Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions

Barnabas Poczos, Liang Xiong, Jeff Schneider
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:665-674, 2011.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-poczos11a, title = {Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions}, author = {Poczos, Barnabas and Xiong, Liang and Schneider, Jeff}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {665--674}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/poczos11a/poczos11a.pdf}, url = {https://proceedings.mlr.press/r9/poczos11a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions %A Barnabas Poczos %A Liang Xiong %A Jeff Schneider %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-poczos11a %I PMLR %P 665--674 %U https://proceedings.mlr.press/r9/poczos11a.html %V R9 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Poczos, B., Xiong, L. & Schneider, J.. (2011). Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:665-674 Available from https://proceedings.mlr.press/r9/poczos11a.html. Reissued by PMLR on 04 October 2026.

Related Material