Improvement on Implementation with Rmosek: Normalization

Introduction

When fitting Gaussian derivatives, normalization could potentially increase the parity in the magnitude of the coefficients and thus make the results more accurate.

data.list = readRDS("../output/z_null_liver_777_select.RDS")
zscore = data.list[[3]]
sel.num = length(zscore)
data.list.index = readRDS("../output/z_null_liver_777_select_index.RDS")
ord = data.list.index[[3]]$gd.ord

source("../code/gdash.R")
library(ashr)
library(PolynomF)
x <- polynom()
H <- polylist(x, - 1 + x^2)
for(n in 2 : 19)
  H[[n+1]] <- x * H[[n]] - n * H[[n-1]]

Correlated null

Fitted w: -0.03642797 0.2788315 0.02632224 -0.106871 
Time Cost in Seconds: 0.492 0.022 0.493 

Fitted w: 0.03361434 1.037918 -0.3782364 0.9186735 -0.6135029 0.6083007 -0.5077214 0.2384846 -0.2000794 
Time Cost in Seconds: 0.522 0.013 0.46 

Fitted w: 0.02273596 1.301977 0.05448238 0.8574552 -0.1466924 0.09679719 -0.3403967 -0.1284122 -0.1752019 
Time Cost in Seconds: 0.527 0.01 0.437 

Fitted w: 0.04544396 -0.1800044 0.02158272 0.04857491 
Time Cost in Seconds: 0.491 0.009 0.371 

Fitted w: 0.006084177 0.5623754 -0.02229827 0.1278911 
Time Cost in Seconds: 0.357 0.006 0.377 

Signal \(+\) correlated error

Converged: TRUE 
Number of Iteration: 21 
Time Cost in Seconds: 38.654 2.382 38.811 

Converged: TRUE 
Number of Iteration: 24 
Time Cost in Seconds: 65.451 4.351 58.666 

Converged: TRUE 
Number of Iteration: 21 
Time Cost in Seconds: 53.677 3.877 53.751 

Converged: TRUE 
Number of Iteration: 27 
Time Cost in Seconds: 59.707 3.056 38.881 

Converged: TRUE 
Number of Iteration: 12 
Time Cost in Seconds: 30.248 1.343 23.311 

Conclusion

It appears normalization indeed increases the accuracy, although the computation seems slowing down a little bit? Not sure.

Session information

sessionInfo()

R version 3.3.3 (2017-03-06)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.4

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] backports_1.0.5 magrittr_1.5    rprojroot_1.2   tools_3.3.3    
 [5] htmltools_0.3.5 yaml_2.1.14     Rcpp_0.12.10    stringi_1.1.2  
 [9] rmarkdown_1.3   knitr_1.15.1    git2r_0.18.0    stringr_1.2.0  
[13] digest_0.6.11   evaluate_0.10