mmultinom1
Zihao
2021-07-05
Last updated: 2021-07-05
Checks: 7 0
Knit directory: ebpmf_data_analysis/
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Untracked: output/fastTopics_fit/fit_pbmc_68k_fastTopics_k10.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_fastTopics_k10.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_fastTopics_k9.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_fastTopics_k9.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k10.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k10.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k11.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k11.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k12.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k12.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k13.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k13.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k14.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k14.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k15.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k16.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k17.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k18.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k18.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k19.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k19.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k2.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k2.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k20.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k20.Rout
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k3.Rds
Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k3.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k8.Rout
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Untracked: output/fastTopics_fit/fit_pbmc_68k_simulated_fastTopics_k9.Rout
Untracked: output/fastTopics_fit/fit_sla_fastTopics_k10.Rds
Untracked: output/fastTopics_fit/fit_sla_fastTopics_k10.Rout
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Untracked: output/fastTopics_fit/fit_sla_fastTopics_k11.Rout
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Untracked: output/fastTopics_fit/fit_sla_fastTopics_k19.Rout
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Untracked: output/fastTopics_fit/fit_sla_fastTopics_k2.Rout
Untracked: output/fastTopics_fit/fit_sla_fastTopics_k20.Rds
Untracked: output/fastTopics_fit/fit_sla_fastTopics_k20.Rout
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Untracked: output/fastTopics_fit/fit_sla_fastTopics_k7.Rout
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Untracked: output/fastTopics_fit/fit_sla_fastTopics_k9.Rout
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Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_evals.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k10.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k10.Rout
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Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k11.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k12.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k12.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k13.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k13.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k13_comparison.pdf
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k14.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k14.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k15.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k15.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k16.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k16.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k17.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k17.Rout
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k18.Rds
Untracked: output/fastTopics_fit/fit_sla_sim_fastTopics_k18.Rout
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These are the previous versions of the repository in which changes were made to the R Markdown (analysis/mmultinom1.Rmd) and HTML (docs/mmultinom1.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.
| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 5c67270 | Zihao | 2021-07-05 | mmultinom1.Rmd |
The mmultinom subproblem
In PMF using EM, to estimate \(F\) we need to solve the subproblem (except we use \(E(Z_{ijk})\) instead of \(Z_{ijk}\)):
\[\begin{align} & \sum_i Z_{ijk} \sim \mathrm{Pois}(\sum_i l_{ik} f_{jk}), \ \forall k \in [K] \end{align}\]If we do some scaling so that \(\sum_j f_{jk} = 1\), and denote \(m_{jk} := \sum_i Z_{ijk}, \ n_k := \sum_i l_{ik}, \ \beta_{jk} := f_{jk}\), we have can map it to the mmultinom problem defined below (not equivalent, but 1-1 between the MLEs)
The mmultinom problem becomes hard in high-dimensional setting (when \(n_k < p\), say), and I expect MLE performs poorly in this setting. This scenario occurs in PMF when we use large \(K\), or the total number of words is too small compared to \(p\) (the data cannot support good estimation of desired number of topics)
Possible improvement by borrowing information
Perhaps in reality most words are not active in any of those topics (the same logic behind removing some words before applying models). Therefore, we can assume \(\beta_{jk} = \beta_{j0} d_{jk}\). We can estimate \(\beta_{j0}\) with all \(\sum_k n_k\) occurences of words, and then estimate each \(d_{jk}\) with \(n_k\) occurences but assuming sparsity on \(|d_{jk} - 1|\).
I haven’t figured out a prior for \(d_{jk}\) yet, but it’s much easier if we use an “equivalent” Poisson model.
Fit with MLE
Below I create situations where MLE fits poorly
rm(list = ls())
library(fastTopics)
source("code/mmultinom.R")
source("code/mmultinom_util.R")
set.seed(123)Load data
dataname = "sla"
K = 20
fitted = readRDS(sprintf("output/fastTopics_fit/fit_%s_fastTopics_k%d.Rds",
dataname, K))
m = nrow(fitted$L)Use all documents, full document length
model = fitted
data_sim = TM2mmultinom(fit = model)
fit_mle = mmultinom.mle(M = data_sim$M, n = data_sim$n)
par(mfrow = c(K/4, 4))
ce = replicate(K, 0)
for(k in 1:K){
ce[k] = cross_entropy(p1 = data_sim$beta[k,],
p2 = fit_mle[k, ])
plot(data_sim$beta[k,], fit_mle[k, ],
xlab = "beta", ylab = "betahat",
main = sprintf("topic %d", k))
abline(a = 0, b = 1, col = "blue")
}
round(ce, digits = 3) [1] 0.713 1.122 0.566 0.642 0.714 1.216 0.483 1.110 0.967 0.564 0.337
[12] 0.840 0.605 0.671 0.452 0.133 0.939 0.497 0.673 0.534sum(ce)[1] 13.77742Use less documents
Suppose we only observe 20% of the documents
model = fitted
idx = sample(x = 1:m, size = round(0.2*m))
model$L <- model$L[idx, ]
model$s <- model$s[idx]
data_sim = TM2mmultinom(fit = model)
fit_mle = mmultinom.mle(M = data_sim$M, n = data_sim$n)
par(mfrow = c(K/4, 4))
ce = replicate(K, NA)
for(k in 1:K){
ce[k] = cross_entropy(p1 = data_sim$beta[k,],
p2 = fit_mle[k, ])
plot(data_sim$beta[k,], fit_mle[k, ],
xlab = "beta", ylab = "betahat",
main = sprintf("topic %d", k))
abline(a = 0, b = 1, col = "blue")
}
round(ce, digits = 3) [1] 5.221 5.472 3.807 4.352 4.329 7.062 3.612 6.823 6.175 3.489 2.209
[12] 4.686 3.563 4.158 2.714 0.979 5.411 2.657 4.141 4.033sum(ce)[1] 84.89279use shorter & less documents
I use half of the documents and 1/5 document length
model = fitted
idx = sample(x = 1:m, size = round(0.5*m))
model$L <- model$L[idx, ]
model$s <- model$s[idx]/5
data_sim = TM2mmultinom(fit = model)
fit_mle = mmultinom.mle(M = data_sim$M, n = data_sim$n)
par(mfrow = c(K/4, 4))
ce = replicate(K, 0)
for(k in 1:K){
ce[k] = cross_entropy(p1 = data_sim$beta[k,],
p2 = fit_mle[k, ])
plot(data_sim$beta[k,], fit_mle[k, ],
xlab = "beta", ylab = "betahat",
main = sprintf("topic %d", k))
abline(a = 0, b = 1, col = "blue")
}
round(ce, digits = 3) [1] 8.407 10.991 5.788 7.206 6.437 12.731 5.199 8.643 8.910 5.562
[11] 4.305 8.768 7.329 6.528 4.833 1.981 8.200 5.609 6.239 6.033sum(ce)[1] 139.6989
sessionInfo()R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)
Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] fastTopics_0.5-53 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] ggrepel_0.9.1 Rcpp_1.0.5 invgamma_1.1
[4] lattice_0.20-38 tidyr_1.1.0 prettyunits_1.0.2
[7] assertthat_0.2.1 rprojroot_1.3-2 digest_0.6.20
[10] truncnorm_1.0-8 R6_2.4.0 backports_1.1.4
[13] MatrixModels_0.4-1 evaluate_0.14 coda_0.19-3
[16] httr_1.4.1 ggplot2_3.3.3 pillar_1.4.2
[19] rlang_0.4.10 progress_1.2.2 lazyeval_0.2.2
[22] data.table_1.13.2 irlba_2.3.3 SparseM_1.77
[25] whisker_0.3-2 Matrix_1.2-18 rmarkdown_1.13
[28] Rtsne_0.15 stringr_1.4.0 htmlwidgets_1.3
[31] uwot_0.1.5 munsell_0.5.0 mixsqp_0.3-43
[34] compiler_3.6.1 httpuv_1.5.1 xfun_0.8
[37] pkgconfig_2.0.2 SQUAREM_2017.10-1 mcmc_0.9-6
[40] htmltools_0.3.6 tidyselect_1.1.0 tibble_2.1.3
[43] quadprog_1.5-7 viridisLite_0.3.0 crayon_1.3.4
[46] dplyr_0.8.3 later_0.8.0 MASS_7.3-51.4
[49] grid_3.6.1 jsonlite_1.6 gtable_0.3.0
[52] lifecycle_0.1.0 git2r_0.26.1 magrittr_1.5
[55] scales_1.1.0 RcppParallel_4.4.3 stringi_1.4.3
[58] fs_1.3.1 promises_1.0.1 vctrs_0.3.1
[61] cowplot_1.0.0 tools_3.6.1 glue_1.3.1
[64] purrr_0.3.4 hms_0.5.3 yaml_2.2.0
[67] colorspace_1.4-1 ashr_2.2-47 plotly_4.9.0
[70] knitr_1.23 quantreg_5.41 MCMCpack_1.4-5