Last updated: 2021-06-13

Checks: 7 0

Knit directory: ebpmf_data_analysis/

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    Modified:   topicView-app/app.R

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Introduction

  • When \(n \ll p\), I think it’s easier to estimate \(L\), but because of the alternating update of \(L, F\) we can end up with bad fits of both.
  • Below I show an example where we can get better fit with cone_NMF_l2 (it’s technically still alternating between \(B, W\) but their estimates are very very similar, so I think of it as fitting \(W\) (or equivalently \(L\)) alone).
rm(list = ls())
source("code/cone_NMF_l2.R")
source("code/smallsim2_functions.R")
source("code/misc.R")
source("code/util.R")
set.seed(123)

An instance where both L and F are fitted badly (with regular PMF)

In the small subset of data used in fitting, there are 50 documents with 1000 words in the dictionary. The document length is 80 on average.

n <- 300
m <- 1000
k <- 3
n_sample = 50
doc_len = round(0.08*m) ## average number of words in each document

S <- 15*diag(k) - 2
F <- simulate_factors(m = m, k = k)
L <- simulate_loadings(n,k,S)
s <- simulate_sizes(n = n, doc_len = doc_len)
X <- simulate_multinom_counts(L,F,s)
fit_kl_small <- NNLM::nnmf(A = X[1:n_sample,], k = k, loss = "mkl", method = "scd", trace = 1, max.iter = 200)
fit_kl_big <- NNLM::nnmf(A = X, k = k, loss = "mkl", method = "scd", trace = 1)

fit_kl_small.m = get_multinom_from_pnmf(L = fit_kl_small$W, F = t(fit_kl_small$H))
fit_kl_big.m = get_multinom_from_pnmf(L = fit_kl_big$W, F = t(fit_kl_big$H))

We can see below that both \(L, F\) are fitted badly

model = fit_kl_small.m
idx = match_topics(F1 = F, F2 = model$F)
idx
[1] 3 2 1
par(mfrow = c(3,2))
compare_truth_fitted(model, idx, L, F, n_sample)

Version Author Date
4ef042b zihao12 2021-06-13
4a7ec3e zihao12 2021-06-13

With more documents we can fit both much better

model = fit_kl_big.m
idx = match_topics(F1 = F, F2 = model$F)
idx
[1] 1 3 2
par(mfrow = c(3,2))
compare_truth_fitted(model, idx, L, F, n)

Version Author Date
4ef042b zihao12 2021-06-13
4a7ec3e zihao12 2021-06-13

Can we estimate L well with cone-NMF?

Initialize with fit_kl_small. I project the \(F\) on to \(\text{cone}(X^T)\)

## dim(X) = (n, p)
## dim(L) = (n, k)
## dim(F) = (p, k)
init_ <- function(X, L, F){
  k = ncol(L)
  n = nrow(L)
  B = matrix(NaN, nrow = n, ncol = k)
  W = t(L)
  for(i in 1:k){
    B[,i]  = nnls::nnls(A = X, b = F[,i])$x
  }
  d = sqrt(rowSums(W^2))
  W <- W / d
  B <- t(t(B) * d)
  R = diag(replicate(n, 1)) - B %*% W
  return(list(B = B, W = W, R = R))
}

init_small <- init_(X = t(X[1:n_sample,]), L = fit_kl_small$W, F = t(fit_kl_small$H))

Fit with cone_NMF_l2

fit_cone_small = cone_nmf_l2(X = t(X[1:n_sample,]), K = k, init = init_small, maxiter = 50)
fit_cone_small.m =   get_multinom_from_pnmf(F = fit_cone_small$A, L = t(fit_cone_small$W))

The \(L\) fit is much much better!

model = fit_cone_small.m
idx = match_topics(F1 = F, F2 = model$F)
idx
[1] 3 2 1
par(mfrow = c(3,2))
compare_truth_fitted(model, idx, L, F, n_sample)

Version Author Date
4ef042b zihao12 2021-06-13
4a7ec3e zihao12 2021-06-13

Refit regular PMF initialized from cone_NMF_l2

  • cone_NMF_l2 helps the regular PMF gets out of local maxima (probably by getting a better \(L\)).
fit_cone_small.p = multinom2poisson(fit_cone_small.m, X = X[1:n_sample, ])
fit_kl_small.p = multinom2poisson(fit_kl_small.m, X = X[1:n_sample, ])

fit_kl_small_refit <- NNLM::nnmf(A = X[1:n_sample,], k = k, loss = "mkl", method = "scd", 
                                 init = list(W = fit_cone_small.p$L, H = t(fit_cone_small.p$F)),
                                 trace = 1, max.iter = 200)
fit_kl_small_refit.m = get_multinom_from_pnmf(L = fit_kl_small_refit$W, F = t(fit_kl_small_refit$H))
fit_kl_small_refit.p = multinom2poisson(fit_kl_small_refit.m, X = X[1:n_sample, ])
model = fit_kl_small_refit.m
idx = match_topics(F1 = F, F2 = model$F)
idx
[1] 3 2 1
par(mfrow = c(3,2))
compare_truth_fitted(model, idx, L, F, n_sample)

log_lik(X = X[1:n_sample, ], lam = fit_cone_small.p$L %*% t(fit_cone_small.p$F))
[1] -11148.09
log_lik(X = X[1:n_sample, ], lam = fit_kl_small.p$L %*% t(fit_kl_small.p$F))
[1] -11183.23
log_lik(X = X[1:n_sample, ], lam = fit_kl_small_refit.p$L %*% t(fit_kl_small_refit.p$F))
[1] -10899.21

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.15.7

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] pheatmap_1.0.12 mvtnorm_1.1-0   workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.5         knitr_1.28         whisker_0.3-2      magrittr_1.5      
 [5] nnls_1.4           munsell_0.5.0      colorspace_1.4-1   R6_2.4.1          
 [9] rlang_0.4.5        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_0.5.0   
[17] yaml_2.2.0         digest_0.6.25      rprojroot_1.3-2    lifecycle_0.2.0   
[21] RColorBrewer_1.1-2 later_1.1.0.1      promises_1.1.1     fs_1.3.1          
[25] NNLM_0.4.2         glue_1.4.1         evaluate_0.14      rmarkdown_2.1     
[29] stringi_1.6.2      compiler_3.5.1     scales_1.1.1       backports_1.1.7   
[33] httpuv_1.5.4