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Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks

Kovachki, Nikola B. and Stuart, Andrew M. (2019) Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. Inverse Problems, 35 (9). Art. No. 095005. ISSN 0266-5611. http://resolver.caltech.edu/CaltechAUTHORS:20190404-111033209

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Abstract

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, gradient-free algorithm for finding a solution to these problems using ensemble Kalman inversion (EKI). The method is inherently parallelizable and is applicable to problems with non-differentiable loss functions, for which back-propagation is not possible. Applications of our approach include offline and online supervised learning with deep neural networks, as well as graph-based semi-supervised learning. The essence of the EKI procedure is an ensemble based approximate gradient descent in which derivatives are replaced by differences from within the ensemble. We suggest several modifications to the basic method, derived from empirically successful heuristics developed in the context of SGD. Numerical results demonstrate wide applicability and robustness of the proposed algorithm.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1361-6420/ab1c3aDOIArticle
https://arxiv.org/abs/1808.03620arXivDiscussion Paper
ORCID:
AuthorORCID
Kovachki, Nikola B.0000-0002-3650-2972
Additional Information:© 2019 IOP Publishing Ltd. Published 20 August 2019. Both authors are supported, in part, by the US National Science Foundation (NSF) grant DMS 1818977, the US Office of Naval Research (ONR) grant N00014-17-1-2079, and the US Army Research Office (ARO) grant W911NF-12-2-0022.
Funders:
Funding AgencyGrant Number
NSFDMS-1818977
Office of Naval Research (ONR)N00014-17-1-2079
Army Research LaboratoryW911NF-12-2-0022
Subject Keywords:Machine learning, Deep learning, Derivative-free optimization, Ensemble Kalman inversion, Ensemble Kalman filtering
Issue or Number:9
Record Number:CaltechAUTHORS:20190404-111033209
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190404-111033209
Official Citation:Nikola B Kovachki and Andrew M Stuart 2019 Inverse Problems 35 095005
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94460
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Apr 2019 19:40
Last Modified:20 Aug 2019 17:55

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