Last updated: 2020-08-31

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Knit directory: single-cell-topics/analysis/

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Here we compare the quality of the fits obtained from the different updates (EM, CCD, SCD, with and without extrapolation), and with different \(k\).

Load the packages used in the analysis below, as well as some additional functions for creating the plots.

library(fastTopics)
library(ggplot2)
library(cowplot)
source("../code/functions_for_assessing_fits.R")

Load the results of running fit_poisson_nmf on the pulse-seq data, with different algorithms, and for various choices of \(k\) (the number of “topics”).

load("../output/pulseseq/fits-pulseseq.RData")

This plot shows the improvement in the log-likelihood as the rank, \(k\), is increased. The log-likelihoods are shown relative to the log-likelihood at \(k = 2\).

plot_loglik_vs_rank(fits) +
  theme_cowplot(font_size = 12)

Version Author Date
147da1f Peter Carbonetto 2020-08-10

As expected, the likelihood consistently improves as the rank, \(k\), is increased.

The next set of plots shows the improvement in the fit over time, for all choices of \(k\), and for each of the three optimization methods (EM, CCD, SCD), with and without the extrapolation scheme. The quality of the fit is measured by the log-likelihood relative to the best log-likelihood that was identified among all methods compared.

create_progress_plots(dat,fits,"loglik")

Version Author Date
147da1f Peter Carbonetto 2020-08-10

The last set of plots shows the evolution of the KKT residuals over time; the KKT residuals should vanish near a stationary point of the log-likelihood, so looking at the largest KKT residual can be used to assess how close we are to a solution. Note that, unlike the log-likelihood, the KKT residuals are not expected to decrease monotonically over time.

create_progress_plots(dat,fits,"res")

Version Author Date
147da1f Peter Carbonetto 2020-08-10 

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.6
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] cowplot_1.0.0      ggplot2_3.3.0      fastTopics_0.3-165
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.5           lattice_0.20-38     
#  [4] tidyr_1.0.0          prettyunits_1.1.1    assertthat_0.2.1    
#  [7] zeallot_0.1.0        rprojroot_1.3-2      digest_0.6.23       
# [10] R6_2.4.1             backports_1.1.5      MatrixModels_0.4-1  
# [13] evaluate_0.14        coda_0.19-3          httr_1.4.1          
# [16] pillar_1.4.3         rlang_0.4.5          progress_1.2.2      
# [19] lazyeval_0.2.2       data.table_1.12.8    irlba_2.3.3         
# [22] SparseM_1.78         whisker_0.4          Matrix_1.2-18       
# [25] rmarkdown_2.3        labeling_0.3         Rtsne_0.15          
# [28] stringr_1.4.0        htmlwidgets_1.5.1    munsell_0.5.0       
# [31] compiler_3.6.2       httpuv_1.5.2         xfun_0.11           
# [34] pkgconfig_2.0.3      mcmc_0.9-6           htmltools_0.4.0     
# [37] tidyselect_0.2.5     tibble_2.1.3         workflowr_1.6.2.9000
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# [43] dplyr_0.8.3          withr_2.1.2          later_1.0.0         
# [46] MASS_7.3-51.4        grid_3.6.2           jsonlite_1.6        
# [49] gtable_0.3.0         lifecycle_0.1.0      git2r_0.26.1        
# [52] magrittr_1.5         scales_1.1.0         RcppParallel_5.0.2  
# [55] stringi_1.4.3        farver_2.0.1         fs_1.3.1            
# [58] promises_1.1.0       vctrs_0.2.1          tools_3.6.2         
# [61] glue_1.3.1           purrr_0.3.3          hms_0.5.2           
# [64] yaml_2.2.0           colorspace_1.4-1     plotly_4.9.2        
# [67] knitr_1.26           quantreg_5.54        MCMCpack_1.4-5