Revisiting prior families for trees: Part X
Jason Willwerscheid
7/22/2020
Last updated: 2020-08-12
Checks: 6 0
Knit directory: drift-workflow/analysis/
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suppressMessages({
library(flashier)
library(drift.alpha)
library(tidyverse)
})Here I present some more scenarios where point-Laplace priors outperform scale mixtures of normals.
sim_tree <- function(n_range,
p = 10000,
branch_means,
branch_sds,
resid_sd = 0.1,
admix_pops = NULL,
outgroup = FALSE,
seed = 666) {
set.seed(seed)
depth <- length(branch_means)
npop_pure <- 2^(depth - 1)
if (is.null(admix_pops)) {
admix_pops <- matrix(nrow = 0, ncol = 0)
}
npop_admix <- ncol(admix_pops)
npop <- npop_pure + npop_admix + outgroup
if (length(n_range) == 1) {
n <- rep(n_range, npop)
} else {
n <- sample(30:100, npop, replace = TRUE)
}
K <- 2^depth - 1
FF <- matrix(nrow = p, ncol = K)
k <- 1
for (d in 1:depth) {
for (i in 1:(2^(d - 1))) {
FF[, k] <- rnorm(p, sd = branch_means[d] + rnorm(1, sd = branch_sds[d]))
k <- k + 1
}
}
tree_mat <- matrix(0, nrow = npop_pure, ncol = K)
k <- 1
for (d in 1:depth) {
size <- 2^(depth - d)
for (i in 1:(2^(d - 1))) {
tree_mat[((i - 1) * size + 1):(i * size), k] <- 1
k <- k + 1
}
}
pop_means <- FF %*% t(tree_mat)
if (npop_admix > 0) {
pop_means <- cbind(pop_means, pop_means %*% admix_pops)
}
if (outgroup) {
pop_means <- cbind(pop_means, rnorm(p, mean = 0, sd = sqrt(sum(branch_sds^2))))
}
Y <- NULL
for (i in 1:npop) {
Y <- rbind(Y, matrix(pop_means[, i], nrow = n[i], ncol = p, byrow = TRUE))
}
Y <- Y + rnorm(sum(n) * p, sd = resid_sd)
plot_fl <- function(fl) {
dr <- init_from_flash(fl)
sd <- sqrt(dr$prior_s2)
L <- dr$EL
LDsqrt <- L %*% diag(sd)
K <- ncol(LDsqrt)
plot_loadings(LDsqrt[,1:K], rep(letters[1:npop], n)) +
scale_color_brewer(palette="Set3")
}
return(list(Y = Y, plot_fn = plot_fl))
}
init.mean.factor <- function(resids, zero.idx) {
u <- matrix(1, nrow = nrow(resids), ncol = 1)
u[zero.idx, 1] <- 0
v <- t(solve(crossprod(u), crossprod(u, resids)))
return(list(u, v))
}- Populations of unequal sizes (
n_range = 30:100) with an additional 60-40 admixture:
Scale mixtures of normals:
admix_4pop <- sim_tree(n_range = 30:100,
p = 10000,
branch_means = rep(1, 3),
branch_sds = rep(0, 3),
resid_sd = 0.1,
admix_pops = matrix(c(0, 0.6, 0.4, 0), ncol = 1))
fl_nsm <- flash.init(admix_4pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 4,
prior.family = c(prior.normal.scale.mix(), prior.normal())) %>%
flash.backfit(tol = 1e-4)
admix_4pop$plot_fn(fl_nsm)
Point-Laplace:
fl_pl <- flash.init(admix_4pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 4,
prior.family = c(prior.point.laplace(), prior.normal())) %>%
flash.backfit(tol = 1e-4)
admix_4pop$plot_fn(fl_pl)
- Populations of unequal sizes with an additional outgroup:
Scale mixtures of normals:
outgroup_4pop <- sim_tree(n_range = 30:100,
p = 10000,
branch_means = rep(1, 3),
branch_sds = rep(0, 3),
resid_sd = 0.1,
outgroup = TRUE)
fl_nsm <- flash.init(outgroup_4pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 4,
prior.family = c(prior.normal.scale.mix(), prior.normal())) %>%
flash.backfit(tol = 1e-4)
outgroup_4pop$plot_fn(fl_nsm)
Point-Laplace:
fl_pl <- flash.init(outgroup_4pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 4,
prior.family = c(prior.point.laplace(), prior.normal())) %>%
flash.backfit(tol = 1e-4)
outgroup_4pop$plot_fn(fl_pl)
- Balanced tree with eight populations:
Scale mixtures of normals:
tree_8pop <- sim_tree(n_range = 50,
p = 10000,
branch_means = rep(1, 4),
branch_sds = rep(0, 4),
resid_sd = 0.1)
fl_nsm <- flash.init(tree_8pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 8,
prior.family = c(prior.normal.scale.mix(), prior.normal())) %>%
flash.backfit(tol = 1e-4)
tree_8pop$plot_fn(fl_nsm)
Point-Laplace:
fl_pl <- flash.init(tree_8pop$Y) %>%
flash.set.verbose(0) %>%
flash.add.greedy(Kmax = 8,
prior.family = c(prior.point.laplace(), prior.normal())) %>%
flash.backfit(tol = 1e-4, maxiter = 1000)
tree_8pop$plot_fn(fl_pl)
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 ggplot2_3.2.0 tidyverse_1.2.1
#> [10] drift.alpha_0.0.10 flashier_0.2.7
#>
#> loaded via a namespace (and not attached):
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#> [34] htmltools_0.3.6 tidyselect_0.2.5 workflowr_1.2.0
#> [37] withr_2.1.2 crayon_1.3.4 grid_3.5.3
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#> [43] git2r_0.25.2 magrittr_1.5 scales_1.0.0
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