Last updated: 2019-11-02

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    Modified:   analysis/minque.Rmd

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File Version Author Date Message
Rmd 0e9e766 Matthew Stephens 2019-11-02 workflowr::wflow_publish(“mr.ash.changepoint.Rmd”)
html 15c0630 Matthew Stephens 2019-11-02 Build site.
Rmd a0bc392 Matthew Stephens 2019-11-02 workflowr::wflow_publish(“mr.ash.changepoint.Rmd”) 
library("mr.ash.alpha")
library("glmnet")
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-18
library("genlasso")
Loading required package: igraph

Attaching package: 'igraph'
The following objects are masked from 'package:stats':

    decompose, spectrum
The following object is masked from 'package:base':

    union

Introduction

I’m going to try the current version of mr.ash.alpha on a changepoint problem for my own interest.

Single changepoint

First simulate data:

set.seed(100)
n = 100
p = n
X = matrix(0,nrow=n,ncol=n)
for(i in 1:n){
  X[i:n,i] = 1
}

btrue = rep(0,n)
btrue[50] = 8 
Y = X %*% btrue + rnorm(n)
plot(Y)
lines(X %*% btrue)

Version Author Date
15c0630 Matthew Stephens 2019-11-02

This works great out of the box:

fit.ma = mr.ash(X,Y)
plot(Y)
lines(X %*% btrue,lwd=1)
lines(predict(fit.ma,X),col=2,lwd=2)

fit.glmnet = glmnet(X,Y)
fit.glmnet.cv = glmnet::cv.glmnet(X,Y)
lines(predict(fit.glmnet.cv,X),col=3,lwd=2)

fit.genlasso = trendfilter(Y,ord=0)
fit.genlasso.cv = cv.trendfilter(fit.genlasso)
Fold 1 ... Fold 2 ... Fold 3 ... Fold 4 ... Fold 5 ... 
lines(fit.genlasso$fit[,which(fit.genlasso.cv$lambda==fit.genlasso.cv$lambda.min)],lwd=2,col=4)

Version Author Date
15c0630 Matthew Stephens 2019-11-02

Double changepoint

Now we do a harder case, similar to the Susie paper:

btrue[52] = -8 
Y = X %*% btrue + rnorm(n,0,0.1)
plot(Y)
lines(X %*% btrue)

Version Author Date
15c0630 Matthew Stephens 2019-11-02 
fit.ma = mr.ash(X,Y)
plot(Y)
lines(predict(fit.ma,X),col=2)

fit.glmnet = glmnet(X,Y)
fit.glmnet.cv = glmnet::cv.glmnet(X,Y)
lines(predict(fit.glmnet.cv,X),col=3,lwd=2)

fit.genlasso = trendfilter(Y,ord=0)
fit.genlasso.cv = cv.trendfilter(fit.genlasso)
Fold 1 ... Fold 2 ... Fold 3 ... Fold 4 ... Fold 5 ... 
lines(fit.genlasso$fit[,which(fit.genlasso.cv$lambda==fit.genlasso.cv$lambda.min)],lwd=2,col=4)

Version Author Date
15c0630 Matthew Stephens 2019-11-02

It is interesting that glmnet and genlasso give quite different answers. Clearly glmnet is entirely missing the changepoint. If you zoom in you will see that genlasso is overfitting - it is not just getting the single changepoint but fitting the data everywhere!

Also it looks like in this case mr.ash is converging to local optima. (the change is a bit too early…) Here we try warmstarts of mr.ash from genlasso solution, and from truth. However, both give NaN as answers. Not sure why.

b.genlasso  = fit.genlasso$beta[,which(fit.genlasso.cv$lambda==fit.genlasso.cv$lambda.min)]

plot(Y)
lines(b.genlasso)

Version Author Date
15c0630 Matthew Stephens 2019-11-02 
fit.ma.warm = mr.ash(X,Y,beta.init = b.genlasso)
fit.ma.warm2 = mr.ash(X,Y,beta.init = btrue)


predict(fit.ma.warm,X)
  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [18] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [35] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [52] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [69] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [86] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
predict(fit.ma.warm2,X)
  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [18] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [35] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [52] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [69] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
 [86] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

sessionInfo()
R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.4

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] genlasso_1.4       igraph_1.2.4.1     glmnet_2.0-18     
[4] foreach_1.4.7      Matrix_1.2-17      mr.ash.alpha_0.1-3

loaded via a namespace (and not attached):
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 [5] workflowr_1.4.0  lattice_0.20-38  stringr_1.4.0    tools_3.6.0     
 [9] grid_3.6.0       xfun_0.8         git2r_0.26.1     htmltools_0.3.6 
[13] iterators_1.0.12 yaml_2.2.0       rprojroot_1.3-2  digest_0.6.20   
[17] fs_1.3.1         codetools_0.2-16 glue_1.3.1       evaluate_0.14   
[21] rmarkdown_1.14   stringi_1.4.3    compiler_3.6.0   backports_1.1.4 
[25] pkgconfig_2.0.2