mr-ash demo
Peter Carbonetto
February 20, 2020
Last updated: 2020-02-21
Checks: 7 0
Knit directory: mr-ash/analysis/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | bca4f7a | Peter Carbonetto | 2020-02-20 | Minor edit to Rmd text. |
| html | 80585bf | Peter Carbonetto | 2020-02-20 | Re-built it one more time to be safe. |
| html | 63891ce | Peter Carbonetto | 2020-02-20 | Build site. |
| html | 1b60536 | Peter Carbonetto | 2020-02-20 | Re-built mr_ash_demo after a few minor edits. |
| Rmd | a255a44 | Peter Carbonetto | 2020-02-20 | wflow_publish(“mr_ash_demo.Rmd”) |
| html | 582e465 | Peter Carbonetto | 2020-02-20 | Created first draft of mr_ash_demo workflowr page. |
| html | c1f830f | Peter Carbonetto | 2020-02-20 | Created first draft of mr_ash_demo workflowr page. |
| Rmd | 12ad071 | Peter Carbonetto | 2020-02-20 | wflow_publish(“mr_ash_demo.Rmd”) |
An illustration of the “mr-ash” co-ordinate ascent algorithm applied to a small, simulated data set.
Script parameters
These are the data simulation settings.
n <- 500
p <- 1000
sd <- c(0, 1, 2)
w <- c(0.98, 0.01, 0.01)This specifies the variances for the mixture-of-normals prior on the regression coefficients.
s0 <- c(0.01,0.5,1)^2Load functions
This R code provides a very simple implementation of the mr-ash algorithm.
source("../code/misc.R")
source("../code/mr_ash.R")Simulate data
set.seed(1)
X <- matrix(rnorm(n*p),n,p)
k <- sample(length(w),p,replace = TRUE,prob = w)
beta <- sd[k] * rnorm(p)
y <- drop(X %*% beta + rnorm(n))Fit model
These are the initial estimates of residual variance (s), mixture weights (w0) and posterior mean estimates of the regression coefficients (b).
b <- rep(0,p)
s <- 1
w0 <- c(0.5,0.25,0.25)Fit the model by running 20 EM updates.
fit <- mr_ash(X,y,s,s0,w0,b,20)
# iter elbo max|b-b'|
# 1 -1.756557184890e+03 6.927e-01
# 2 -1.099123931192e+03 4.780e-01
# 3 -8.578720448759e+02 2.738e-01
# 4 -8.091518626699e+02 5.838e-02
# 5 -8.058755580814e+02 9.888e-03
# 6 -8.057118084929e+02 3.166e-03
# 7 -8.056811273699e+02 8.567e-04
# 8 -8.056629085272e+02 3.231e-04
# 9 -8.056505966230e+02 1.970e-04
# 10 -8.056421813525e+02 1.526e-04
# 11 -8.056363928186e+02 1.260e-04
# 12 -8.056323873106e+02 1.056e-04
# 13 -8.056296004148e+02 8.869e-05
# 14 -8.056276519072e+02 7.458e-05
# 15 -8.056262837294e+02 6.277e-05
# 16 -8.056253194612e+02 5.288e-05
# 17 -8.056246376769e+02 4.458e-05
# 18 -8.056241542917e+02 3.761e-05
# 19 -8.056238107616e+02 3.176e-05
# 20 -8.056235661300e+02 2.684e-05Review model fit
Compare the mr-ash estimates against the values used to simulate the data.
plot(beta,fit$b,pch = 20,col = "black")
abline(a = 0,b = 1,col = "skyblue",lty = "dotted",xlab = "true",
ylab = "estimated")
Plot the improvement in the model fit over time, as measured by the ELBO.
plot(max(fit$elbo) - fit$elbo + 1e-5,type = "l",col = "dodgerblue",
lwd = 2,log = "y",xlab = "iteration",ylab = "distance to \"best\" ELBO")
sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.3
#
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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
#
# loaded via a namespace (and not attached):
# [1] workflowr_1.6.0 Rcpp_1.0.3 rprojroot_1.3-2 digest_0.6.23
# [5] later_1.0.0 R6_2.4.1 backports_1.1.5 git2r_0.26.1
# [9] magrittr_1.5 evaluate_0.14 stringi_1.4.3 rlang_0.4.2
# [13] fs_1.3.1 promises_1.1.0 whisker_0.4 rmarkdown_2.0
# [17] tools_3.6.2 stringr_1.4.0 glue_1.3.1 httpuv_1.5.2
# [21] xfun_0.11 yaml_2.2.0 compiler_3.6.2 htmltools_0.4.0
# [25] knitr_1.26