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2018 Supervised dimensionality reduction via distance correlation maximization
Praneeth Vepakomma, Chetan Tonde, Ahmed Elgammal
Electron. J. Statist. 12(1): 960-984 (2018). DOI: 10.1214/18-EJS1403


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 $\mathbf{z}$, which maximizes the squared sum of Distance Correlations between low-dimensional features $\mathbf{z}$ and response $y$, and also between features $\mathbf{z}$ and covariates $\mathbf{x}$. 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.


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Praneeth Vepakomma. Chetan Tonde. Ahmed Elgammal. "Supervised dimensionality reduction via distance correlation maximization." Electron. J. Statist. 12 (1) 960 - 984, 2018.


Received: 1 November 2016; Published: 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06864482
MathSciNet: MR3772810
Digital Object Identifier: 10.1214/18-EJS1403

Keywords: Distance correlation , fixed point iteration , minorization maximization , multivariate statistical independence , optimization , representation learning , supervised dimensionality reduction


Vol.12 • No. 1 • 2018
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