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html | 1f86ead | Peter Carbonetto | 2024-07-28 | Added ELBO plots to assess_fits_newsgroups 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(Matrix)
library(fastTopics)
library(ggplot2)
library(cowplot)
library(ggrepel)
set.seed(1)
source("../code/plot_functions.R")
Load the newsgroups data, and the results of running
fit_poisson_nmf
on the “20 newsgroups” data, with different
algorithms, and for various settings of \(K\). Also load the results of running LDA
with different initializations.
load("../data/newsgroups.RData")
load("../output/newsgroups/fits-newsgroups.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)
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)
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$k == i],i,y = "res")
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
p[[6]],p[[7]],p[[8]],p[[9]],
p[[10]],p[[11]],p[[12]],
nrow = 3,ncol = 4)
An example in which the EM and (extrapolated) CD estimates largely agree:
topic_colors <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99",
"#e31a1c","#fdbf6f","#ff7f00","#cab2d6","#6a3d9a")
fit1 <- fits[["fit-newsgroups-em-k=9"]]
fit2 <- fits[["fit-newsgroups-scd-ex-k=9"]]
n <- nrow(fit1$L)
pdat <- data.frame(x = as.vector(fit1$L),
y = as.vector(fit2$L),
k = factor(rep(1:9,each = n)))
pdat <- pdat[sample(9*n),]
p1 <- ggplot(pdat,aes(x = x,y = y,fill = k)) +
geom_point(color = "white",shape = 21,size = 2) +
geom_abline(color = "black",linetype = "dotted") +
scale_fill_manual(values = topic_colors) +
labs(x = "EM estimate",y = "extrapolated CD estimate") +
theme_cowplot(font_size = 12)
print(p1)
An example in which the EM and (extrapolated) CD estimates greatly differ:
fit1 <- fits[["fit-newsgroups-em-k=10"]]
fit2 <- fits[["fit-newsgroups-scd-ex-k=10"]]
n <- nrow(fit1$L)
pdat <- data.frame(x = as.vector(fit1$L),
y = as.vector(fit2$L),
k = factor(rep(1:10,each = n)))
pdat <- pdat[sample(10*n),]
p2 <- ggplot(pdat,aes(x = x,y = y,fill = k)) +
geom_point(color = "white",shape = 21,size = 2) +
geom_abline(color = "black",linetype = "dotted") +
scale_fill_manual(values = topic_colors) +
labs(x = "EM estimate",y = "extrapolated CD estimate") +
theme_cowplot(font_size = 12)
print(p2)
For a closer look at the \(K = 10\) (extrapolated) CD estimates, we create a Structure plot:
set.seed(1)
topics <- factor(topics,
c("sci.med","rec.autos","rec.motorcycles","alt.atheism",
"soc.religion.christian","talk.religion.misc",
"rec.sport.baseball","rec.sport.hockey",
"talk.politics.mideast","talk.politics.guns","sci.crypt",
"talk.politics.misc","sci.space","sci.electronics",
"misc.forsale","comp.sys.ibm.pc.hardware",
"comp.sys.mac.hardware","comp.os.ms-windows.misc",
"comp.graphics","comp.windows.x"))
topic_colors <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99",
"#e31a1c","#fdbf6f","#ff7f00","#cab2d6","#6a3d9a")
fit <- fits[["fit-newsgroups-scd-ex-k=10"]]
p3 <- structure_plot(fit,grouping = topics,topics = 10:1,
colors = topic_colors[10:1],perplexity = 20,gap = 20,
verbose = FALSE)
print(p3)
Topic 1 appears to be capturing “off-topic” discussion:
pdat <- data.frame(word = colnames(counts),
x = pmax(1e-6,apply(fit$F[,-1],1,max)),
y = pmax(1e-6,fit$F[,1]),
stringsAsFactors = FALSE)
pdat <- transform(pdat,fc = y/x)
pdat[with(pdat,!((fc > 4 & x > 1e-5) | (fc > 2 & x > 0.002))),"word"] <- ""
p4 <- ggplot(pdat,aes(x = x,y = y,label = word)) +
geom_point(color = "white",fill = "royalblue",shape = 21) +
geom_text_repel(color = "darkgray",size = 2.25,segment.color = "darkgray",
segment.size = 0.25,min.segment.length = 0,
max.overlaps = Inf) +
geom_abline(intercept = 0,slope = 1,color = "black",linetype = "dotted") +
scale_x_continuous(trans = "log10",limits=10^c(-6,-1),breaks=10^seq(-6,-1)) +
scale_y_continuous(trans = "log10",limits=10^c(-6,-1),breaks=10^seq(-6,-1)) +
labs(x = "highest frequency in another topic",
y = "frequency in topic 1") +
theme_cowplot(font_size = 10)
print(p4)
Finally, let’s have a look at the results of running LDA with the various initializations:
load("../output/newsgroups/lda-newsgroups.RData")
p <- vector("list",12)
runs <- which(dat$k == 2)
p[[1]] <- create_elbo_plot(fits[runs],dat[runs,"runtime"],2)
for (i in 2:12) {
runs <- which(dat$k == i)
p[[i]] <- create_elbo_plot(fits[runs],dat[runs,"runtime"],i) +
guides(color = "none",linetype = "none")
}
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
p[[6]],p[[7]],p[[8]],p[[9]],
p[[10]],p[[11]],p[[12]],p[[1]],
nrow = 3,ncol = 4)
Version | Author | Date |
---|---|---|
1f86ead | Peter Carbonetto | 2024-07-28 |
sessionInfo()
# R version 4.3.3 (2024-02-29)
# Platform: aarch64-apple-darwin20 (64-bit)
# Running under: macOS Sonoma 14.5
#
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
#
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#
# time zone: America/Chicago
# tzcode source: internal
#
# attached base packages:
# [1] stats graphics grDevices utils datasets methods base
#
# other attached packages:
# [1] ggrepel_0.9.5 cowplot_1.1.3 ggplot2_3.5.0 fastTopics_0.6-184
# [5] Matrix_1.6-5
#
# loaded via a namespace (and not attached):
# [1] gtable_0.3.4 xfun_0.42 bslib_0.6.1
# [4] htmlwidgets_1.6.4 lattice_0.22-5 quadprog_1.5-8
# [7] vctrs_0.6.5 tools_4.3.3 generics_0.1.3
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# [13] highr_0.10 pkgconfig_2.0.3 data.table_1.15.2
# [16] SQUAREM_2021.1 RcppParallel_5.1.7 lifecycle_1.0.4
# [19] truncnorm_1.0-9 farver_2.1.1 compiler_4.3.3
# [22] stringr_1.5.1 git2r_0.33.0 textshaping_0.3.7
# [25] progress_1.2.3 munsell_0.5.0 RhpcBLASctl_0.23-42
# [28] httpuv_1.6.14 htmltools_0.5.7 sass_0.4.8
# [31] yaml_2.3.8 lazyeval_0.2.2 plotly_4.10.4
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# [37] jquerylib_0.1.4 whisker_0.4.1 tidyr_1.3.1
# [40] uwot_0.1.16 cachem_1.0.8 gtools_3.9.5
# [43] tidyselect_1.2.1 digest_0.6.34 Rtsne_0.17
# [46] stringi_1.8.3 dplyr_1.1.4 purrr_1.0.2
# [49] ashr_2.2-66 labeling_0.4.3 rprojroot_2.0.4
# [52] fastmap_1.1.1 grid_4.3.3 colorspace_2.1-0
# [55] cli_3.6.2 invgamma_1.1 magrittr_2.0.3
# [58] utf8_1.2.4 withr_3.0.0 prettyunits_1.2.0
# [61] scales_1.3.0 promises_1.2.1 rmarkdown_2.26
# [64] httr_1.4.7 workflowr_1.7.1 ragg_1.2.7
# [67] hms_1.1.3 pbapply_1.7-2 evaluate_0.23
# [70] knitr_1.45 viridisLite_0.4.2 irlba_2.3.5.1
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