Electronic Journal of Statistics, volume 12 No.1, Pages 960--984, The Institute of Mathematical Statistics and the Bernoulli Society, 2018

Abstract

In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, (Szekely et al., 2007). We propose an objective which is free of distributional assumptions on regression variables and regression model assumptions. Our proposed formulation is based on learning a low-dimensional feature representation z, which maximizes the squared sum of Distance Correlations between low-dimensional features z and response y, and also between features z and covariates x. We propose a novel algorithm to optimize our proposed objective using the Generalized Minimization Maximization method of (Parizi et al., 2015). We show superior empirical results on multiple datasets proving the effectiveness of our proposed approach over several relevant state-of-the-art supervised dimensionality reduction methods.