Praneeth Vepakomma — Page 4

arXiv2016

Optimal bandwidth estimation for a fast manifold learning algorithm to detect circular structure in high-dimensional data

We provide a way to infer about existence of topological circularity in high-dimensional data sets in $\mathbb{R}^d$ from its projection in $\mathbb{R}^2$ obtained through a fast manifold learning map as a function of the high-dimensional dataset $\mathbb{X}$ and a particular choice of a positive real $σ$ known as bandwidth parameter. At the same time we also provide a way to estimate the optimal bandwidth for fast manifold learning in this setting through minimization of these functions of bandwidth. We also provide limit theorems to characterize the behavior of our proposed functions of bandwidth.

stat.ML↗

arXiv2016

Supervised Dimensionality Reduction via Distance Correlation Maximization

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 $\mathbf{z}$, 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 Maximizaiton 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.

cs.LG↗