Last updated: 2023-02-09

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Introduction

Recall the model is

\[y_{ij}\sim Poisson(l_{i0}f_{j0}\exp(\sum_k l_{ik}f_{jk}+\epsilon_{ij}).\]

I compare the fit between fix \(f_{j0} = y_{+j}/\sqrt{y_{++}}\), and update \(f_{j0}\).

ALL other parameters are the same.

When estimating \(f_{j0}\), I got an error saying:

running initial flash fit
Running iterations...
iter 10, elbo=-18401566.4360083, K=8
iter 20, elbo=-17763539.8435548, K=8
iter 30, elbo=-17393989.0758334, K=8
Error in (function (f, p, ..., hessian = FALSE, typsize = rep(1, length(p)),  : 
  missing value in parameter
Calls: ebpmf_log ... parametric_workhorse -> mle_parametric -> do.call -> <Anonymous>
In addition: Warning message:
In handle_standard_errors(x, s) :
  Nonpositive SEs have been replaced by small positive SEs.
Execution halted

My general impression is that the point exponential prior implementation in ebnm is less stable, and can yield less desirable results, but much faster, when comparing to unimodal nonnegative prior.

Since I only got results from first 30 iterations, I’ll compare the 30th iterations results.

source('code/poisson_STM/plot_factors_general.R')
source('code/poisson_STM/structure_plot.R')
library(fastTopics)
library(Matrix)
library(stm)
data(pbmc_facs)

fix f0

fit = readRDS(paste('output/pbmc3k_iteration_results/ebpmf_pbmc3k_nonnegLF_pe_vga3_iter',30,'.rds',sep=''))
plt = plot.factors.general(fit$fit_flash$L.pm,pbmc_facs$samples$subpop,title=paste('pbmc3k nonneg L F iteration',30))
print(plt)

Version Author Date
3e1fad0 DongyueXie 2023-02-09 
fit$elbo
[1] -19765312
structure_plot_general(fit$fit_flash$L.pm,fit$fit_flash$F.pm,pbmc_facs$samples$subpop)
Running tsne on 417 x 7 matrix.
Read the 417 x 7 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.07 seconds (sparsity = 0.873557)!
Learning embedding...
Iteration 50: error is 42.997166 (50 iterations in 0.04 seconds)
Iteration 100: error is 41.868908 (50 iterations in 0.03 seconds)
Iteration 150: error is 41.868062 (50 iterations in 0.03 seconds)
Iteration 200: error is 41.868149 (50 iterations in 0.04 seconds)
Iteration 250: error is 41.868091 (50 iterations in 0.03 seconds)
Iteration 300: error is 0.090940 (50 iterations in 0.03 seconds)
Iteration 350: error is 0.090530 (50 iterations in 0.03 seconds)
Iteration 400: error is 0.090535 (50 iterations in 0.03 seconds)
Iteration 450: error is 0.090537 (50 iterations in 0.03 seconds)
Iteration 500: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 550: error is 0.090537 (50 iterations in 0.03 seconds)
Iteration 600: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 650: error is 0.090537 (50 iterations in 0.03 seconds)
Iteration 700: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 750: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 800: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 850: error is 0.090537 (50 iterations in 0.03 seconds)
Iteration 900: error is 0.090535 (50 iterations in 0.03 seconds)
Iteration 950: error is 0.090538 (50 iterations in 0.03 seconds)
Iteration 1000: error is 0.090538 (50 iterations in 0.03 seconds)
Fitting performed in 0.61 seconds.
Running tsne on 91 x 7 matrix.
Read the 91 x 7 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 29.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.00 seconds (sparsity = 0.987320)!
Learning embedding...
Iteration 50: error is 53.493352 (50 iterations in 0.01 seconds)
Iteration 100: error is 48.356461 (50 iterations in 0.00 seconds)
Iteration 150: error is 49.518330 (50 iterations in 0.00 seconds)
Iteration 200: error is 48.106554 (50 iterations in 0.00 seconds)
Iteration 250: error is 47.422229 (50 iterations in 0.00 seconds)
Iteration 300: error is 1.112187 (50 iterations in 0.00 seconds)
Iteration 350: error is 0.697176 (50 iterations in 0.00 seconds)
Iteration 400: error is 0.690709 (50 iterations in 0.00 seconds)
Iteration 450: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 500: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 550: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 600: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 650: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 700: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 750: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 800: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 850: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 900: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 950: error is 0.690712 (50 iterations in 0.00 seconds)
Iteration 1000: error is 0.690712 (50 iterations in 0.00 seconds)
Fitting performed in 0.06 seconds.
Running tsne on 358 x 7 matrix.
Read the 358 x 7 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.06 seconds (sparsity = 0.951437)!
Learning embedding...
Iteration 50: error is 44.073232 (50 iterations in 0.03 seconds)
Iteration 100: error is 41.466782 (50 iterations in 0.03 seconds)
Iteration 150: error is 41.448750 (50 iterations in 0.03 seconds)
Iteration 200: error is 41.448801 (50 iterations in 0.03 seconds)
Iteration 250: error is 41.448774 (50 iterations in 0.03 seconds)
Iteration 300: error is 0.073591 (50 iterations in 0.03 seconds)
Iteration 350: error is 0.072700 (50 iterations in 0.02 seconds)
Iteration 400: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 450: error is 0.072698 (50 iterations in 0.03 seconds)
Iteration 500: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 550: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 600: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 650: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 700: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 750: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 800: error is 0.072699 (50 iterations in 0.03 seconds)
Iteration 850: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 900: error is 0.072698 (50 iterations in 0.02 seconds)
Iteration 950: error is 0.072699 (50 iterations in 0.02 seconds)
Iteration 1000: error is 0.072699 (50 iterations in 0.02 seconds)
Fitting performed in 0.49 seconds.
Running tsne on 359 x 7 matrix.
Read the 359 x 7 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.05 seconds (sparsity = 0.952631)!
Learning embedding...
Iteration 50: error is 41.095007 (50 iterations in 0.03 seconds)
Iteration 100: error is 40.915822 (50 iterations in 0.02 seconds)
Iteration 150: error is 40.915712 (50 iterations in 0.02 seconds)
Iteration 200: error is 40.915706 (50 iterations in 0.02 seconds)
Iteration 250: error is 40.915701 (50 iterations in 0.02 seconds)
Iteration 300: error is 0.074192 (50 iterations in 0.02 seconds)
Iteration 350: error is 0.074106 (50 iterations in 0.02 seconds)
Iteration 400: error is 0.074102 (50 iterations in 0.02 seconds)
Iteration 450: error is 0.074105 (50 iterations in 0.02 seconds)
Iteration 500: error is 0.074103 (50 iterations in 0.03 seconds)
Iteration 550: error is 0.074103 (50 iterations in 0.02 seconds)
Iteration 600: error is 0.074103 (50 iterations in 0.02 seconds)
Iteration 650: error is 0.074102 (50 iterations in 0.02 seconds)
Iteration 700: error is 0.074103 (50 iterations in 0.02 seconds)
Iteration 750: error is 0.074103 (50 iterations in 0.03 seconds)
Iteration 800: error is 0.074102 (50 iterations in 0.02 seconds)
Iteration 850: error is 0.074103 (50 iterations in 0.02 seconds)
Iteration 900: error is 0.074103 (50 iterations in 0.03 seconds)
Iteration 950: error is 0.074103 (50 iterations in 0.03 seconds)
Iteration 1000: error is 0.074103 (50 iterations in 0.02 seconds)
Fitting performed in 0.48 seconds.
Running tsne on 775 x 7 matrix.
Read the 775 x 7 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.12 seconds (sparsity = 0.498091)!
Learning embedding...
Iteration 50: error is 45.482085 (50 iterations in 0.07 seconds)
Iteration 100: error is 41.615579 (50 iterations in 0.06 seconds)
Iteration 150: error is 41.017730 (50 iterations in 0.07 seconds)
Iteration 200: error is 40.805126 (50 iterations in 0.06 seconds)
Iteration 250: error is 40.708478 (50 iterations in 0.06 seconds)
Iteration 300: error is 0.183027 (50 iterations in 0.06 seconds)
Iteration 350: error is 0.125610 (50 iterations in 0.06 seconds)
Iteration 400: error is 0.116738 (50 iterations in 0.06 seconds)
Iteration 450: error is 0.114335 (50 iterations in 0.07 seconds)
Iteration 500: error is 0.113508 (50 iterations in 0.06 seconds)
Iteration 550: error is 0.113136 (50 iterations in 0.06 seconds)
Iteration 600: error is 0.112980 (50 iterations in 0.07 seconds)
Iteration 650: error is 0.112861 (50 iterations in 0.06 seconds)
Iteration 700: error is 0.112738 (50 iterations in 0.06 seconds)
Iteration 750: error is 0.112710 (50 iterations in 0.06 seconds)
Iteration 800: error is 0.112659 (50 iterations in 0.06 seconds)
Iteration 850: error is 0.112640 (50 iterations in 0.06 seconds)
Iteration 900: error is 0.112656 (50 iterations in 0.06 seconds)
Iteration 950: error is 0.112646 (50 iterations in 0.06 seconds)
Iteration 1000: error is 0.112634 (50 iterations in 0.06 seconds)
Fitting performed in 1.26 seconds.

f00 = colSums(pbmc_facs$counts)/sqrt(sum(pbmc_facs$counts))

update f0

fit = readRDS(paste('output/pbmc3k_iteration_results/ebpmf_pbmc3k_nonnegLF_pe_vga3_est_f0_iter30.rds'))
plt = plot.factors.general(fit$fit_flash$L.pm,pbmc_facs$samples$subpop,title=paste('pbmc3k update f0 nonneg L F iteration',30))
print(plt)

Version Author Date
3e1fad0 DongyueXie 2023-02-09 
fit$elbo
[1] -19580914
structure_plot_general(fit$fit_flash$L.pm,fit$fit_flash$F.pm,pbmc_facs$samples$subpop)
Running tsne on 417 x 8 matrix.
Read the 417 x 8 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.07 seconds (sparsity = 0.875306)!
Learning embedding...
Iteration 50: error is 45.701851 (50 iterations in 0.04 seconds)
Iteration 100: error is 41.959043 (50 iterations in 0.03 seconds)
Iteration 150: error is 41.904270 (50 iterations in 0.03 seconds)
Iteration 200: error is 41.903176 (50 iterations in 0.03 seconds)
Iteration 250: error is 41.903098 (50 iterations in 0.04 seconds)
Iteration 300: error is 0.092093 (50 iterations in 0.03 seconds)
Iteration 350: error is 0.087865 (50 iterations in 0.03 seconds)
Iteration 400: error is 0.087711 (50 iterations in 0.03 seconds)
Iteration 450: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 500: error is 0.087729 (50 iterations in 0.03 seconds)
Iteration 550: error is 0.087731 (50 iterations in 0.03 seconds)
Iteration 600: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 650: error is 0.087731 (50 iterations in 0.03 seconds)
Iteration 700: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 750: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 800: error is 0.087731 (50 iterations in 0.03 seconds)
Iteration 850: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 900: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 950: error is 0.087732 (50 iterations in 0.03 seconds)
Iteration 1000: error is 0.087732 (50 iterations in 0.03 seconds)
Fitting performed in 0.58 seconds.
Running tsne on 91 x 8 matrix.
Read the 91 x 8 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 29.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.00 seconds (sparsity = 0.986837)!
Learning embedding...
Iteration 50: error is 49.735471 (50 iterations in 0.00 seconds)
Iteration 100: error is 48.569182 (50 iterations in 0.00 seconds)
Iteration 150: error is 50.621830 (50 iterations in 0.00 seconds)
Iteration 200: error is 50.788143 (50 iterations in 0.00 seconds)
Iteration 250: error is 52.077153 (50 iterations in 0.00 seconds)
Iteration 300: error is 1.641253 (50 iterations in 0.00 seconds)
Iteration 350: error is 0.800636 (50 iterations in 0.00 seconds)
Iteration 400: error is 0.796971 (50 iterations in 0.00 seconds)
Iteration 450: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 500: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 550: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 600: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 650: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 700: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 750: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 800: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 850: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 900: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 950: error is 0.796977 (50 iterations in 0.00 seconds)
Iteration 1000: error is 0.796977 (50 iterations in 0.00 seconds)
Fitting performed in 0.06 seconds.
Running tsne on 358 x 8 matrix.
Read the 358 x 8 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.05 seconds (sparsity = 0.950953)!
Learning embedding...
Iteration 50: error is 43.493234 (50 iterations in 0.03 seconds)
Iteration 100: error is 43.493234 (50 iterations in 0.03 seconds)
Iteration 150: error is 43.493234 (50 iterations in 0.03 seconds)
Iteration 200: error is 43.493234 (50 iterations in 0.03 seconds)
Iteration 250: error is 43.493234 (50 iterations in 0.03 seconds)
Iteration 300: error is 0.164546 (50 iterations in 0.03 seconds)
Iteration 350: error is 0.160839 (50 iterations in 0.02 seconds)
Iteration 400: error is 0.159392 (50 iterations in 0.03 seconds)
Iteration 450: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 500: error is 0.159391 (50 iterations in 0.02 seconds)
Iteration 550: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 600: error is 0.159391 (50 iterations in 0.02 seconds)
Iteration 650: error is 0.159391 (50 iterations in 0.02 seconds)
Iteration 700: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 750: error is 0.159391 (50 iterations in 0.02 seconds)
Iteration 800: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 850: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 900: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 950: error is 0.159392 (50 iterations in 0.02 seconds)
Iteration 1000: error is 0.159392 (50 iterations in 0.02 seconds)
Fitting performed in 0.51 seconds.
Running tsne on 359 x 8 matrix.
Read the 359 x 8 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.05 seconds (sparsity = 0.952615)!
Learning embedding...
Iteration 50: error is 43.105018 (50 iterations in 0.03 seconds)
Iteration 100: error is 41.222909 (50 iterations in 0.03 seconds)
Iteration 150: error is 41.222379 (50 iterations in 0.02 seconds)
Iteration 200: error is 41.222379 (50 iterations in 0.02 seconds)
Iteration 250: error is 41.222380 (50 iterations in 0.02 seconds)
Iteration 300: error is 0.090568 (50 iterations in 0.02 seconds)
Iteration 350: error is 0.090346 (50 iterations in 0.02 seconds)
Iteration 400: error is 0.090346 (50 iterations in 0.02 seconds)
Iteration 450: error is 0.090345 (50 iterations in 0.02 seconds)
Iteration 500: error is 0.090345 (50 iterations in 0.03 seconds)
Iteration 550: error is 0.090346 (50 iterations in 0.03 seconds)
Iteration 600: error is 0.090346 (50 iterations in 0.04 seconds)
Iteration 650: error is 0.090346 (50 iterations in 0.04 seconds)
Iteration 700: error is 0.090346 (50 iterations in 0.02 seconds)
Iteration 750: error is 0.090346 (50 iterations in 0.03 seconds)
Iteration 800: error is 0.090345 (50 iterations in 0.03 seconds)
Iteration 850: error is 0.090346 (50 iterations in 0.03 seconds)
Iteration 900: error is 0.090346 (50 iterations in 0.03 seconds)
Iteration 950: error is 0.090345 (50 iterations in 0.03 seconds)
Iteration 1000: error is 0.090345 (50 iterations in 0.04 seconds)
Fitting performed in 0.58 seconds.
Running tsne on 775 x 8 matrix.
Read the 775 x 8 data matrix successfully!
OpenMP is working. 1 threads.
Using no_dims = 1, perplexity = 100.000000, and theta = 0.100000
Computing input similarities...
Building tree...
Done in 0.15 seconds (sparsity = 0.500172)!
Learning embedding...
Iteration 50: error is 46.009739 (50 iterations in 0.07 seconds)
Iteration 100: error is 43.831645 (50 iterations in 0.06 seconds)
Iteration 150: error is 43.565172 (50 iterations in 0.09 seconds)
Iteration 200: error is 43.487247 (50 iterations in 0.09 seconds)
Iteration 250: error is 43.457697 (50 iterations in 0.06 seconds)
Iteration 300: error is 0.240611 (50 iterations in 0.07 seconds)
Iteration 350: error is 0.186438 (50 iterations in 0.09 seconds)
Iteration 400: error is 0.178554 (50 iterations in 0.09 seconds)
Iteration 450: error is 0.176758 (50 iterations in 0.07 seconds)
Iteration 500: error is 0.176225 (50 iterations in 0.06 seconds)
Iteration 550: error is 0.176036 (50 iterations in 0.06 seconds)
Iteration 600: error is 0.175941 (50 iterations in 0.06 seconds)
Iteration 650: error is 0.175917 (50 iterations in 0.06 seconds)
Iteration 700: error is 0.175878 (50 iterations in 0.06 seconds)
Iteration 750: error is 0.175807 (50 iterations in 0.07 seconds)
Iteration 800: error is 0.175806 (50 iterations in 0.06 seconds)
Iteration 850: error is 0.175784 (50 iterations in 0.08 seconds)
Iteration 900: error is 0.175774 (50 iterations in 0.08 seconds)
Iteration 950: error is 0.175774 (50 iterations in 0.06 seconds)
Iteration 1000: error is 0.175777 (50 iterations in 0.07 seconds)
Fitting performed in 1.44 seconds.

plot(f00,fit$f0,xlab='init f0',ylab='fitted f0',main='fixed vs updated')
abline(a=0,b=1,lty=2)


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          Matrix_1.5-3       fastTopics_0.6-142 ggplot2_3.4.0     
[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    fs_1.5.2           rstudioapi_0.14   
 [10] farver_2.1.1       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 fastmap_1.1.0     
 [28] lazyeval_0.2.2     cli_3.4.1          later_1.3.0       
 [31] htmltools_0.5.4    quantreg_5.94      prettyunits_1.1.1 
 [34] tools_4.2.2        coda_0.19-4        gtable_0.3.1      
 [37] glue_1.6.2         reshape2_1.4.4     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      sass_0.4.4         stringi_1.7.8     
 [64] SQUAREM_2021.1     highr_0.9          deconvolveR_1.2-1 
 [67] foreach_1.5.2      caTools_1.18.2     truncnorm_1.0-8   
 [70] shape_1.4.6        horseshoe_0.2.0    rlang_1.0.6       
 [73] pkgconfig_2.0.3    matrixStats_0.63.0 bitops_1.0-7      
 [76] ebnm_1.0-11        evaluate_0.19      lattice_0.20-45   
 [79] invgamma_1.1       purrr_0.3.5        labeling_0.4.2    
 [82] htmlwidgets_1.6.0  Rfast_2.0.6        cowplot_1.1.1     
 [85] processx_3.8.0     tidyselect_1.2.0   plyr_1.8.8        
 [88] magrittr_2.0.3     R6_2.5.1           generics_0.1.3    
 [91] pillar_1.8.1       whisker_0.4.1      withr_2.5.0       
 [94] survival_3.5-0     mixsqp_0.3-48      tibble_3.1.8      
 [97] crayon_1.5.2       utf8_1.2.2         plotly_4.10.1     
[100] rmarkdown_2.19     progress_1.2.2     grid_4.2.2        
[103] data.table_1.14.6  callr_3.7.3        git2r_0.30.1      
[106] digest_0.6.31      vebpm_0.4.0        tidyr_1.2.1       
[109] httpuv_1.6.7       MCMCpack_1.6-3     RcppParallel_5.1.5
[112] munsell_0.5.0      glmnet_4.1-6       viridisLite_0.4.1 
[115] flashier_0.2.34    bslib_0.4.2        quadprog_1.5-8