Last updated: 2019-10-22

Checks: 7 0

Knit directory: ebpmf_demo/

This reproducible R Markdown analysis was created with workflowr (version 1.4.0). 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(20190923)

The command set.seed(20190923) 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: c1b9997

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.

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/

Untracked files:
    Untracked:  analysis/.ipynb_checkpoints/
    Untracked:  analysis/ebpmf_demo.Rmd
    Untracked:  analysis/ebpmf_rank1_demo2.Rmd
    Untracked:  analysis/softmax_experiments.ipynb
    Untracked:  data/trash/
    Untracked:  docs/figure/Experiment_ebpmf_rankk.Rmd/
    Untracked:  docs/figure/test.Rmd/
    Untracked:  verbose_log_1571583163.21966.txt
    Untracked:  verbose_log_1571583324.71036.txt
    Untracked:  verbose_log_1571583741.94199.txt
    Untracked:  verbose_log_1571588102.40356.txt

Unstaged changes:
    Modified:   analysis/ebpmf_rank1_demo.Rmd
    Modified:   analysis/ebpmf_rankk_demo.Rmd
    Modified:   analysis/softmax_experiments.Rmd

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 R Markdown and HTML files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view them.

File Version Author Date Message
Rmd c1b9997 zihao12 2019-10-22 update debug
html b444dcf zihao12 2019-10-22 Build site.
Rmd df40a88 zihao12 2019-10-22 debug ebpmf exp

I managed to find the bug in ebpmf_exponential_mixture. Now we can make ELBO increase monotonically if we fix the scale/grid. When we unfix the grid, the ELBO also increase monotonically if the grids chosen are dense enough. (As suggested by Jason, setting \(m = 2^{0.25}\) works).

Another thing that’s unexpected is: rank-1 fit gets better RMSE than rank-K fit (where K is truth) in both MLE and EBPMF.

rm(list  = ls())
devtools::load_all("../ebpmf")
Loading ebpmf
set.seed(123)
library(NNLM)
library(ebpmf)

simulate_data <- function(n, p, K, params, seed = 1234){
  set.seed(seed)
  L = matrix(rgamma(n = n*K, shape = params$al, rate = params$bl), ncol = K)
  F = matrix(rgamma(n = p*K, shape = params$af, rate = params$bf), ncol = K)
  Lam =  L %*% t(F)
  X = matrix(rpois(n*p, Lam), nrow = n)
  Y = matrix(rpois(n*p, Lam), nrow = n)
  return(list(params = params,Lam = Lam,X = X, Y = Y))
}
n = 100
p = 200
K = 3
params = list(al = 100, bl =  109, af = 100, bf = 100, a = 1)
sim = simulate_data(n, p, K, params, seed =  1234)

maxiter = 100

rank 1

mle

## MLE
mle_rank1 = NNLM::nnmf(A = sim$X, k = 1, method = "lee", loss = "mkl", max.iter = 1)
lam_mle_rank1 =  mle_rank1$W %*% mle_rank1$H
ll_train_mle_rank1  = sum(dpois(sim$X, lam_mle_rank1, log = T))
ll_val_mle_rank1  = sum(dpois(sim$Y, lam_mle_rank1, log = T))
rmse_mle_rank1 = sqrt(mean((lam_mle_rank1 - sim$Lam)^2))
data.frame(ll_train = ll_train_mle_rank1,  ll_val = ll_val_mle_rank1, rmse = rmse_mle_rank1)
   ll_train    ll_val      rmse
1 -37606.75 -37849.52 0.1978021

ebpmf

As expected rank-1 gets optimal after the first iteration.

## rank 1 case
out_rank1 =  ebpmf::ebpmf_rank1_exponential_helper(X = sim$X, maxiter = 10, verbose = T)
[1] "iter         elbo        kl_l         kl_f       sum_El       sum_Ef"
[1] "  1   872.6991298338  278.0301190863   487.6792227247   54185.0958645029   1.0310122992"
[1] "  2   872.6991298338  278.0301190863   487.6792227247   54160.3288666399   1.0314837712"
[1] "  3   872.6991298338  278.0301190863   487.6792227248   54135.5731893102   1.0319554588"
[1] "  4   872.6991298338  278.0301190863   487.6792227247   54110.8288273395   1.0324273621"
[1] "  5   872.6991298338  278.0301190863   487.6792227247   54086.0957755556   1.0328994812"
[1] "  6   872.6991298337  278.0301190863   487.6792227248   54061.3740287889   1.0333718162"
[1] "  7   872.6991298338  278.0301190863   487.6792227247   54036.6635818721   1.0338443672"
[1] "  8   872.6991298338  278.0301190863   487.6792227247   54011.9644296403   1.0343171343"
[1] "  9   872.6991298337  278.0301190863   487.6792227248   53987.2765669308   1.0347901176"
[1] " 10   872.6991298338  278.0301190863   487.6792227247   53962.5999885834   1.0352633172"
lam_rank1 =  out_rank1$ql$mean  %*% t(out_rank1$qf$mean)
ll_train_rank1  = sum(dpois(sim$X, lam_rank1, log = T))
ll_val_rank1  = sum(dpois(sim$Y, lam_rank1, log = T))
rmse_rank1 = sqrt(mean((lam_rank1 - sim$Lam)^2))
data.frame(ll_train = ll_train_rank1,  ll_val = ll_val_rank1, rmse = rmse_rank1)
   ll_train    ll_val      rmse
1 -37606.76 -37849.06 0.1973981

rank k

ebpmf, fix g

In each iteration (> 2), the algorithm fixes \(g\).

## rank-k: fix gl, gf after first iteration
out =  ebpmf::ebpmf_exponential_mixture(X = sim$X, K = K, maxiter.out = 100, verbose = F, fix_g = T)

lam_out =  out$qg$qls_mean  %*% t(out$qg$qfs_mean)
ll_train_out  = sum(dpois(sim$X, lam_out, log = T))
ll_val_out  = sum(dpois(sim$Y, lam_out, log = T))
rmse_out = sqrt(mean((lam_out - sim$Lam)^2))
data.frame(ll_train = ll_train_out,  ll_val = ll_val_out, rmse = rmse_out)
  ll_train    ll_val      rmse
1 -37080.8 -38292.97 0.4078132
plot(out$ELBO, xlab = "iter", ylab = "ELBO")

Version Author Date
b444dcf zihao12 2019-10-22

ebpmf, fix scale

In each iteration (>2), the algorithm fixes the scale (grid)

rm(out)
## rank-k: fix scale after first iteration
out =  ebpmf::ebpmf_exponential_mixture(X = sim$X, K = K, maxiter.out = maxiter, verbose = F, fix_grid = T)

lam_out =  out$qg$qls_mean  %*% t(out$qg$qfs_mean)
ll_train_out  = sum(dpois(sim$X, lam_out, log = T))
ll_val_out  = sum(dpois(sim$Y, lam_out, log = T))
rmse_out = sqrt(mean((lam_out - sim$Lam)^2))
data.frame(ll_train = ll_train_out,  ll_val = ll_val_out, rmse = rmse_out)
   ll_train    ll_val      rmse
1 -37080.79 -38292.98 0.4078154
plot(out$ELBO, xlab = "iter", ylab = "ELBO")

Version Author Date
b444dcf zihao12 2019-10-22

ebpmf, free

In each iteration, the algorithm estimates scale (grid)

rm(out)
## rank-k: fix nothing
out =  ebpmf::ebpmf_exponential_mixture(X = sim$X, K = K, maxiter.out = maxiter, verbose = F,m = sqrt(2))

lam_out =  out$qg$qls_mean  %*% t(out$qg$qfs_mean)
ll_train_out  = sum(dpois(sim$X, lam_out, log = T))
ll_val_out  = sum(dpois(sim$Y, lam_out, log = T))
rmse_out = sqrt(mean((lam_out - sim$Lam)^2))
data.frame(ll_train = ll_train_out,  ll_val = ll_val_out, rmse = rmse_out)
   ll_train    ll_val      rmse
1 -37081.34 -38287.39 0.4064913
plot(out$ELBO, xlab = "iter", ylab = "ELBO")

Version Author Date
b444dcf zihao12 2019-10-22

Now it is not strictly increasing. Let’s use denser grids:

rm(out)
## rank-k: fix nothing
out =  ebpmf::ebpmf_exponential_mixture(X = sim$X, K = K, maxiter.out = maxiter, verbose = F,m = 2^0.25)

lam_out =  out$qg$qls_mean  %*% t(out$qg$qfs_mean)
ll_train_out  = sum(dpois(sim$X, lam_out, log = T))
ll_val_out  = sum(dpois(sim$Y, lam_out, log = T))
rmse_out = sqrt(mean((lam_out - sim$Lam)^2))
data.frame(ll_train = ll_train_out,  ll_val = ll_val_out, rmse = rmse_out)
   ll_train    ll_val      rmse
1 -37081.08 -38288.78 0.4069499
plot(out$ELBO, xlab = "iter", ylab = "ELBO")

mle

mle_rankK = NNLM::nnmf(A = sim$X, init = list(W0 = out$qg$qls_mean, H0 = t(out$qg$qfs_mean)),k = K, method = "lee", loss = "mkl", rel.tol = 1e-10, max.iter = 100)
lam_mle_rankK =  mle_rankK$W %*% mle_rankK$H
ll_train_mle_rankK  = sum(dpois(sim$X, lam_mle_rankK, log = T))
ll_val_mle_rankK  = sum(dpois(sim$Y, lam_mle_rankK, log = T))
rmse_mle_rankK = sqrt(mean((lam_mle_rankK - sim$Lam)^2))
data.frame(ll_train = ll_train_mle_rankK,  ll_val = ll_val_mle_rankK, rmse = rmse_mle_rankK)
   ll_train    ll_val      rmse
1 -36541.67 -38811.36 0.5495442

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] NNLM_0.4.2     ebpmf_0.1.0    testthat_2.2.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2          compiler_3.5.1      git2r_0.25.2       
 [4] workflowr_1.4.0     prettyunits_1.0.2   remotes_2.1.0      
 [7] tools_3.5.1         digest_0.6.21       pkgbuild_1.0.3     
[10] pkgload_1.0.2       evaluate_0.14       memoise_1.1.0      
[13] rlang_0.4.0         cli_1.1.0           rstudioapi_0.10    
[16] yaml_2.2.0          xfun_0.8            withr_2.1.2        
[19] stringr_1.4.0       knitr_1.25          gtools_3.8.1       
[22] desc_1.2.0          fs_1.3.1            devtools_2.2.1.9000
[25] rprojroot_1.3-2     glue_1.3.1          R6_2.4.0           
[28] processx_3.3.1      rmarkdown_1.13      sessioninfo_1.1.1  
[31] mixsqp_0.1-121      callr_3.2.0         magrittr_1.5       
[34] whisker_0.3-2       backports_1.1.5     ps_1.3.0           
[37] ellipsis_0.3.0      htmltools_0.3.6     usethis_1.5.1      
[40] assertthat_0.2.1    stringi_1.4.3       ebpm_0.0.0.9001    
[43] crayon_1.3.4