Assess topic model fits in droplet data
Peter Carbonetto
Last updated: 2021-04-10
Checks: 7 0
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)
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
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# [1] cowplot_1.0.0 ggplot2_3.3.0 fastTopics_0.5-24
#
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