kos_K20_ebpmf.alpha_v0.3.8
zihao12
2020-05-11
Last updated: 2020-05-13
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Knit directory: ebpmf_data_analysis/
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|---|---|---|---|---|
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| html | 90f2fbd | zihao12 | 2020-05-12 | Build site. |
| Rmd | 8558495 | zihao12 | 2020-05-12 | update analysis/kos_K20_ebpmf.alpha_v0.3.8.Rmd |
| html | b45dcd7 | zihao12 | 2020-05-12 | Build site. |
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| html | 1e99b86 | zihao12 | 2020-05-11 | Build site. |
| Rmd | 6d474b8 | zihao12 | 2020-05-11 | kos_K20_ebpmf.alpha_v0.3.8.Rmd |
Introduction
I apply ebpmf.alpha (version 0.3.8) to KOS dataset. I use \(K = 20\). The data has \(n = 3430,p = 6906\) and sparsity around \(98\) percent.
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 initialize \(l_{i0}, f_{j0}\) by rank-1 pNMF. Then let posterior mean and exp of posterior log mean of \(q(l_{ik}), q(f_{jk})\) be all 1.
library(pheatmap)Warning: package 'pheatmap' was built under R version 3.5.2library(gridExtra)
source("code/misc.R")
output_dir = "output/uci_BoW/"
data_dir = "data/uci_BoW/"
model_name = "kos_ebpmf_bg_K20_maxiter5000.Rds"
dict_name = "vocab.kos.txt"
model = readRDS(sprintf("%s/%s", output_dir, model_name))
dict = read.csv(sprintf("%s/%s", data_dir, dict_name), header = FALSE)[,1]
dict = as.vector(dict)ELBO
- The progress of ELBO (in the first 1000 iterations) is very interesting, different from the curves we see before.
- From the \(g\) below, I guess it is because: \(g\) remains the same for many iterations, during which the algo is similar to pNMF (EM) and has siimilar convergence behavior; then \(g\) makes one discrete change(mostly), which repeats the convergence behavior …
- It might be because of initialization
plot(model$ELBO, xlab = "niter", ylab = "elbo")
## runtime
model$runtime user system elapsed
58135.647 49.558 37755.845 look at \(g_L, g_F\)
- I show component proportions for \(g_L, g_F\).
- It is interesting that almost all topics have only one component… (at iteration 500, all topic have one component). Is it because of initialization? Or is the discrete component truly a good global solution? (If that’s the case we can just do a grid search instead of solving a convex problem).
get_prior_summary <- function(gs){
K = length(gs)
phi_L = gs[[1]][["scale"]]
idx = order(phi_L, decreasing = TRUE)
L = length(phi_L)
Pi = matrix(, nrow = L, ncol = K)
for(k in 1:K){
Pi[,k] = gs[[k]][["pi"]][idx]
}
rownames(Pi) = paste("phi=", round(phi_L[idx], digits = 4), sep = "")
colnames(Pi) = paste("Topic", 1:K, sep = "")
pheatmap(Pi, cluster_rows=FALSE, cluster_cols=FALSE)
}\(g_L\)
get_prior_summary(model$qg$gls)
Some topics are almost the same.
- Note that a few \((l_k, f_k)\) pairs are very similar to each other (like the first 5 topics are almost identical). Below are the \(|\bar{f}_{J,2} - \bar{f}_{J,k}|_1, k = 1,3,4,5\) and \(|\bar{l}_{J,2} - \bar{l}_{J,k}|_1, k = 1,3,4,5\).
- Those almost identical topics/loadings are adjacent in our update order. It seems we need to randomize the update order?
print("|f_2 - f_k|_1, k = 1,3,4,5")[1] "|f_2 - f_k|_1, k = 1,3,4,5"f = model$qg$qfs_mean
sum(abs(f[,2] - f[,1]))[1] 1.941782sum(abs(f[,2] - f[,3]))[1] 1.042236e-07sum(abs(f[,2] - f[,4]))[1] 2.084468e-07sum(abs(f[,2] - f[,5]))[1] 3.126695e-07print("|l_2 - l_k|_1, k = 1,3,4,5")[1] "|l_2 - l_k|_1, k = 1,3,4,5"l = model$qg$qls_mean
sum(abs(l[,2] - l[,1]))[1] 3.230945sum(abs(l[,2] - l[,3]))[1] 3.03823e-10sum(abs(l[,2] - l[,4]))[1] 6.076523e-10sum(abs(l[,2] - l[,5]))[1] 9.114836e-10quantile of \(f_{J0}\)
f = model$f0
probs = seq(0, 1, 0.002)
plot(probs, quantile(f, probs = probs), main = sprintf("topic %d",0))
quantile of \(f_{Jk} (k > 0)\)
It seems that many topics contain lots of finer structure (not easily explained by a few words). This is not DIFFERENT from what we see from pNMF results.
K = length(model$qg$gls)
par(mfrow = c(5,4))
for(k in 1:K){
f = model$qg$qfs_mean[,k]
probs = seq(0, 1, 0.002)
plot(probs, quantile(f, probs = probs), main = sprintf("topic %d",k))
}
quantile of \(f_{J0} f_{Jk}\) (scaled to multinom model)
lf = poisson2multinom(F = model$f0 * model$qg$qfs_mean,
L = model$l0 * model$qg$qls_mean)
K = length(model$qg$gls)
par(mfrow = c(5,4))
for(k in 1:K){
f = lf$F[,k]
probs = seq(0, 1, 0.002)
plot(probs, quantile(f, probs = probs), main = sprintf("topic %d",k))
}
| Version | Author | Date |
|---|---|---|
| 90f2fbd | zihao12 | 2020-05-12 |
look at \(s_k\)
\(s_k := \sum_i l_i0 \bar{l}_{ik}\). 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 = "")
#round(s_k[1:5], digits = 0)
step = 5
for(i in 1:round(K/step)){
print(round(s_k[((i-1)*step + 1):(i*step)]))
}Topic1 Topic2 Topic3 Topic4 Topic5
5802 5791 5791 5791 5791
Topic6 Topic7 Topic8 Topic9 Topic10
6334 7757 5778 5812 5802
Topic11 Topic12 Topic13 Topic14 Topic15
7999 361414 15154 25447 5808
Topic16 Topic17 Topic18 Topic19 Topic20
5810 5807 5805 5805 5805 look at top words for topics
look at the top words in \(\bar{f}_{Jk}\).
K_sub <- 1:K
#par(mfrow = c(5,4))
p = length(model$l0)
n_top_word = round(0.002 * p)
f = model$qg$qfs_mean
show_topic <- function(k){
#print(sprintf("topic %d", k))
word_idx = order(f[,k], decreasing = TRUE)[1:n_top_word]
F_sub = model$qg$qfs_mean[word_idx,]
rownames(F_sub) = dict[word_idx]
colnames(F_sub) = paste("Topic", 1:K, sep = "")
pheatmap(F_sub,
cluster_rows=FALSE, cluster_cols=FALSE,
silent = TRUE,
main = sprintf("topic %d", k))[[4]]
}
gs = lapply(K_sub, FUN = show_topic)
grid.arrange(grobs = gs, ncol = 4)
look at the top words in \(f_{J0}\bar{f}_{Jk}\) (after scaling to multinom model).
K_sub <- 1:K
#par(mfrow = c(5,4))
p = length(model$l0)
n_top_word = round(0.002 * p)
f = lf$F
show_topic <- function(k){
#print(sprintf("topic %d", k))
word_idx = order(f[,k], decreasing = TRUE)[1:n_top_word]
F_sub = model$qg$qfs_mean[word_idx,]
rownames(F_sub) = dict[word_idx]
colnames(F_sub) = paste("Topic", 1:K, sep = "")
pheatmap(F_sub,
cluster_rows=FALSE, cluster_cols=FALSE,
silent = TRUE,
main = sprintf("topic %d", k))[[4]]
}
gs = lapply(K_sub, FUN = show_topic)
grid.arrange(grobs = gs, ncol = 4)
| Version | Author | Date |
|---|---|---|
| 90f2fbd | zihao12 | 2020-05-12 |
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