Last updated: 2020-11-14

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Knit directory: single-cell-topics/analysis/

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Rmd 9419a6c Peter Carbonetto 2020-11-14 A couple small revisions to the progress plots.
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html c8ab215 Peter Carbonetto 2020-11-14 Adjusted progress plots in assess_fits_droplet.
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Rmd 68d8a4a Peter Carbonetto 2020-08-09 Added comments and made minor adjustments to create_progress_plots.
Rmd 94c632a Peter Carbonetto 2020-08-09 Working on assess_fits_droplet analysis.

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 droplet data, with different algorithms, and for various settings of \(K\) (the number of topics, or equivalently the dimension of the matrix factorization).

load("../output/droplet/fits-droplet.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
e15be6f Peter Carbonetto 2020-10-26
bc18c04 Peter Carbonetto 2020-08-09
b8a783d Peter Carbonetto 2020-08-09

Oddly, the likelihood did not improve from 4 to 5, and same from 8 to 9. Otherwise, the likelihood improved with larger rank, \(K\).

The next set of plots shows the improvement in the fit over time, for \(K\) from 2 to 13, and for each of the three updates (EM, CCD, SCD) with and without extrapolation. 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
15a4c62 Peter Carbonetto 2020-11-14
c8ab215 Peter Carbonetto 2020-11-14
6703ed1 Peter Carbonetto 2020-11-14
e66e2c5 Peter Carbonetto 2020-11-13
f970ef9 Peter Carbonetto 2020-08-31
bc18c04 Peter Carbonetto 2020-08-09
b8a783d Peter Carbonetto 2020-08-09

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
15a4c62 Peter Carbonetto 2020-11-14
c8ab215 Peter Carbonetto 2020-11-14
6703ed1 Peter Carbonetto 2020-11-14
e66e2c5 Peter Carbonetto 2020-11-13
f970ef9 Peter Carbonetto 2020-08-31
bc18c04 Peter Carbonetto 2020-08-09
b8a783d Peter Carbonetto 2020-08-09

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# 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_0.3-184
# 
# 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_1.4.2          
# [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
# [40] quadprog_1.5-8       viridisLite_0.3.0    crayon_1.3.4        
# [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_4.4.2  
# [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