Training Gaussian Mixture Models at Scale via Coresets
Abstract
How can we train a statistical mixture model on a massive data set? In this work we show how to construct \emph{coresets} for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being \emph{independent} of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real- world data sets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error.
Additional Information
© 2018 Mario Lucic, Matthew Faulkner, Andreas Krause, Dan Feldman. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Submitted 9/15; Revised 1/18; Published 5/18. We thank Olivier Bachem for invaluable discussions, suggestions and comments. This research was partially supported by ONR grant N00014-09-1-1044, NSF grants CNS-0932392, IIS-0953413, DARPA MSEE grant FA8650-11-1-7156, and the Zurich Information Security Center.Attached Files
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Additional details
- Eprint ID
- 87060
- Resolver ID
- CaltechAUTHORS:20180613-103427463
- N00014-09-1-1044
- Office of Naval Research (ONR)
- CNS-0932392
- NSF
- IIS-0953413
- NSF
- FA8650-11-1-7156
- Defense Advanced Research Projects Agency (DARPA)
- Zurich Information Security Center
- Created
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2018-06-13Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field