Last updated: 2020-05-16

Checks: 7 0

Knit directory: ebpmf_data_analysis/

This reproducible R Markdown analysis was created with workflowr (version 1.6.2). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20200511)

The command set.seed(20200511) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 20a60fd

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 20a60fd. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: 


Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    analysis/ebpmf_bg_tutorial_cache/

Untracked files:
    Untracked:  code/.util.R.swp

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

These are the previous versions of the repository in which changes were made to the R Markdown (analysis/kos_K100_ebpmf.alpha_v0.3.9.Rmd) and HTML (docs/kos_K100_ebpmf.alpha_v0.3.9.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 20a60fd zihao12 2020-05-16 update analysis for results in v0.3.9
html 7928026 zihao12 2020-05-16 Build site.
Rmd 3e38a38 zihao12 2020-05-16 analysis for results in v0.3.9

Introduction

  • I apply ebpmf.alpha (version 0.3.9) to KOS dataset. I use \(K = 100\). The data has \(n = 3430,p = 6906\) and sparsity around \(98\) percent.
  • Besides, I also apply to PMF (lee’s, but I implemented a version for sparse data) to the same dataset with the same initialization. In each iteration, ebpmf_bg does two things: MLE for prior and updates posterior. The second part has almost the same computation as in PMF.

model

\[\begin{align} & X_{ij} = \sum_k Z_{ijk}\\ & Z_{ijk} \sim Pois(l_{i0} f_{j0} l_{ik} f_{jk})\\ & l_{ik} \sim g_{L, k}(.), f_{jk} \sim g_{F, k}(.) \end{align}\]

For details see ebpmf_bg

prior options

I use gamma mixture \(\sum_l \pi_{l} Ga(1/\phi_l, 1/\phi_l)\) as prior for both \(L, F\). Note that each grid component has \(E = 1, Var = \phi_L\)

initialization

I initialized with 50 runs of NNLM::nnmf (scd). Then I used medians of each row of \(L, F\) as \(l_{i0}, f_{j0}\), and \(l_{ik} = l^0_{ik}/l_{i0}, f_{jk} = f^0_{jk}/f_{j0}\).

library(pheatmap)
Warning: package 'pheatmap' was built under R version 3.5.2
library(gridExtra)
source("code/misc.R")

output_dir = "output/uci_BoW/v0.3.9/"
data_dir = "data/uci_BoW/"
model_name = "kos_ebpmf_bg_initLF50_K100_maxiter1000.Rds"
model_pmf_name = "kos_pmf_initLF50_K100_maxiter1000.Rds"
dict_name = "vocab.kos.txt"
model = readRDS(sprintf("%s/%s", output_dir, model_name))
model_pmf = readRDS(sprintf("%s/%s", output_dir, model_pmf_name))
dict = read.csv(sprintf("%s/%s", data_dir, dict_name), header = FALSE)[,1]
dict = as.vector(dict)

K = ncol(model_pmf$L)
L_pmf = model_pmf$L; F_pmf = model_pmf$F
L_bg = model$l0 * model$qg$qls_mean; F_bg = model$f0 * model$qg$qfs_mean
lf = poisson2multinom(L=L_bg,F=F_bg)
lf_pmf = poisson2multinom(L = L_pmf,F = F_pmf)

ELBO and runtime

plot(model$ELBO, xlab = "niter", ylab = "elbo")

Version Author Date
7928026 zihao12 2020-05-16 
## see when it "converges"
plot(model$ELBO[1:400], xlab = "niter", ylab = "elbo")

Version Author Date
7928026 zihao12 2020-05-16 
## ebpmf_bg runtime per iteration
model$runtime/length(model$ELBO)
     user    system   elapsed 
50.314172  0.136145 50.470211 
## pmf runtime per iteration
model_pmf$runtime/length(model_pmf$log_liks)
     user    system   elapsed 
23.371322  0.057601 23.437102

look at priors in ebpmf_bg

\(g_L\)

get_prior_summary(model$qg$gls)

Version Author Date
7928026 zihao12 2020-05-16

\(g_F\)

get_prior_summary(model$qg$gfs)

Version Author Date
7928026 zihao12 2020-05-16

look at \(s_k\) (ebpmf_bg)

\(s_k := \sum_i l_i0 \bar{l}_{ik}\). I make \(\sum_j f_{j0} = 1\) for interpretability.

d = sum(model$f0)
s_k = colSums(d * model$l0 * model$qg$qls_mean)
names(s_k) <- paste("Topic", 1:K, sep = "")
step = 5
for(i in 1:round(K/step)){
  print(round(s_k[((i-1)*step + 1):(i*step)]))
}
Topic1 Topic2 Topic3 Topic4 Topic5 
  6100   7463   2527   9813   9611 
 Topic6  Topic7  Topic8  Topic9 Topic10 
   2451    5700   11695    7501    5056 
Topic11 Topic12 Topic13 Topic14 Topic15 
   5547    4801    7764    9970    4393 
Topic16 Topic17 Topic18 Topic19 Topic20 
   6855   11303   10004    4446    5743 
Topic21 Topic22 Topic23 Topic24 Topic25 
   6862    2628    7187    7728    8059 
Topic26 Topic27 Topic28 Topic29 Topic30 
  14796   11319    8344    8342    5926 
Topic31 Topic32 Topic33 Topic34 Topic35 
   7371    5690    9397    7500    7162 
Topic36 Topic37 Topic38 Topic39 Topic40 
   7983    6760    5926    4726    6605 
Topic41 Topic42 Topic43 Topic44 Topic45 
   2866    6867    8744    4141    6490 
Topic46 Topic47 Topic48 Topic49 Topic50 
   6272    6405    7473    5720    4669 
Topic51 Topic52 Topic53 Topic54 Topic55 
   6904    6627    6137    8954    5042 
Topic56 Topic57 Topic58 Topic59 Topic60 
   6803    9932    5795    5194    4467 
Topic61 Topic62 Topic63 Topic64 Topic65 
   6985    6906    7221    5321    5497 
Topic66 Topic67 Topic68 Topic69 Topic70 
   7086    6926    8036    6334    4695 
Topic71 Topic72 Topic73 Topic74 Topic75 
  12059    3829    7234   13910    5799 
Topic76 Topic77 Topic78 Topic79 Topic80 
   4038   11648    6461   10701    9003 
Topic81 Topic82 Topic83 Topic84 Topic85 
  11363   13916    5486    5528    7190 
Topic86 Topic87 Topic88 Topic89 Topic90 
   9447    7110    7491    3969    5587 
Topic91 Topic92 Topic93 Topic94 Topic95 
   9672    9673    6689    8947    6647 
 Topic96  Topic97  Topic98  Topic99 Topic100 
    5256    14561     6790     7292     6443

look at top words for topics

show_topic <- function(k, other_var){
  K = ncol(F)
  n_top_word = other_var$n_top_word
  F = other_var$F
  word_idx = order(F[,k], decreasing = TRUE)[1:n_top_word]
  F_sub = F[word_idx,]
  rownames(F_sub) = dict[word_idx]
  #colnames(F_sub) = paste("Topic", 1:K, sep = "")
  colnames(F_sub) = NULL
  pheatmap(F_sub, 
           cluster_rows=FALSE, cluster_cols=FALSE,
           silent = TRUE, 
           main = sprintf("topic %d", k))[[4]]
}

top words in \(\bar{f}_{Jk}\) (ebpmf_bg)

K_sub = 1:K
p = length(model$l0)
n_top_word = round(0.002 * p)
F = model$qg$qfs_mean[, K_sub]
other_var = list(n_top_word = n_top_word,F = F)
gs = lapply(K_sub, FUN = show_topic, other_var = other_var)
grid.arrange(grobs = gs, ncol = 4)

Version Author Date
7928026 zihao12 2020-05-16

top words in \(f_{J0}\bar{f}_{Jk}\) (ebpmf_bg) (scaled to multinom).

F = lf$F[, K_sub]
other_var = list(n_top_word = n_top_word,F = F)
gs = lapply(K_sub, FUN = show_topic, other_var = other_var)
grid.arrange(grobs = gs, ncol = 4)

Version Author Date
7928026 zihao12 2020-05-16

top words in \(f_{jk}\) (PMF) (scaled to multinom).

F = lf_pmf$F[, K_sub]

other_var = list(n_top_word = n_top_word,F = F)
gs = lapply(K_sub, FUN = show_topic, other_var = other_var)
grid.arrange(grobs = gs, ncol = 4)

Compare \(L, F\) (in the context of PMF model)

## scale L, F so that colSums(F) = 1
L_pmf = L_pmf %*% diag(colSums(F_pmf))
F_pmf = F_pmf %*% diag(1/colSums(F_pmf))

L_bg = L_bg %*% diag(colSums(F_bg))
F_bg = F_bg %*% diag(1/colSums(F_bg))

\(L\)

par(mfrow = c(25,4))
for(k in 1:K){
  plot(L_pmf[,k], L_bg[,k], pch = 18, 
       xlab = "pmf", ylab = "bg", main = sprintf("loading %d", k))
  abline(0,1,lwd=1,col="blue")
}

Version Author Date
7928026 zihao12 2020-05-16

\(F\)

par(mfrow = c(25,4))
for(k in 1:K){
  plot(F_pmf[,k], F_bg[,k], pch = 18, 
       xlab = "pmf", ylab = "bg", main = sprintf("factor %d", k))
  abline(0,1,lwd=1,col="blue")
}

Version Author Date
7928026 zihao12 2020-05-16 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] gridExtra_2.3   pheatmap_1.0.12

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2         knitr_1.28         whisker_0.3-2      magrittr_1.5      
 [5] workflowr_1.6.2    munsell_0.5.0      colorspace_1.4-1   R6_2.4.0          
 [9] stringr_1.4.0      tools_3.5.1        grid_3.5.1         gtable_0.3.0      
[13] xfun_0.8           git2r_0.26.1       htmltools_0.3.6    yaml_2.2.0        
[17] digest_0.6.22      rprojroot_1.3-2    RColorBrewer_1.1-2 later_0.8.0       
[21] promises_1.0.1     fs_1.3.1           glue_1.3.1         evaluate_0.14     
[25] rmarkdown_2.1      stringi_1.4.3      compiler_3.5.1     scales_1.0.0      
[29] backports_1.1.5    httpuv_1.5.1