Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions

TL;DR

This paper introduces nonparametric methods for estimating divergences between probability distributions from samples, enabling machine learning tasks like clustering and anomaly detection directly on distributions.

Contribution

It proposes novel divergence estimation algorithms for distributions based on samples, facilitating machine learning applications on distributional data.

Findings

Effective divergence estimators demonstrated on synthetic data

Successful application to real-world image and astronomical datasets

Improved clustering and anomaly detection performance

Abstract

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed, finite-dimensional feature representation. Here we consider a different setting. We assume that each instance corresponds to a continuous probability distribution. These distributions are unknown, but we are given some i.i.d. samples from each distribution. Our goal is to estimate the distances between these distributions and use these distances to perform low-dimensional embedding, clustering/classification, or anomaly detection for the distributions. We present estimation algorithms, describe how to apply them for machine learning tasks on distributions, and show empirical results on synthetic data, real word images, and astronomical data sets.