Unified Structure Variable Selection (USVS)

This repository provides python coding implementing Unified Structure Variable Selection (USVS) for respecting various selection rules The optimization solver is Gurobi https://www.gurobi.com

The method is inspired by the BEST SUBSET SELECTION VIA A MODERN OPTIMIZATION LENS by D. Bertsimas, A. King, and R. Mazumder (Annals of Statistics, 2016, Vol., 44, N0. 2, 813-852)

AIM:

1. methods performance comparison
2. show the benefits of specifing correct selection rule
3. as an example, show USVS can respect the selection rule that existing method cannot

group.py

AIM 1

Selection rule: Correlated variable selected collectively

Compare to the group Lasso

IfthenRule.py

AIM 1

Selection rule: if the interaction is selected, then the main terms must be selected

Compare to the overlapping group Lasso

UnitRule.py

AIM 2, 3

Selection rule: select 2 out of 4 correlated variables

Compare to Lasso (no selection rule)