kos_K100_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 \(K = 100\). 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_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_K100_maxiter2000.Rds"
model_pmf_name = "kos_pmf_initLF50_K100_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$ELBO[1:400], xlab = "niter", ylab = "elbo")
| Version | Author | Date |
|---|---|---|
| 7928026 | zihao12 | 2020-05-16 |
## ebpmf_bg runtime per iteration
model$runtime/length(model$ELBO) user system elapsed
49.1382770 0.1047385 49.2636325 ## pmf runtime per iteration
model_pmf$runtime/length(model_pmf$log_liks) user system elapsed
23.3493840 0.0607845 23.4182915 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
6127 7488 2660 10167 9964
Topic6 Topic7 Topic8 Topic9 Topic10
2557 5557 11819 7535 5104
Topic11 Topic12 Topic13 Topic14 Topic15
5593 4821 7736 10043 4349
Topic16 Topic17 Topic18 Topic19 Topic20
7005 11345 10087 4514 5787
Topic21 Topic22 Topic23 Topic24 Topic25
6912 2635 7217 7775 8093
Topic26 Topic27 Topic28 Topic29 Topic30
14903 11400 8410 8391 5961
Topic31 Topic32 Topic33 Topic34 Topic35
7411 5711 9417 7548 7218
Topic36 Topic37 Topic38 Topic39 Topic40
7842 6813 5983 4770 6656
Topic41 Topic42 Topic43 Topic44 Topic45
2891 6891 8804 4176 6551
Topic46 Topic47 Topic48 Topic49 Topic50
6388 6488 7657 5764 4718
Topic51 Topic52 Topic53 Topic54 Topic55
6954 6695 6268 9018 5088
Topic56 Topic57 Topic58 Topic59 Topic60
6855 10080 5850 5235 4496
Topic61 Topic62 Topic63 Topic64 Topic65
7053 6959 7270 5365 5534
Topic66 Topic67 Topic68 Topic69 Topic70
7140 6980 8090 6387 4757
Topic71 Topic72 Topic73 Topic74 Topic75
12123 3861 7261 13980 5848
Topic76 Topic77 Topic78 Topic79 Topic80
4076 11736 6507 10753 9073
Topic81 Topic82 Topic83 Topic84 Topic85
11450 14064 5522 5565 7209
Topic86 Topic87 Topic88 Topic89 Topic90
9514 7169 7494 4002 5618
Topic91 Topic92 Topic93 Topic94 Topic95
9744 9667 6735 9001 6662
Topic96 Topic97 Topic98 Topic99 Topic100
5313 14731 6857 7350 6482 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_pmf are all 0, so I use mean instead
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
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