Last updated: 2020-06-05

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What’s new in ebpmf.alpha_v0.4.2

  • Implemented ebpmf_wbg.

  • Implemented a version of greedy pmf. (Would be easy to extend to other models, but I am dubious about its effects).

  • Used a numerical trick to improve stability in computing \(B_{ij}\) (in the link below).

  • Used another way of initialization (only using L). 

Model and implementation details:

ebpmf_wbg & pmf_greedy

Individual data analysis results: 

kos_K20,
greedy_pmf_experiment,
I also show all topics here: topics

More comparisons across different \(K\) and different models

Note that

\[ELBO = E_q(\text{log-lik}) - KL(q || g)\]

    K  ELBO_bg ELBO_wbg    KL_bg   KL_wbg  E_ll_bg E_ll_wbg   ll_pmf
1  20 -1700057 -1690036 151380.3 141562.7 -1548677 -1548473 -1504099
2  50 -1688549 -1681001 232036.2 214114.5 -1456512 -1466886 -1379746
3 100 -1702420 -1681872 313105.3 263899.2 -1389315 -1417972 -1264891

why greedy_pmf may not work?

The rank-1 model for pmfis a mean of row and column, ignoring the structures. This is in contrast to svd type methods (PCA itself is a greedy approach that achieves global optimality: the best rank-K approximation).

TODO:

  • Find a better dataset and run with bigger \(K\) to see if our method has an advantage over pmf + poisson2binom.
  • Try to estimate \(K\). it might be easier to do coordinate update and weed out \(w\) (or accept more moves that propose \(w_k = 0\), to think about it another way), than using greedy approach (\(\lambda^{k}_{ij}\) is a weighted sum of previous \(k-1\) components and the current one).
  • Think about getting rid of some computational difficulty by approximating posterior of \(L, F\) with mixture of normal.

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] workflowr_1.6.2

loaded via a namespace (and not attached):
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[13] whisker_0.3-2   rmarkdown_2.1   tools_3.5.1     stringr_1.4.0  
[17] glue_1.4.1      httpuv_1.5.1    xfun_0.8        yaml_2.2.0     
[21] compiler_3.5.1  htmltools_0.3.6 knitr_1.28