Last updated: 2023-11-10

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Rmd 77bf15c Matthew Stephens 2023-11-10 workflowr::wflow_publish("flashier_nmf_shifted_prior.Rmd")

Introduction

I wanted to try out the idea of using a shifted prior when doing NMF. The idea is that when greedily adding factors you can simultaneously “shift” the baseline factor so that it adjusts for the factors you add. However, this simple idea does not work very well in practice in this example, probably due to convergence issues (that may not be so easy to solve).

Read in the data and filter

These steps are following ones in other files. I copy and pasted so there is more code here than I actually need….

library(Matrix)
library(readr)
library(tm)
Loading required package: NLP
library(fastTopics)
library(flashier)
Loading required package: ebnm
Loading required package: magrittr
Loading required package: ggplot2

Attaching package: 'ggplot2'
The following object is masked from 'package:NLP':

    annotate
library(ebpmf)
library(RcppML)
RcppML v0.5.5 using 'options(RcppML.threads = 0)' (all available threads), 'options(RcppML.verbose = FALSE)'
sla <- read_csv("../../gsmash/data/SLA/SCC2016/Data/paperList.txt")
Rows: 3248 Columns: 5
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (3): DOI, title, abstract
dbl (2): year, citCounts

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
sla <- sla[!is.na(sla$abstract),]
sla$docnum = 1:nrow(sla)
datax = readRDS('../../gsmash/data/sla_full.rds')
dim(datax$data)
[1]  3207 10104
sum(datax$data==0)/prod(dim(datax$data))
[1] 0.9948157
datax$data = Matrix(datax$data,sparse = TRUE)

filtering

doc_to_use = order(rowSums(datax$data),decreasing = T)[1:round(nrow(datax$data)*0.6)]
mat = datax$data[doc_to_use,]
sla = sla[doc_to_use,]
samples = datax$samples
samples = lapply(samples, function(z){z[doc_to_use]})

Filter out words that appear in less than 5 documents. Note: if you don’t do this you can still get real factors that capture very rare words co-occuring. Eg two authors that are cited together. If you are interested in those factors, no need to filter…

word_to_use = which(colSums(mat>0)>4)
mat = mat[,word_to_use]
mat = Matrix(mat,sparse=TRUE)
lmat = Matrix(log(mat+1),sparse=TRUE)

docsize = rowSums(mat)
s = docsize/mean(docsize)
lmat_s_10 = Matrix(log(0.1*mat/s+1),sparse=TRUE)
lmat_s_1 = Matrix(log(mat/s+1),sparse=TRUE)
lmat_s_01 = Matrix(log(10*mat/s+1),sparse=TRUE)
lmat_s_001 = Matrix(log(100*mat/s+1),sparse=TRUE)

Compute minimum variances/standard deviations.

mhat = 4/nrow(lmat)
xx = rpois(1e7,mhat) # random poisson
S10 = sd(log(0.1*xx+1))
S1 = sd(log(xx+1)) # sd of log(X+1)
S01 = sd(log(10*xx+1)) # sd if log(10X+1)
S001 = sd(log(100*xx+1)) # sd if log(10X+1)
print(c(S10,S1,S01,S001))
[1] 0.004339581 0.031536221 0.109033434 0.209811829

Shifted point exponential

Define a function that estimates the mode instead of fixing it to 0.

ebnm_shift_point_exponential = function(x,s,g_init,fix_g,output){ebnm_point_exponential(x,s,g_init=g_init, fix_g = fix_g, output=output, mode="estimate")}

The problems comes up on the second factor so I fit 2 factors.

set.seed(1)
fit.1 = flash(lmat_s_1,ebnm_fn = ebnm_shift_point_exponential, S=S1, greedy_Kmax = 2)
Adding factor 1 to flash object...
Adding factor 2 to flash object...
Wrapping up...
Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.
Done.
Nullchecking 2 factors...
Done.

Here we see that the L and F are non-sparse and far from non-negative. The fitted gs are shifted exponentials (essentially no point mass). Possibly flash is initializing using an unconstrained fit, so essentially PCA. Maybe part of a solution could be to initialize to non-negative?

plot(fit.1$L_pm[,2])

plot(fit.1$F_pm[,2])

fit.1$F_ghat[2]
[[1]]
$pi
[1] 6.072199e-18 1.000000e+00

$shape
[1] 1 1

$scale
[1]   0.0000 144.1321

$shift
[1] -144.129 -144.129

attr(,"class")
[1] "gammamix"
attr(,"row.names")
[1] 1 2
fit.1$L_ghat[2]
[[1]]
$pi
[1] 4.422449e-07 9.999996e-01

$shape
[1] 1 1

$scale
[1] 0.00000000 0.00727064

$shift
[1] -0.006962347 -0.006962347

attr(,"class")
[1] "gammamix"
attr(,"row.names")
[1] 1 2

Here I try initializing using point exponential and then relaxing.

fit.nn = flash(lmat_s_1,ebnm_fn = ebnm_point_exponential, S=S1, greedy_Kmax = 2)
Adding factor 1 to flash object...
Adding factor 2 to flash object...
Wrapping up...
Done.
Nullchecking 2 factors...
Done.
fit.2 = flash_init(lmat_s_1, S=S1)
fit.2 = flash_factors_init(fit.2, fit.nn, ebnm_fn = ebnm_shift_point_exponential)
fit.2 = flash_backfit(fit.2)
Backfitting 2 factors (tolerance: 6.23e-02)...
  Difference between iterations is within 1.0e+03...
  Difference between iterations is within 1.0e+02...
  Difference between iterations is within 1.0e+01...
  Difference between iterations is within 1.0e+00...
  Difference between iterations is within 1.0e-01...
Wrapping up...
Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.

Warning in ebnm_workhorse(x = x, s = s, mode = mode, scale = scale, g_init =
g_init, : Since they're not well defined for nonzero modes, local false sign
rates won't be returned.
Done.

We can see the original non-negative fit produces very sparse factors:

plot(fit.nn$L_pm[,2])

plot(fit.nn$F_pm[,2])

But the refit produces something much less sparse, again with no point mass at 0.

plot(fit.2$L_pm[,2])

plot(fit.2$F_pm[,2])

fit.2$L_ghat[2]
[[1]]
$pi
[1] 1.578854e-05 9.999842e-01

$shape
[1] 1 1

$scale
[1] 0.0000000 0.1906966

$shift
[1] -0.07448485 -0.07448485

attr(,"class")
[1] "gammamix"
attr(,"row.names")
[1] 1 2
fit.2$F_ghat[2]
[[1]]
$pi
[1] 4.148026e-15 1.000000e+00

$shape
[1] 1 1

$scale
[1] 0.0000000 0.0554266

$shift
[1] -0.01173853 -0.01173853

attr(,"class")
[1] "gammamix"
attr(,"row.names")
[1] 1 2

I thought this might still be a convergence issue, but it seems that the elbo is better for the relaxed fit.

fit.2$elbo - fit.nn$elbo
[1] 12080.06

Here is a direct comparison of the two fits; quite a big difference.

plot(fit.2$L_pm[,1],fit.nn$L_pm[,1])

plot(fit.2$L_pm[,2],fit.nn$L_pm[,2])

plot(fit.2$F_pm[,1],fit.nn$F_pm[,1])

plot(fit.2$F_pm[,2],fit.nn$F_pm[,2])


sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur ... 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/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] RcppML_0.5.6       ebpmf_2.3.2        flashier_1.0.0     ggplot2_3.4.3     
 [5] magrittr_2.0.3     ebnm_1.0-55        fastTopics_0.6-158 tm_0.7-11         
 [9] NLP_0.2-1          readr_2.1.4        Matrix_1.5-3      

loaded via a namespace (and not attached):
  [1] Rtsne_0.16         ebpm_0.0.1.3       colorspace_2.1-0  
  [4] smashr_1.2-9       ellipsis_0.3.2     rprojroot_2.0.3   
  [7] fs_1.6.3           rstudioapi_0.14    MatrixModels_0.5-1
 [10] ggrepel_0.9.3      bit64_4.0.5        fansi_1.0.5       
 [13] mvtnorm_1.2-3      xml2_1.3.3         splines_4.2.1     
 [16] cachem_1.0.7       knitr_1.42         jsonlite_1.8.7    
 [19] workflowr_1.7.0    nloptr_2.0.3       mcmc_0.9-7        
 [22] ashr_2.2-63        smashrgen_1.2.5    uwot_0.1.14       
 [25] compiler_4.2.1     httr_1.4.5         RcppZiggurat_0.1.6
 [28] fastmap_1.1.1      lazyeval_0.2.2     cli_3.6.1         
 [31] later_1.3.0        htmltools_0.5.4    quantreg_5.94     
 [34] prettyunits_1.2.0  tools_4.2.1        coda_0.19-4       
 [37] gtable_0.3.4       glue_1.6.2         dplyr_1.1.3       
 [40] Rcpp_1.0.11        softImpute_1.4-1   slam_0.1-50       
 [43] jquerylib_0.1.4    vctrs_0.6.4        wavethresh_4.7.2  
 [46] xfun_0.37          stringr_1.5.0      trust_0.1-8       
 [49] lifecycle_1.0.3    irlba_2.3.5.1      MASS_7.3-58.2     
 [52] scales_1.2.1       vroom_1.6.1        hms_1.1.2         
 [55] promises_1.2.0.1   parallel_4.2.1     SparseM_1.81      
 [58] yaml_2.3.7         pbapply_1.7-0      sass_0.4.5        
 [61] stringi_1.7.12     SQUAREM_2021.1     highr_0.10        
 [64] deconvolveR_1.2-1  caTools_1.18.2     truncnorm_1.0-9   
 [67] horseshoe_0.2.0    rlang_1.1.1        pkgconfig_2.0.3   
 [70] matrixStats_1.0.0  bitops_1.0-7       evaluate_0.22     
 [73] lattice_0.20-45    invgamma_1.1       purrr_1.0.2       
 [76] htmlwidgets_1.6.1  bit_4.0.5          Rfast_2.0.8       
 [79] cowplot_1.1.1      tidyselect_1.2.0   R6_2.5.1          
 [82] generics_0.1.3     pillar_1.9.0       whisker_0.4.1     
 [85] withr_2.5.1        survival_3.5-3     mixsqp_0.3-48     
 [88] tibble_3.2.1       crayon_1.5.2       utf8_1.2.3        
 [91] plotly_4.10.2      tzdb_0.3.0         rmarkdown_2.20    
 [94] progress_1.2.2     grid_4.2.1         data.table_1.14.8 
 [97] git2r_0.31.0       digest_0.6.33      vebpm_0.4.9       
[100] tidyr_1.3.0        httpuv_1.6.9       MCMCpack_1.6-3    
[103] RcppParallel_5.1.7 munsell_0.5.0      viridisLite_0.4.2 
[106] bslib_0.4.2        quadprog_1.5-8