Supervised dimensionality reduction via distance correlation maximization

Praneeth Vepakomma, Chetan Tonde, Ahmed Elgammal

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, (Székely 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.

Original languageEnglish (US)
Pages (from-to)960-984
Number of pages25
JournalElectronic Journal of Statistics
Volume12
Issue number1
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Distance correlation
  • Fixed point iteration
  • Minorization maximization
  • Multivariate statistical independence
  • Optimization
  • Representation learning
  • Supervised dimensionality reduction

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