shrinkage
Matthew Stephens
April 9, 2018
Last updated: 2020-04-24
Checks: 7 0
Knit directory: stat34800/analysis/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 63128c9 | Matthew Stephens | 2020-04-24 | workflowr::wflow_publish(“analysis/eb_vs_soft.Rmd”) |
| html | d66f560 | Matthew Stephens | 2019-04-16 | Build site. |
| Rmd | 8d23226 | Matthew Stephens | 2019-04-16 | workflowr::wflow_publish(“analysis/eb_vs_soft.Rmd”) |
| html | 8f13d93 | stephens999 | 2018-05-21 | Build site. |
| Rmd | 5b61f90 | stephens999 | 2018-05-21 | workflowr::wflow_publish(“eb_vs_soft.Rmd”) |
| Rmd | fcfdba2 | stephens999 | 2018-04-09 | add comparison of eb vs soft thresholding |
Prerequisites
Before running this you will need to install the packages ashr from CRAN and ebnm from github, by running something like the following code chunk.
install.packages("ashr")
install.packages("devtools")
devtools::install_github("stephenslab/ebnm")library("ashr")
library("ebnm")Simulate some data
Here we simulate a pretty sparse situation: 90% sparsity.
set.seed(1)
theta = c(rep(0,900),rnorm(100,0,4))
x = theta + rnorm(1000)
hist(theta,breaks = seq(-10,10,length=20),xlim=c(-10,10))
Now do inference under the EBNM model. Notice how the small values are shrunk hard, and the big values are hardly shrunk at all.
x.pn = ebnm_point_normal(x,1)
plot(x,x.pn$posterior$mean,main="observation (x) vs posterior mean", ylab="posterior mean")
abline(a=0,b=1,col="red")
What about soft thresholding?
soft_thresh = function(x,lambda){
ifelse(abs(x)>lambda, sign(x)*(abs(x)-lambda), 0)
}
plot(x,soft_thresh(x,1.5),main="observation (x) vs soft-thresholding estimate (lambda=1.5)",ylab="soft-thresholded estimate")
abline(a=0,b=1,col="red")
| Version | Author | Date |
|---|---|---|
| d66f560 | Matthew Stephens | 2019-04-16 |
Now look at Mean Squared Error. Notice that both do much better than no shrinkage!!
mse = rep(0,100)
l = seq(0,5,length=100)
for(i in 1:100){
mse[i] = mean((theta-soft_thresh(x,l[i]))^2)
}
plot(l,mse,ylim=c(0,1.2), main="blue = no shrinkage; red=Empirical Bayes; points= soft-thresholding", xlab="lambda")
abline(h=mean((theta-get_pm(x.pn))^2),col="red")
abline(h=mean((theta-x)^2),col="blue")
| Version | Author | Date |
|---|---|---|
| d66f560 | Matthew Stephens | 2019-04-16 |
sessionInfo()R version 3.6.0 (2019-04-26)
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/3.6/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
other attached packages:
[1] ebnm_0.1-24 ashr_2.2-47 workflowr_1.6.1
loaded via a namespace (and not attached):
[1] Rcpp_1.0.4 knitr_1.28 whisker_0.4 magrittr_1.5
[5] SQUAREM_2020.2 lattice_0.20-40 R6_2.4.1 rlang_0.4.5
[9] stringr_1.4.0 tools_3.6.0 grid_3.6.0 xfun_0.12
[13] irlba_2.3.3 invgamma_1.1 git2r_0.26.1 htmltools_0.4.0
[17] yaml_2.2.1 digest_0.6.25 rprojroot_1.3-2 mixsqp_0.3-31
[21] Matrix_1.2-18 later_1.0.0 promises_1.1.0 fs_1.3.2
[25] glue_1.4.0 evaluate_0.14 rmarkdown_2.1 stringi_1.4.6
[29] compiler_3.6.0 backports_1.1.5 truncnorm_1.0-8 httpuv_1.5.2