Last updated: 2020-01-17

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File Version Author Date Message
Rmd 37e8139 Jason Willwerscheid 2020-01-17 wflow_publish(“analysis/admix_sim_full.Rmd”)
html e9d8a29 Jason Willwerscheid 2020-01-17 Build site.
Rmd 3715e43 Jason Willwerscheid 2020-01-17 wflow_publish(“analysis/admix_sim_full.Rmd”)
html f73773f Jason Willwerscheid 2020-01-16 Build site.
Rmd 3da801d Jason Willwerscheid 2020-01-16 wflow_publish(“analysis/admix_sim_full.Rmd”) 
suppressMessages({
  library(flashier)
  library(drift.alpha)
  library(ggplot2)
  library(reshape2)
  library(tidyverse)
})

Time to try out drift on the full admixture graph from Pickrell and Pritchard (Figure 1, Example Graph C). To make the problem easier, I set \(p\) large and \(\sigma_e\) small.

set.seed(666)
simple.admix <- admix_graph_sim(n_per_pop = 20, p = 20000, 
                                c1 = 1, c2 = 1, c3 = 1, c4 = 1,
                                c5 = 0.5, c6 = 1, c7 = 0.5,
                                w = 0.25, sigma_e = sqrt(0.1))
plot_cov(simple.admix$covmat, as.is = TRUE)

Version Author Date
f73773f Jason Willwerscheid 2020-01-16

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...
#> 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 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)

Version Author Date
f73773f Jason Willwerscheid 2020-01-16

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()

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16 
drift.flg[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -657041.9
#> 
#> $KL_l
#> [1] -154.41924 -166.45078 -139.16191  -65.79745 -171.93078  -45.12987
#> 
#> $KL_f
#> [1] -228345.1

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

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16 
plot_cov(drift.flg)

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16

Flash initialization (backfit)

Initial values

fl <- fl %>% flash.backfit() %>% flash.nullcheck(remove = TRUE)
#> Backfitting 6 factors (tolerance: 2.38e-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.
#>   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.

#> 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+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.

#> 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+00...
#>   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.

#> 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...
#> Wrapping up...
#> Done.
#> Nullchecking 6 factors...
#> Wrapping up...
#> Done.
plot_loadings(fl$flash.fit$EF[[1]], labs)

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16

Drift results

drift.flb <- drift(init_from_flash(fl), miniter = 750, maxiter = 1000, tol = 0.001, verbose = FALSE)
ggplot(drift.flb$iterations, aes(x = iter, y = elbo)) + geom_line()

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16 
drift.flb[c("elbo", "KL_l", "KL_f")]
#> $elbo
#> [1] -656960.3
#> 
#> $KL_l
#> [1] -254.19492 -164.70741 -105.11501  -45.12987
#> 
#> $KL_f
#> [1] -228419.6

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

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16 
plot_cov(drift.flb)

Version Author Date
e9d8a29 Jason Willwerscheid 2020-01-17
f73773f Jason Willwerscheid 2020-01-16

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 -660071.7 -657041.9 3029.805 1769 -742.890 -228345.1 0.1
flash.backfit -657762.9 -656960.3 802.553 750 -569.147 -228419.6 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
#> 
#> 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):
#>  [1] Rcpp_1.0.1        lubridate_1.7.4   lattice_0.20-38  
#>  [4] assertthat_0.2.1  rprojroot_1.3-2   digest_0.6.18    
#>  [7] foreach_1.4.4     truncnorm_1.0-8   R6_2.4.0         
#> [10] cellranger_1.1.0  plyr_1.8.4        backports_1.1.3  
#> [13] evaluate_0.13     highr_0.8         httr_1.4.0       
#> [16] pillar_1.3.1      rlang_0.4.2       lazyeval_0.2.2   
#> [19] pscl_1.5.2        readxl_1.3.1      rstudioapi_0.10  
#> [22] ebnm_0.1-24       irlba_2.3.3       whisker_0.3-2    
#> [25] Matrix_1.2-15     rmarkdown_1.12    labeling_0.3     
#> [28] munsell_0.5.0     mixsqp_0.3-15     broom_0.5.1      
#> [31] compiler_3.5.3    modelr_0.1.5      xfun_0.6         
#> [34] pkgconfig_2.0.2   SQUAREM_2017.10-1 htmltools_0.3.6  
#> [37] tidyselect_0.2.5  workflowr_1.2.0   codetools_0.2-16 
#> [40] crayon_1.3.4      withr_2.1.2       MASS_7.3-51.1    
#> [43] grid_3.5.3        nlme_3.1-137      jsonlite_1.6     
#> [46] gtable_0.3.0      git2r_0.25.2      magrittr_1.5     
#> [49] scales_1.0.0      cli_1.1.0         stringi_1.4.3    
#> [52] fs_1.2.7          doParallel_1.0.14 xml2_1.2.0       
#> [55] generics_0.0.2    iterators_1.0.10  tools_3.5.3      
#> [58] glue_1.3.1        hms_0.4.2         parallel_3.5.3   
#> [61] yaml_2.2.0        colorspace_1.4-1  ashr_2.2-38      
#> [64] rvest_0.3.4       knitr_1.22        haven_2.1.1