Branching + admixture simulation: large p and longer runs
Jason Willwerscheid
1/10/2020
Last updated: 2020-01-15
Checks: 6 0
Knit directory: drift-workflow/analysis/
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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$covmat, as.is = TRUE)
Flash initialization (greedy)
Initial values
fl <- flash(simple.admix$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)
Drift results
drift.flg <- drift(init_from_flash(fl), miniter = 1000, maxiter = 1000, tol = 1e-4, verbose = FALSE)
ggplot(drift.flg$elbo.df, aes(x = iter, y = elbo)) + geom_line()
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
#>
#> $KL_f
#> [1] -76753.65
lblr <- paste("s2:", round(drift.flg$prior_s2, 2))
names(lblr) <- 1:length(drift.flg$prior_s2)
lblr <- as_labeller(lblr)
plot_loadings(drift.flg$EL, labs, lblr)
plot_cov(drift.flg$EL * rep(sqrt(drift.flg$prior_s2), each = 80))
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)
Drift results
drift.flb <- drift(init_from_flash(fl), miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.flb$elbo.df, aes(x = iter, y = elbo)) + geom_line()
drift.flb[c("elbo", "KL_l", "KL_f")]#> $elbo
#> [1] -657394.7
#>
#> $KL_l
#> [1] -236.45097 -162.40373 -45.12987
#>
#> $KL_f
#> [1] -76717.34
lblr <- paste("s2:", round(drift.flb$prior_s2, 2))
names(lblr) <- 1:length(drift.flb$prior_s2)
lblr <- as_labeller(lblr)
plot_loadings(drift.flb$EL, labs, lblr)
plot_cov(drift.flb$EL * rep(sqrt(drift.flb$prior_s2), each = 80))
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)
Drift results
drift.true <- drift(init, miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.true$elbo.df, aes(x = iter, y = elbo)) + geom_line()
drift.true[c("elbo", "KL_l", "KL_f")]#> $elbo
#> [1] -657492.2
#>
#> $KL_l
#> [1] -166.04887 -54.34254 -155.82065 -162.33425
#>
#> $KL_f
#> [1] -76834.54
lblr <- paste("s2:", round(drift.true$prior_s2, 2))
names(lblr) <- 1:length(drift.true$prior_s2)
lblr <- as_labeller(lblr)
plot_loadings(drift.true$EL, labs, lblr)
plot_cov(drift.true$EL * rep(sqrt(drift.true$prior_s2), each = 80))
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)
Drift results
drift.3factor <- drift(init, miniter = 1000, maxiter = 1000, tol = 0.0005, verbose = FALSE)
ggplot(drift.3factor$elbo.df, aes(x = iter, y = elbo)) + geom_line()
drift.3factor[c("elbo", "KL_l", "KL_f")]#> $elbo
#> [1] -658682
#>
#> $KL_l
#> [1] -45.12987 -172.80963 -162.40321
#>
#> $KL_f
#> [1] -78074.79
lblr <- paste("s2:", round(drift.3factor$prior_s2, 2))
names(lblr) <- 1:length(drift.3factor$prior_s2)
lblr <- as_labeller(lblr)
plot_loadings(drift.3factor$EL, labs, lblr)
plot_cov(drift.3factor$EL * rep(sqrt(drift.3factor$prior_s2), each = 80))
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$elbo.df$elbo[1]),
FinalELBO = sapply(all.drift, function(x) x$elbo),
ELBOdiff = sapply(all.drift, function(x) x$elbo - x$elbo.df$elbo[1]),
n_iter = sapply(all.drift, function(x) max(x$elbo.df$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)
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#> attached base packages:
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#>
#> other attached packages:
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