Last updated: 2021-06-30

Checks: 7 0

Knit directory: ebpmf_data_analysis/

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    Untracked:  output/fastTopics_fit/fit_sla_fastTopics_k10.Rds
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    Untracked:  output/fastTopics_fit/fit_sla_fastTopics_k20.Rout
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    Untracked:  output/fastTopics_fit/fit_sla_fastTopics_k4.Rout
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Rmd 983a327 Zihao 2021-06-30 sla_simulated_compare_mle_eb.Rmd

Introduction

  • I thin sla dataset by half to get training and test dataset (see prepare_sla_sim). I first fit MLE (fastTopics) on original dataset, and call it truth . (Probably not a good name but it’s convenient…). Then I fit MLE and EB on thinned dataset. A good model should have good likelihood on test data, and should be close to truth.
  • I initialize MLE (fastTopics) and EB (ebpmf-wbg) methods using the truth.
  • EB approach is much better than MLE in the two cases shown below: \(K = 6\) & \(K = 20\).
  • Note that the mean matrix is slightly different bewteen the original data and train/test, as I remove some columns with 0 counts on training.
rm(list = ls())
source("code/misc.R")
library(fastTopics)
library(ebpmf.alpha)

datafile = "data/sim/sla_simulated.Rds"
data = readRDS(datafile)
data$Y_train = as(data$Y_train, "sparseMatrix")
data$Y_test = as(as.matrix(data$Y_test), "sparseMatrix") ## the way i generate simulated data is a bit stupid

dim(data$Y_train)
[1] 3207 8030
dim(data$Y_test)
[1] 3207 8030
sum(data$Y_train != 0)/(nrow(data$Y_train) * ncol(data$Y_train))
[1] 0.004549318
sum(data$Y_test != 0)/(nrow(data$Y_test) * ncol(data$Y_test))
[1] 0.004498682

\(K = 6\)

k = 6
truth.file = sprintf("output/fastTopics_fit/fit_sla_fastTopics_k%d.Rds", k)
fitted.mle.file = sprintf("output/fastTopics_fit/fit_sla_simualted_fastTopics_init_truth_k%d.Rds", k)
fitted.eb.file = sprintf("output/fastTopics_fit/fit_sla_simualted_ebpmf_wbg_init_truth_k%d.Rds", k)


truth = readRDS(truth.file)
fitted.mle = readRDS(fitted.mle.file)
fitted.eb = readRDS(fitted.eb.file)

## get "truth"
truth = fastTopics::multinom2poisson(truth)
truth = list(L = truth$L, F = truth$F[data$w_idx,])
class(truth) <- c("poisson_nmf_fit","list")
truth = fastTopics::poisson2multinom(truth) ## s is not right, but this does not affect computation of log-likelihood


fitted.mle.m = fastTopics::poisson2multinom(fitted.mle)
fitted.eb.p = ebpmf2fastTopics_pmf(fitted.eb)
fitted.eb.m = fastTopics::poisson2multinom(fitted.eb.p)

idx.mle = match_topics(truth$F, fitted.mle.m$F)
idx.eb = match_topics(truth$F, fitted.eb.m$F)

## see if there is 1-1 correspondence bewteen topics
idx.mle
[1] 1 2 3 4 5 6
idx.eb
[1] 1 2 3 4 5 6

compare log-lik on training/test

loglik.train.truth = fastTopics::loglik_multinom_topic_model(X = data$Y_train, truth)
loglik.train.mle = fastTopics::loglik_multinom_topic_model(X = data$Y_train, fitted.mle.m)
loglik.train.eb = fastTopics::loglik_multinom_topic_model(X = data$Y_train, fitted.eb.m)

loglik.test.truth = fastTopics::loglik_multinom_topic_model(X = data$Y_test, truth)
loglik.test.mle = fastTopics::loglik_multinom_topic_model(X = data$Y_test, fitted.mle.m)
loglik.test.eb = fastTopics::loglik_multinom_topic_model(X = data$Y_test, fitted.eb.m)


## training error
###  truth          mle             eb
c(mean(loglik.train.truth), mean(loglik.train.mle), mean(loglik.train.eb))
[1] -187.0736 -184.3535 -188.8222
## test error
###  truth          mle             eb
c(mean(loglik.test.truth), mean(loglik.test.mle), mean(loglik.test.eb))
[1] -183.5079 -204.8046 -191.4603

MLE vs truth

model = fitted.mle.m
idx = match_topics(truth$F, model$F)
l_mse <- c()
f_mse <- c()

par(mfrow = c(k, 2))
for(i in 1:k){
  j = idx[i]
  plot(truth$L[,i], model$L[,j], xlab = "loading (truth)", ylab = "loading (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  plot(truth$F[,i], model$F[,j], xlab = "factor (truth)", ylab = "factor (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  l_mse = c(l_mse, mean((truth$L[,i] - model$L[,j])^2))
  f_mse = c(l_mse, mean((truth$F[,i] - model$F[,j])^2))
}

l_mse.mle = l_mse
f_mse.mle = f_mse

EB vs truth

model = fitted.eb.m
idx = match_topics(truth$F, model$F)
l_mse <- c()
f_mse <- c()

par(mfrow = c(k, 2))
for(i in 1:k){
  j = idx[i]
  plot(truth$L[,i], model$L[,j], xlab = "loading (truth)", ylab = "loading (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  plot(truth$F[,i], model$F[,j], xlab = "factor (truth)", ylab = "factor (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  l_mse = c(l_mse, mean((truth$L[,i] - model$L[,j])^2))
  f_mse = c(l_mse, mean((truth$F[,i] - model$F[,j])^2))
}

l_mse.eb = l_mse
f_mse.eb = f_mse

compare RMSE from truth

round(rbind(l_mse.mle, l_mse.eb), digits = 4)
            [,1]   [,2]   [,3]   [,4]   [,5]   [,6]
l_mse.mle 0.0174 0.0105 0.0161 0.0144 0.0156 0.0100
l_mse.eb  0.0096 0.0067 0.0120 0.0080 0.0062 0.0035
round(rbind(f_mse.mle, f_mse.eb), digits = 4)
            [,1]   [,2]   [,3]   [,4]   [,5]   [,6] [,7]
f_mse.mle 0.0174 0.0105 0.0161 0.0144 0.0156 0.0100    0
f_mse.eb  0.0096 0.0067 0.0120 0.0080 0.0062 0.0035    0

\(K = 20\)

k = 20
truth.file = sprintf("output/fastTopics_fit/fit_sla_fastTopics_k%d.Rds", k)
fitted.mle.file = sprintf("output/fastTopics_fit/fit_sla_simualted_fastTopics_init_truth_k%d.Rds", k)
fitted.eb.file = sprintf("output/fastTopics_fit/fit_sla_simualted_ebpmf_wbg_init_truth_k%d.Rds", k)

truth = readRDS(truth.file)
fitted.mle = readRDS(fitted.mle.file)
fitted.eb = readRDS(fitted.eb.file)

## get "truth"
truth = fastTopics::multinom2poisson(truth)
truth = list(L = truth$L, F = truth$F[data$w_idx,])
class(truth) <- c("poisson_nmf_fit","list")
truth = fastTopics::poisson2multinom(truth) ## s is not right, but this does not affect computation of log-likelihood


fitted.mle.m = fastTopics::poisson2multinom(fitted.mle)
fitted.eb.p = ebpmf2fastTopics_pmf(fitted.eb)
fitted.eb.m = fastTopics::poisson2multinom(fitted.eb.p)

idx.mle = match_topics(truth$F, fitted.mle.m$F)
idx.eb = match_topics(truth$F, fitted.eb.m$F)

## see if there is 1-1 correspondence bewteen topics
idx.mle
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
idx.eb
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

compare log-lik on training/test

loglik.train.truth = fastTopics::loglik_multinom_topic_model(X = data$Y_train, truth)
loglik.train.mle = fastTopics::loglik_multinom_topic_model(X = data$Y_train, fitted.mle.m)
loglik.train.eb = fastTopics::loglik_multinom_topic_model(X = data$Y_train, fitted.eb.m)

loglik.test.truth = fastTopics::loglik_multinom_topic_model(X = data$Y_test, truth)
loglik.test.mle = fastTopics::loglik_multinom_topic_model(X = data$Y_test, fitted.mle.m)
loglik.test.eb = fastTopics::loglik_multinom_topic_model(X = data$Y_test, fitted.eb.m)


## training error
###  truth          mle             eb
c(mean(loglik.train.truth), mean(loglik.train.mle), mean(loglik.train.eb))
[1] -172.6338 -167.1411 -174.7843
## test error
###  truth          mle             eb
c(mean(loglik.test.truth), mean(loglik.test.mle), mean(loglik.test.eb))
[1] -169.4004 -218.8784 -188.2133

MLE vs truth

model = fitted.mle.m
idx = match_topics(truth$F, model$F)
l_mse <- c()
f_mse <- c()

par(mfrow = c(k, 2))
for(i in 1:k){
  j = idx[i]
  plot(truth$L[,i], model$L[,j], xlab = "loading (truth)", ylab = "loading (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  plot(truth$F[,i], model$F[,j], xlab = "factor (truth)", ylab = "factor (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  l_mse = c(l_mse, mean((truth$L[,i] - model$L[,j])^2))
  f_mse = c(l_mse, mean((truth$F[,i] - model$F[,j])^2))
}

l_mse.mle = l_mse
f_mse.mle = f_mse

EB vs truth

model = fitted.eb.m
idx = match_topics(truth$F, model$F)
l_mse <- c()
f_mse <- c()

par(mfrow = c(k, 2))
for(i in 1:k){
  j = idx[i]
  plot(truth$L[,i], model$L[,j], xlab = "loading (truth)", ylab = "loading (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  plot(truth$F[,i], model$F[,j], xlab = "factor (truth)", ylab = "factor (fitted)", main = sprintf("topic %d", i))
  abline(a = 0, b = 1, col = "blue")
  l_mse = c(l_mse, mean((truth$L[,i] - model$L[,j])^2))
  f_mse = c(l_mse, mean((truth$F[,i] - model$F[,j])^2))
}

l_mse.eb = l_mse
f_mse.eb = f_mse

compare RMSE from truth

round(rbind(l_mse.mle, l_mse.eb), digits = 4)
            [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]   [,8]   [,9]
l_mse.mle 0.0050 0.0074 0.0052 0.0060 0.0049 0.0037 0.0034 0.0043 0.0056
l_mse.eb  0.0019 0.0019 0.0019 0.0025 0.0019 0.0010 0.0021 0.0012 0.0018
           [,10]  [,11]  [,12]  [,13]  [,14]  [,15]  [,16]  [,17]  [,18]
l_mse.mle 0.0061 0.0077 0.0029 0.0065 0.0040 0.0098 0.0065 0.0040 0.0043
l_mse.eb  0.0028 0.0045 0.0011 0.0027 0.0018 0.0039 0.0059 0.0018 0.0024
           [,19]  [,20]
l_mse.mle 0.0049 0.0056
l_mse.eb  0.0024 0.0028
round(rbind(f_mse.mle, f_mse.eb), digits = 4)
            [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]   [,8]   [,9]
f_mse.mle 0.0050 0.0074 0.0052 0.0060 0.0049 0.0037 0.0034 0.0043 0.0056
f_mse.eb  0.0019 0.0019 0.0019 0.0025 0.0019 0.0010 0.0021 0.0012 0.0018
           [,10]  [,11]  [,12]  [,13]  [,14]  [,15]  [,16]  [,17]  [,18]
f_mse.mle 0.0061 0.0077 0.0029 0.0065 0.0040 0.0098 0.0065 0.0040 0.0043
f_mse.eb  0.0028 0.0045 0.0011 0.0027 0.0018 0.0039 0.0059 0.0018 0.0024
           [,19]  [,20] [,21]
f_mse.mle 0.0049 0.0056     0
f_mse.eb  0.0024 0.0028     0

sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ebpmf.alpha_0.4.5 fastTopics_0.5-53 pheatmap_1.0.12   workflowr_1.6.2  

loaded via a namespace (and not attached):
 [1] httr_1.4.1         tidyr_1.1.0        jsonlite_1.6      
 [4] viridisLite_0.3.0  gtools_3.8.1       RcppParallel_4.4.3
 [7] assertthat_0.2.1   mixsqp_0.3-43      yaml_2.2.0        
[10] progress_1.2.2     ggrepel_0.9.1      pillar_1.4.2      
[13] backports_1.1.4    lattice_0.20-38    quantreg_5.41     
[16] glue_1.3.1         quadprog_1.5-7     digest_0.6.20     
[19] RColorBrewer_1.1-2 promises_1.0.1     colorspace_1.4-1  
[22] cowplot_1.0.0      htmltools_0.3.6    httpuv_1.5.1      
[25] Matrix_1.2-18      pkgconfig_2.0.2    invgamma_1.1      
[28] SparseM_1.77       purrr_0.3.4        scales_1.1.0      
[31] whisker_0.3-2      later_0.8.0        Rtsne_0.15        
[34] MatrixModels_0.4-1 git2r_0.26.1       tibble_2.1.3      
[37] ggplot2_3.3.3      ashr_2.2-47        lazyeval_0.2.2    
[40] magrittr_1.5       crayon_1.3.4       mcmc_0.9-6        
[43] evaluate_0.14      ebpm_0.0.1.1       fs_1.3.1          
[46] MASS_7.3-51.4      truncnorm_1.0-8    tools_3.6.1       
[49] data.table_1.13.2  prettyunits_1.0.2  hms_0.5.3         
[52] lifecycle_0.1.0    stringr_1.4.0      MCMCpack_1.4-5    
[55] plotly_4.9.0       munsell_0.5.0      irlba_2.3.3       
[58] compiler_3.6.1     rlang_0.4.10       grid_3.6.1        
[61] htmlwidgets_1.3    rmarkdown_1.13     gtable_0.3.0      
[64] R6_2.4.0           knitr_1.23         dplyr_0.8.3       
[67] uwot_0.1.5         rprojroot_1.3-2    stringi_1.4.3     
[70] SQUAREM_2017.10-1  Rcpp_1.0.5         vctrs_0.3.1       
[73] tidyselect_1.1.0   xfun_0.8           coda_0.19-3