Robust Selection

R and Python Package by C Tran, P Cisneros-Velarde, A Petersen and S-Y Oh

This repository provides a Python package for Robust Selection algorithm for estimation of the graphical lasso regularization parameter.

P Cisneros-Velarde, A Petersen and S-Y Oh (2020). Distributionally Robust Formulation and Model Selection for the Graphical Lasso. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics. [PMLR][Papers with Code]

Python

Installation

To install python package from pypi:

pip install robust-selection

Example

The basic example of RobSel can be found in this binder

R

Installation

To install from CRAN

install.packages("robsel")

Example

This is a basic example which shows you how to solve a common problem:

library(robsel)
## basic example codex<-matrix(rnorm(100*5),ncol=5)

Estimate lambda for glasso

lambda<- robsel(x, alpha=0.9, B=200)
lambda#> [1] 0.1561845

Use glasso directly with robsel estimate

glasso.model<- robsel.glasso(x, alpha=0.9)
glasso.model#> $alpha#> [1] 0.9#> #> $lambda#> [1] 0.1596663#> #> $Sigma#> $Sigma[[1]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1.04954034 0.02769511 0.000000 -0.08435207 0.000000#> [2,] 0.02769511 1.25358486 0.000000 -0.00222587 0.000000#> [3,] 0.00000000 0.00000000 1.092117 0.00000000 0.000000#> [4,] -0.08435207 -0.00222587 0.000000 1.12448050 0.000000#> [5,] 0.00000000 0.00000000 0.000000 0.00000000 1.246764#> #> #> $Omega#> $Omega[[1]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 0.95913305 -0.02106219 0.0000000 0.07190696 0.0000000#> [2,] -0.02106219 0.79817757 0.0000000 0.00000000 0.0000000#> [3,] 0.00000000 0.00000000 0.9156528 0.00000000 0.0000000#> [4,] 0.07190696 0.00000000 0.0000000 0.89469360 0.0000000#> [5,] 0.00000000 0.00000000 0.0000000 0.00000000 0.8020765

Using robsel with multiple confidence levels alpha

robsel(x, alpha=c(0.1,0.9))
#> [1] 0.3266095 0.1571961
robsel.glasso(x, alpha=c(0.1,0.9))
#> $alpha#> [1] 0.1 0.9#> #> $lambda#> [1] 0.3179958 0.1588493#> #> $Sigma#> $Sigma[[1]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1.20787 0.000000 0.000000 0.00000 0.000000#> [2,] 0.00000 1.411914 0.000000 0.00000 0.000000#> [3,] 0.00000 0.000000 1.250446 0.00000 0.000000#> [4,] 0.00000 0.000000 0.000000 1.28281 0.000000#> [5,] 0.00000 0.000000 0.000000 0.00000 1.405093#> #> $Sigma[[2]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1.04872328 0.028512174 0.0000 -0.085169133 0.000000#> [2,] 0.02851217 1.252767801 0.0000 -0.002315537 0.000000#> [3,] 0.00000000 0.000000000 1.0913 0.000000000 0.000000#> [4,] -0.08516913 -0.002315537 0.0000 1.123663436 0.000000#> [5,] 0.00000000 0.000000000 0.0000 0.000000000 1.245947#> #> #> $Omega#> $Omega[[1]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 0.8279038 0.0000000 0.0000000 0.0000000 0.0000000#> [2,] 0.0000000 0.7082583 0.0000000 0.0000000 0.0000000#> [3,] 0.0000000 0.0000000 0.7997144 0.0000000 0.0000000#> [4,] 0.0000000 0.0000000 0.0000000 0.7795387 0.0000000#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.7116965#> #> $Omega[[2]]#> [,1] [,2] [,3] [,4] [,5]#> [1,] 0.96003670 -0.02171539 0.0000000 0.07272214 0.0000000#> [2,] -0.02171539 0.79872675 0.0000000 0.00000000 0.0000000#> [3,] 0.00000000 0.00000000 0.9163384 0.00000000 0.0000000#> [4,] 0.07272214 0.00000000 0.0000000 0.89545824 0.0000000#> [5,] 0.00000000 0.00000000 0.0000000 0.00000000 0.8026025