Last updated: 2021-04-10

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Knit directory: fastTopics-experiments/analysis/

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

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

library(fastTopics)
library(ggplot2)
library(cowplot)

Load the results of running fit_poisson_nmf on the droplet data, with different algorithms, and for various settings of \(K\).

load("../output/droplet/fits-droplet.RData")
fits <- lapply(fits,poisson2multinom)

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
c0cbe8c Peter Carbonetto 2021-04-07

The next set of plots shows the improvement in the fit over time, for \(K\) from 2 to 12, using EM or 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.

prune_prefit_iters <- function (fit) {
  n <- nrow(fit$progress)
  fit$progress <- fit$progress[1000:n,]
  fit$progress <- transform(fit$progress,timing = timing/60^2)
  return(fit)
}
create_progress_plot <- function (fits, k, y = "loglik")
  plot_progress(fits,y = y,add.point.every = 100,shapes = 21,
                colors = c("dodgerblue","red","dodgerblue","red"),
                fills = c("dodgerblue","red","white","white")) +
  scale_y_continuous(trans = "log10",breaks = 10^seq(-8,8)) +
  guides(color = "none",fill = "none",size = "none",
         shape = "none",linetype = "none") +
  labs(x = "runtime (h)",title = paste("K =",k)) +
  theme_cowplot(font_size = 10) +
  theme(plot.title = element_text(size = 10,face = "plain"))
fits <- lapply(fits,prune_prefit_iters)
p <- vector("list",12)
for (i in 2:12)
  p[[i]] <- create_progress_plot(fits[dat$k == i],i)
p[[2]] <- p[[2]] + scale_y_continuous()
p[[3]] <- p[[3]] + scale_y_continuous()
p[[4]] <- p[[4]] + scale_y_continuous()
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
          p[[6]],p[[7]],p[[8]],p[[9]],
          p[[10]],p[[11]],p[[12]],
          nrow = 3,ncol = 4)

Version Author Date
c81db07 Peter Carbonetto 2021-04-07
c0cbe8c Peter Carbonetto 2021-04-07

These plots shows the evolution of the KKT residuals over time.

for (i in 2:12)
  p[[i]] <- create_progress_plot(fits[dat$k == i],i,y = "res")
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
          p[[6]],p[[7]],p[[8]],p[[9]],
          p[[10]],p[[11]],p[[12]],
          nrow = 3,ncol = 4)

Version Author Date
c0cbe8c Peter Carbonetto 2021-04-07

For the most part, the EM and CD algorithms achieve similar estimates in this data set. For example, for \(K = 7\), the difference in the topic model likelihoods between the EM and CD estimates is very small, and indeed the estimated topic proportions are nearly identical:

fit1 <- fits[["fit-droplet-em-k=7"]]
fit2 <- fits[["fit-droplet-scd-k=7"]]
pdat <- data.frame(x = as.vector(fit1$L),y = as.vector(fit2$L))
p1 <- ggplot(pdat,aes(x = x,y = y)) +
  geom_point(shape = 21,size = 2,color = "white",fill = "royalblue") +
  geom_abline(color = "black",linetype = "dotted") +
  labs(x = "EM estimate",y = "CD estimate") +
  theme_cowplot(font_size = 12)
print(p1)


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_0.5-24
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.5           invgamma_1.1        
#  [4] lattice_0.20-38      tidyr_1.0.0          prettyunits_1.1.1   
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# [37] pkgconfig_2.0.3      SQUAREM_2017.10-1    mcmc_0.9-6          
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# [49] later_1.0.0          MASS_7.3-51.4        grid_3.6.2          
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# [64] tools_3.6.2          glue_1.3.1           purrr_0.3.3         
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