_publish("analysis/example_unimodal_nonnegative_better_than_point_exponential.Rmd")

When imposing nonnegative constraint on L and F, there are two choices of priors in ebnm - unimodal nonnegative, and point exponential.

Here I show an example where unimodal nonnegative performs better in terms of recovering structure. But point exponential is much faster.

library(stm)
set.seed(12345)
N = 1000
p = 100
K = 3
sigma2 = 0.25
Ftrue = matrix(0,nrow=p,ncol=K)
Ftrue[1:20,1] = 3
Ftrue[21:40,2] = 2
Ftrue[41:60,3] = 1
Ltrue = matrix(rnorm(N*K), ncol=K)

point exponential fit

Lambda = exp(tcrossprod(abs(Ltrue),abs(Ftrue))+ matrix(rnorm(N*p,0,sqrt(sigma2)),nrow=N))
Y = matrix(rpois(N*p,Lambda),nrow=N,ncol=p)
fit = ebpmf_log(Y,verbose=TRUE,l0=1,f0=1,est_f0 = F,
                ebnm.fn = c(ebnm::ebnm_point_exponential, ebnm::ebnm_point_exponential),
                loadings_sign = 1,factors_sign = 1,maxiter = 100,printevery = 1,return_sigma2_trace = T)
Initializing M...Solving VGA for column 1...1 ...2 ...3 ...4 ...5 ...6 ...7 ...8 ...9 ...10 ...11 ...12 ...13 ...14 ...15 ...16 ...17 ...18 ...19 ...20 ...21 ...22 ...23 ...24 ...25 ...26 ...27 ...28 ...29 ...30 ...31 ...32 ...33 ...34 ...35 ...36 ...37 ...38 ...39 ...40 ...41 ...42 ...43 ...44 ...45 ...46 ...47 ...48 ...49 ...50 ...51 ...52 ...53 ...54 ...55 ...56 ...57 ...58 ...59 ...60 ...61 ...62 ...63 ...64 ...65 ...66 ...67 ...68 ...69 ...70 ...71 ...72 ...73 ...74 ...75 ...76 ...77 ...78 ...79 ...80 ...81 ...82 ...83 ...84 ...85 ...86 ...87 ...88 ...89 ...90 ...91 ...92 ...93 ...94 ...95 ...96 ...97 ...98 ...99 ...100 ...
running initial flash fit
Running iterations...
iter 1, elbo=-249456.04629, K=3
iter 2, elbo=-240237.19642, K=4
iter 3, elbo=-233476.637, K=4
iter 4, elbo=-230096.02745, K=4
iter 5, elbo=-228369.74169, K=4
  --Estimate of factor 5 is numerically zero!
  --Estimate of factor 5 is numerically zero!
iter 6, elbo=-227413.64468, K=4
  --Estimate of factor 5 is numerically zero!
  --Estimate of factor 5 is numerically zero!
iter 7, elbo=-226908.35645, K=4
  --Estimate of factor 5 is numerically zero!
  --Estimate of factor 5 is numerically zero!
iter 8, elbo=-226611.44983, K=4
iter 9, elbo=-226438.35721, K=5
  --Estimate of factor 5 is numerically zero!
  --Estimate of factor 5 is numerically zero!
iter 10, elbo=-226329.84149, K=5
iter 11, elbo=-226260.4124, K=6
iter 12, elbo=-226214.3678, K=7
iter 13, elbo=-226183.13017, K=8
iter 14, elbo=-226161.21479, K=9
iter 15, elbo=-226145.3721, K=10
iter 16, elbo=-226133.53182, K=11
iter 17, elbo=-226124.30442, K=12
iter 18, elbo=-226116.86042, K=13
iter 19, elbo=-226110.56894, K=14
iter 20, elbo=-226104.97767, K=15
  --Estimate of factor 10 is numerically zero!
  --Estimate of factor 10 is numerically zero!
iter 21, elbo=-226099.69183, K=15
  --Estimate of factor 9 is numerically zero!
iter 22, elbo=-226095.37783, K=15
iter 23, elbo=-226092.10967, K=16
iter 24, elbo=-226089.46359, K=17
iter 25, elbo=-226087.37294, K=18
iter 26, elbo=-226085.63856, K=19
iter 27, elbo=-226084.18102, K=20
iter 28, elbo=-226082.87433, K=21
iter 29, elbo=-226081.09458, K=22
  --Estimate of factor 10 is numerically zero!
  --Estimate of factor 10 is numerically zero!
for(k in 1:fit$fit_flash$n.factors){
  plot(fit$fit_flash$F.pm[,k],type='l')
}

fit$elbo
[1] -226080.7
plot(fit$fit_flash$pve)

fit$run_time
Time difference of 33.02008 secs
unlist(lapply(fit$run_time_break_down,mean))
         run_time_vga_init        run_time_flash_init 
                0.25305605                 0.53625202 
              run_time_vga run_time_flash_init_factor 
                0.03570487                 0.03501945 
     run_time_flash_greedy run_time_flash_backfitting 
                0.20070823                 0.72873402 
  run_time_flash_nullcheck 
                0.05960391

unimodal nonnegative

Lambda = exp(tcrossprod(abs(Ltrue),abs(Ftrue))+ matrix(rnorm(N*p,0,sqrt(sigma2)),nrow=N))
Y = matrix(rpois(N*p,Lambda),nrow=N,ncol=p)
fit = ebpmf_log(Y,verbose=TRUE,l0=1,f0=1,est_f0 = F,
                ebnm.fn = c(ebnm::ebnm_unimodal_nonnegative, ebnm::ebnm_unimodal_nonnegative),
                loadings_sign = 1,factors_sign = 1,maxiter = 100,printevery = 1,return_sigma2_trace = T)
Initializing M...Solving VGA for column 1...1 ...2 ...3 ...4 ...5 ...6 ...7 ...8 ...9 ...10 ...11 ...12 ...13 ...14 ...15 ...16 ...17 ...18 ...19 ...20 ...21 ...22 ...23 ...24 ...25 ...26 ...27 ...28 ...29 ...30 ...31 ...32 ...33 ...34 ...35 ...36 ...37 ...38 ...39 ...40 ...41 ...42 ...43 ...44 ...45 ...46 ...47 ...48 ...49 ...50 ...51 ...52 ...53 ...54 ...55 ...56 ...57 ...58 ...59 ...60 ...61 ...62 ...63 ...64 ...65 ...66 ...67 ...68 ...69 ...70 ...71 ...72 ...73 ...74 ...75 ...76 ...77 ...78 ...79 ...80 ...81 ...82 ...83 ...84 ...85 ...86 ...87 ...88 ...89 ...90 ...91 ...92 ...93 ...94 ...95 ...96 ...97 ...98 ...99 ...100 ...
running initial flash fit
Running iterations...
iter 1, elbo=-249763.19499, K=3
iter 2, elbo=-240554.79883, K=4
iter 3, elbo=-233788.22043, K=4
iter 4, elbo=-230402.15789, K=4
iter 5, elbo=-228629.00426, K=4
iter 6, elbo=-227637.72587, K=4
iter 7, elbo=-227103.54606, K=4
iter 8, elbo=-226783.48974, K=4
iter 9, elbo=-226591.68011, K=4
iter 10, elbo=-226468.95583, K=4
iter 11, elbo=-226390.60371, K=4
iter 12, elbo=-226340.54857, K=4
iter 13, elbo=-226306.11576, K=4
iter 14, elbo=-226280.57372, K=4
iter 15, elbo=-226262.43144, K=4
iter 16, elbo=-226249.4214, K=4
iter 17, elbo=-226240.09595, K=4
iter 18, elbo=-226233.20663, K=4
iter 19, elbo=-226227.88184, K=4
iter 20, elbo=-226223.4926, K=4
iter 21, elbo=-226219.5519, K=4
iter 22, elbo=-226216.12748, K=4
iter 23, elbo=-226213.32169, K=4
iter 24, elbo=-226211.0799, K=4
iter 25, elbo=-226209.29097, K=4
iter 26, elbo=-226207.83113, K=4
iter 27, elbo=-226206.63343, K=4
for(k in 1:fit$fit_flash$n.factors){
  plot(fit$fit_flash$F.pm[,k],type='l')
}

fit$elbo
[1] -226205.7
plot(fit$fit_flash$pve)

fit$run_time
Time difference of 2.056673 mins
unlist(lapply(fit$run_time_break_down,mean))
         run_time_vga_init        run_time_flash_init 
               0.262950659                3.614609241 
              run_time_vga run_time_flash_init_factor 
               0.030562154                0.139583826 
     run_time_flash_greedy run_time_flash_backfitting 
               0.566023827                3.514735298 
  run_time_flash_nullcheck 
               0.002779348 

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_1.3.5       workflowr_1.7.0

loaded via a namespace (and not attached):
  [1] Rtsne_0.16         ebpm_0.0.1.3       colorspace_2.0-3  
  [4] smashr_1.3-6       ellipsis_0.3.2     mr.ash_0.1-87     
  [7] rprojroot_2.0.3    fastTopics_0.6-142 fs_1.5.2          
 [10] rstudioapi_0.14    MatrixModels_0.5-1 ggrepel_0.9.2     
 [13] fansi_1.0.3        codetools_0.2-19   splines_4.2.2     
 [16] cachem_1.0.6       knitr_1.41         jsonlite_1.8.4    
 [19] nloptr_2.0.3       mcmc_0.9-7         ashr_2.2-54       
 [22] smashrgen_1.1.5    uwot_0.1.14        compiler_4.2.2    
 [25] httr_1.4.4         RcppZiggurat_0.1.6 Matrix_1.5-3      
 [28] fastmap_1.1.0      lazyeval_0.2.2     cli_3.4.1         
 [31] later_1.3.0        htmltools_0.5.4    quantreg_5.94     
 [34] prettyunits_1.1.1  tools_4.2.2        coda_0.19-4       
 [37] gtable_0.3.1       glue_1.6.2         dplyr_1.0.10      
 [40] Rcpp_1.0.9         softImpute_1.4-1   jquerylib_0.1.4   
 [43] vctrs_0.5.1        iterators_1.0.14   wavethresh_4.7.2  
 [46] xfun_0.35          stringr_1.5.0      ps_1.7.2          
 [49] trust_0.1-8        lifecycle_1.0.3    irlba_2.3.5.1     
 [52] NNLM_0.4.4         getPass_0.2-2      MASS_7.3-58.2     
 [55] scales_1.2.1       hms_1.1.2          promises_1.2.0.1  
 [58] parallel_4.2.2     SparseM_1.81       yaml_2.3.6        
 [61] pbapply_1.6-0      ggplot2_3.4.0      sass_0.4.4        
 [64] stringi_1.7.8      SQUAREM_2021.1     highr_0.9         
 [67] deconvolveR_1.2-1  foreach_1.5.2      caTools_1.18.2    
 [70] truncnorm_1.0-8    shape_1.4.6        horseshoe_0.2.0   
 [73] rlang_1.0.6        pkgconfig_2.0.3    matrixStats_0.63.0
 [76] bitops_1.0-7       ebnm_1.0-11        evaluate_0.19     
 [79] lattice_0.20-45    invgamma_1.1       purrr_0.3.5       
 [82] htmlwidgets_1.6.0  Rfast_2.0.6        cowplot_1.1.1     
 [85] processx_3.8.0     tidyselect_1.2.0   magrittr_2.0.3    
 [88] R6_2.5.1           generics_0.1.3     pillar_1.8.1      
 [91] whisker_0.4.1      withr_2.5.0        survival_3.5-0    
 [94] mixsqp_0.3-48      tibble_3.1.8       crayon_1.5.2      
 [97] utf8_1.2.2         plotly_4.10.1      rmarkdown_2.19    
[100] progress_1.2.2     grid_4.2.2         data.table_1.14.6 
[103] callr_3.7.3        git2r_0.30.1       digest_0.6.31     
[106] vebpm_0.4.0        tidyr_1.2.1        httpuv_1.6.7      
[109] MCMCpack_1.6-3     RcppParallel_5.1.5 munsell_0.5.0     
[112] glmnet_4.1-6       viridisLite_0.4.1  flashier_0.2.34   
[115] bslib_0.4.2        quadprog_1.5-8