Experimental Mathematics Seminar
Combinatorics of Distance Covariance: Inclusion-Minimal Maximizers of Quasi-Concave Set Functions for Diverse Variable Selection
Praneeth Vepakomma: Motorola Solutions
Location: Hill 705
Date & time: Thursday, 09 March 2017 at 5:00PM - 5:11PM
In this talk we show that the negative sample distance covariance function is a quasiconcave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to combinatorially optimize some diversity (low statistical dependence) promoting functions of distance covariance. Our greedy algorithm obtains all the inclusion-minimal maximizers of this diversity promoting objective. Inclusion-minimal maximizers are multiple solution sets of globally optimal maximizers that are not a proper subset of any other maximizing set in the solution set. We present results upon applying this approach to obtain diverse features (covariates/variables/predictors) in a feature selection setting for regression (or classification) problems. We also combine our diverse feature selection algorithm with a distance covariance based relevant feature selection algorithm of Kong, Wang, and Wahba to produce subsets of covariates that are both relevant yet ordered in non-increasing levels of diversity of these subsets.