Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions
Barnabas Poczos, Liang Xiong, Jeff Schneider
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.
PDF Link: /papers/11/p599-poczos.pdf
AUTHOR = "Barnabas Poczos
and Liang Xiong and Jeff Schneider",
TITLE = "Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "599--608"