Last updated: 2020-01-16

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suppressMessages({
  library(flashier)
  library(drift.alpha)
  library(ggplot2)
  library(reshape2)
  library(tidyverse)
})

The setup is the same as the previous simulation, but I’ve increased \(p\) to a more realistic 10000 and in each case I run drift for a minimum of 1000 iterations. I only include the more promising initializations.

set.seed(666)
simple.admix <- admix_graph_sim(n_per_pop = 20, p = 10000, 
                                c1 = 2, c2 = 1, c3 = 0, c4 = 0,
                                c5 = 1, c6 = 1, c7 = 0,
                                w = 0.5, sigma_e = sqrt(0.25))
plot_cov(simple.admix$covmat, as.is = TRUE)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Flash initialization (greedy)

Initial values

fl <- flash(simple.admix$Y, prior.family = c(prior.bimodal(), prior.normal()))
#> Adding factor 1 to flash object...
#> Adding factor 2 to flash object...
#> Adding factor 3 to flash object...
#> Adding factor 4 to flash object...
#> Adding factor 5 to flash object...
#> Adding factor 6 to flash object...
#> Factor doesn't significantly increase objective and won't be added.
#> Wrapping up...
#> Done.
#> Nullchecking 5 factors...
#> Done.
labs <- rep(c("A", "B", "C", "D"), each = 20)
plot_loadings(fl$flash.fit$EF[[1]], labs)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Drift results

drift.flg <- drift(init_from_flash(fl), miniter = 1000, maxiter = 1000, tol = 1e-4, verbose = FALSE)
ggplot(drift.flg$iterations, aes(x = iter, y = elbo)) + geom_line()

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
drift.flg[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -657560.1
#> 
#> $KL_l
#> [1] -190.66999 -190.57591  -64.74085 -153.20412    0.00000
#> 
#> $KL_f
#> [1] -76753.65

plot_loadings(drift.flg$EL, labs,  paste("s2:", round(drift.flg$prior_s2, 2)))

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
plot_cov(drift.flg)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Flash initialization (backfit)

Initial values

fl <- fl %>% flash.backfit() %>% flash.nullcheck(remove = TRUE)
#> Backfitting 5 factors (tolerance: 1.19e-02)...
#>   Difference between iterations is within 1.0e+04...
#>   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...
#> Wrapping up...
#> Done.
#> Nullchecking 5 factors...
#> Wrapping up...
#> Done.
plot_loadings(fl$flash.fit$EF[[1]], labs)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Drift results

drift.flb <- drift(init_from_flash(fl), miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.flb$iterations, aes(x = iter, y = elbo)) + geom_line()

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
drift.flb[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -657394.7
#> 
#> $KL_l
#> [1] -236.45097 -162.40373  -45.12987
#> 
#> $KL_f
#> [1] -76717.34

plot_loadings(drift.flb$EL, labs, paste("s2:", round(drift.flb$prior_s2, 2)))

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
plot_cov(drift.flb)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Initialization from “true” solution

Initial values

# I can't give init_from_EL a singular matrix, so I need to fudge the loadings a bit.
EL <- cbind(c(rep(1, 40), rep(0.25, 20), rep(0, 20)),
            c(rep(1, 20), rep(0, 60)),
            c(rep(0, 20), rep(1, 20), rep(0.5, 20), rep(0, 20)),
            c(rep(0, 40), rep(0.5, 20), rep(1, 20)))
init <- init_from_EL(simple.admix$Y, EL)
plot_loadings(init$EL, labs)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Drift results

drift.true <- drift(init, miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.true$iterations, aes(x = iter, y = elbo)) + geom_line()

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
drift.true[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -657492.2
#> 
#> $KL_l
#> [1] -166.04887  -54.34254 -155.82065 -162.33425
#> 
#> $KL_f
#> [1] -76834.54

plot_loadings(drift.true$EL, labs, paste("s2:", round(drift.true$prior_s2, 2)))

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
plot_cov(drift.true)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Initialization using three factors

Initial values

EL <- cbind(c(rep(1, 20), rep(0, 60)),
            c(rep(0, 20), rep(1, 20), rep(0.5, 20), rep(0, 20)),
            c(rep(0, 40), rep(0.5, 20), rep(1, 20)))
init <- init_from_EL(simple.admix$Y, EL)
plot_loadings(init$EL, labs)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Drift results

drift.3factor <- drift(init, miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.3factor$iterations, aes(x = iter, y = elbo)) + geom_line()

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
drift.3factor[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -658682
#> 
#> $KL_l
#> [1]  -45.12987 -172.80963 -162.40321
#> 
#> $KL_f
#> [1] -78074.79

plot_loadings(drift.3factor$EL, labs, paste("s2:", round(drift.3factor$prior_s2, 2)))

Version Author Date
23b773d Jason Willwerscheid 2020-01-15 
plot_cov(drift.3factor)

Version Author Date
23b773d Jason Willwerscheid 2020-01-15

Results summary

all.drift <- list(drift.flg, drift.flb, drift.true, drift.3factor)

res.df <- data.frame(
  Name = c("flash.greedy", "flash.backfit", "true.4factor", "three.factors"),
  InitialELBO = sapply(all.drift, function(x) x$iterations$elbo[1]),
  FinalELBO = sapply(all.drift, function(x) x$elbo),
  ELBOdiff = sapply(all.drift, function(x) x$elbo - x$iterations$elbo[1]),
  n_iter = sapply(all.drift, function(x) max(x$iterations$iter)),
  KL_l = sapply(all.drift, function(x) sum(x$KL_l)),
  KL_f = sapply(all.drift, function(x) x$KL_f),
  ResidS2 = sapply(all.drift, function(x) x$resid_s2)
)

knitr::kable(res.df, digits = 3)
Name InitialELBO FinalELBO ELBOdiff n_iter KL_l KL_f ResidS2
flash.greedy -664277.1 -657560.1 6716.990 1000 -599.191 -76753.65 0.25
flash.backfit -657604.9 -657394.7 210.194 1000 -443.985 -76717.34 0.25
true.4factor -659188.8 -657492.2 1696.551 1000 -538.546 -76834.54 0.25
three.factors -658761.7 -658682.0 79.754 1000 -380.343 -78074.79 0.25 


sessionInfo()
#> R version 3.5.3 (2019-03-11)
#> Platform: x86_64-apple-darwin15.6.0 (64-bit)
#> Running under: macOS Mojave 10.14.6
#> 
#> 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] forcats_0.4.0     stringr_1.4.0     dplyr_0.8.0.1    
#>  [4] purrr_0.3.2       readr_1.3.1       tidyr_0.8.3      
#>  [7] tibble_2.1.1      tidyverse_1.2.1   reshape2_1.4.3   
#> [10] ggplot2_3.2.0     drift.alpha_0.0.6 flashier_0.2.2   
#> 
#> loaded via a namespace (and not attached):
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#> [49] cli_1.1.0         stringi_1.4.3     fs_1.2.7         
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