kos_K50_ebpmf.alpha_v0.3.9
zihao12
2020-05-11
Last updated: 2020-05-18
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Knit directory: ebpmf_data_analysis/
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| 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 \(K = 50\). 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_bgdoes two things: MLE for prior and updates posterior. The second part has almost the same computation as inPMF.
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 3.5.2library(gridExtra)
source("code/misc.R")
source("code/util.R")
output_dir = "output/uci_BoW/v0.3.9/"
data_dir = "data/uci_BoW/"
model_name = "kos_ebpmf_bg_initLF50_K50_maxiter2000.Rds"
model_pmf_name = "kos_pmf_initLF50_K50_maxiter2000.Rds"
dict_name = "vocab.kos.txt"
data_name = "docword.kos.txt"
Y = read_uci_bag_of_words(file= sprintf("%s/%s",
data_dir,data_name))
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$ELBO[1:200], xlab = "niter", ylab = "elbo")
| Version | Author | Date |
|---|---|---|
| 7928026 | zihao12 | 2020-05-16 |
## ebpmf_bg runtime per iteration
model$runtime/length(model$ELBO) user system elapsed
25.1001780 0.0507705 25.1611020 ## pmf runtime per iteration
model_pmf$runtime/length(model_pmf$log_liks) user system elapsed
11.738463 0.042293 11.784945 look at priors in ebpmf_bg
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
7544 7216 7912 25180 35652
Topic6 Topic7 Topic8 Topic9 Topic10
6709 21141 7208 11120 15791
Topic11 Topic12 Topic13 Topic14 Topic15
6953 12764 6206 25344 11313
Topic16 Topic17 Topic18 Topic19 Topic20
21599 13245 25545 25615 17418
Topic21 Topic22 Topic23 Topic24 Topic25
25117 24237 17946 22377 11739
Topic26 Topic27 Topic28 Topic29 Topic30
12942 20370 5179 13057 15220
Topic31 Topic32 Topic33 Topic34 Topic35
19897 22743 18122 17739 14611
Topic36 Topic37 Topic38 Topic39 Topic40
14671 30433 15525 16151 11059
Topic41 Topic42 Topic43 Topic44 Topic45
18014 11715 19915 12562 15720
Topic46 Topic47 Topic48 Topic49 Topic50
22557 23555 13324 18395 20023 what does background capture
compared to rank-1 fit
Is the background very different from the rank-1 model? The rank-1 MLE has \(l_{i0} \propto \sum_j X_{ij}\) and \(f_{j0} \propto \sum_i X_{ij}\). Let’s see if the fitted background model is close to it.
Y_cs = Matrix::colSums(Y)
Y_cs_scaled = Y_cs/sum(Y_cs)
f0_scaled = model$f0/sum(model$f0)
plot(f0_scaled, Y_cs_scaled)
Y_rs = Matrix::rowSums(Y)
Y_rs_scaled = Y_rs/sum(Y_rs)
l0_scaled = model$l0/sum(model$l0)
plot(l0_scaled, Y_rs_scaled)
compared to median/mean of PMF fit
The median of \(L\) from PMF are all 0, so I use mean instead for it
f0_pmf = apply(F_pmf, 1, median)
f0_pmf_scaled = f0_pmf/sum(f0_pmf)
l0_pmf = apply(L_pmf, 1, mean)
l0_pmf_scaled = l0_pmf/sum(l0_pmf)
plot(f0_scaled, f0_pmf_scaled)
plot(l0_scaled, l0_pmf_scaled)
Compare \(L, F\) (in the context of PMF model)
See plots.
Note: I scale them as below
## 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))look at top words for topics
See plots.
Note: for each topic:
* the first row selects the top words from \(\bar{f}_{Jk}\), and show them in \(\bar{f}\)(bg) and \(f\) (PMF) respectively.
* The second row shows the top words from \(f_{J0}0\bar{f}_{Jk}\) (bg) and \(f_{Jk}\) (PMF)
* The third row transforms \(f_{J0}0\bar{f}_{Jk}\) (bg) and \(f_{Jk}\) into multinomial model and show their top words.
take a closer look at some top words
I pick two top words from \(\bar{f}_{J1}\) and two top words from \(f_{J1}\):
d = Matrix::summary(Y)
## `burt`
idx = which(dict == "burt")
### number of occurence
sum(d$j == idx)[1] 16table(Y[,idx])
0 1 2 6
3414 13 2 1 ### background value
model$f0[idx][1] 1.482282e-05## `knowles`
idx = which(dict == "knowles")
### number of occurence
sum(d$j == idx)[1] 78table(Y[,idx])
0 1 2 3 4 5 6 7 8 9 12
3352 42 12 5 6 3 2 3 2 1 2 ### background value
model$f0[idx][1] 4.240542e-05## `campaign`
idx = which(dict == "campaign")
### number of occurence
sum(d$j == idx)[1] 960table(Y[,idx])
0 1 2 3 4 5 6 7 8 9 10 11 12 16
2470 511 204 104 58 36 20 11 7 4 1 2 1 1 ### background value
model$f0[idx][1] 0.001817356## `people`
idx = which(dict == "people")
### number of occurence
sum(d$j == idx)[1] 989table(Y[,idx])
0 1 2 3 4 5 6 7 8 13
2441 632 199 91 35 13 9 3 5 2 ### background value
model$f0[idx][1] 0.001846341
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 lattice_0.20-38 colorspace_1.4-1
[9] R6_2.4.0 stringr_1.4.0 tools_3.5.1 grid_3.5.1
[13] gtable_0.3.0 xfun_0.8 git2r_0.26.1 htmltools_0.3.6
[17] yaml_2.2.0 digest_0.6.22 rprojroot_1.3-2 Matrix_1.2-17
[21] RColorBrewer_1.1-2 later_0.8.0 promises_1.0.1 fs_1.3.1
[25] glue_1.3.1 evaluate_0.14 rmarkdown_2.1 stringi_1.4.3
[29] compiler_3.5.1 scales_1.0.0 backports_1.1.5 httpuv_1.5.1