Full admixture graph simulation
Jason Willwerscheid
1/16/2020
Last updated: 2020-01-18
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 oddest thing about the previous simulation was that populations 1 and 4 were found to be correlated (albeit only slightly). Here I re-run with a different seed and a larger value of \(w\) to see whether that phenomenom persists. (I’ll test smaller \(w\) in a subsequent simulation.)
I also note that the KL divergence term for factors was lower for the greedy initialization, while the KL divergence term for loadings was (as expected) higher for the backfitted initialization. I increase \(p\) a bit here to see whether I can push the greedy ELBO above the backfit ELBO.
set.seed(90210)
simple.admix <- admix_graph_sim(n_per_pop = 20, p = 50000,
c1 = 1, c2 = 1, c3 = 1, c4 = 1,
c5 = 0.5, c6 = 1, c7 = 0.5,
w = 0.35, sigma_e = sqrt(0.1))
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...#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.#> Adding factor 3 to flash object...#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.#> Adding factor 4 to flash object...
#> Adding factor 5 to flash object...
#> Adding factor 6 to flash object...
#> Adding factor 7 to flash object...
#> Factor doesn't significantly increase objective and won't be added.
#> Wrapping up...
#> Done.
#> Nullchecking 6 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 = 1750, maxiter = 2000, tol = 0.001, verbose = FALSE)
ggplot(drift.flg$iterations, aes(x = iter, y = elbo)) + geom_line()
drift.flg[c("elbo", "KL_l", "KL_f")]#> $elbo
#> [1] -1636784
#>
#> $KL_l
#> [1] -247.36172 -171.67651 -173.89632 -74.02671 -173.29096 -45.12987
#>
#> $KL_f
#> [1] -565375.8
plot_loadings(drift.flg$EL, labs, paste("s2:", round(drift.flg$prior_s2, 2)))
plot_cov(drift.flg)
Flash initialization (backfit)
Initial values
fl <- fl %>% flash.backfit() %>% flash.nullcheck(remove = TRUE)#> Backfitting 6 factors (tolerance: 5.96e-02)...
#> Difference between iterations is within 1.0e+05...
#> Difference between iterations is within 1.0e+04...
#> Difference between iterations is within 1.0e+03...#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.
#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.#> Difference between iterations is within 1.0e+02...#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.#> Difference between iterations is within 1.0e+01...#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.#> Difference between iterations is within 1.0e+00...
#> Difference between iterations is within 1.0e-01...
#> Wrapping up...
#> Done.
#> Nullchecking 6 factors...
#> Wrapping up...
#> Done.plot_loadings(fl$flash.fit$EF[[1]], labs)
Drift results
drift.flb <- drift(init_from_flash(fl), miniter = 750, maxiter = 1000, tol = 0.001, verbose = FALSE)#> Warning in estimate_mixprop(data, g, prior, optmethod = optmethod, control
#> = control, : Optimization failed to converge. Results may be unreliable.
#> Try increasing maxiter and rerunning.ggplot(drift.flb$iterations, aes(x = iter, y = elbo)) + geom_line()
drift.flb[c("elbo", "KL_l", "KL_f")]#> $elbo
#> [1] -1636481
#>
#> $KL_l
#> [1] -314.83695 -223.13574 -207.86085 -45.12987
#>
#> $KL_f
#> [1] -565143.8
plot_loadings(drift.flb$EL, labs, paste("s2:", round(drift.flb$prior_s2, 2)))
plot_cov(drift.flb)
Results summary
all.drift <- list(drift.flg, drift.flb)
res.df <- data.frame(
Name = c("flash.greedy", "flash.backfit"),
InitialELBO = sapply(all.drift, function(x) x$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 | -1642712 | -1636784 | 5927.954 | 1856 | -885.382 | -565375.8 | 0.1 |
| flash.backfit | -1638612 | -1636481 | 2130.842 | 792 | -790.963 | -565143.8 | 0.1 |
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
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#> 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
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#>
#> loaded via a namespace (and not attached):
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