TY - JOUR
T1 - Minimax statistical learning with Wasserstein distances
AU - Lee, Jaeho
AU - Raginsky, Maxim
N1 - Funding Information:
⇤Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801, USA. This work was supported in part by NSF grant nos. CIF-1527 388 and CIF-1302438, and in part by the NSF CAREER award 1254041.
Funding Information:
This work was supported in part by NSF grant nos. CIF-1527 388 and CIF-1302438, and in part by the NSF CAREER award 1254041.
Publisher Copyright:
© 2018 Curran Associates Inc.All rights reserved.
PY - 2018
Y1 - 2018
N2 - As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets given by balls in Wasserstein space. In particular, we prove generalization bounds that involve the covering number properties of the original ERM problem. As an illustrative example, we provide generalization guarantees for transport-based domain adaptation problems where the Wasserstein distance between the source and target domain distributions can be reliably estimated from unlabeled samples.
AB - As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets given by balls in Wasserstein space. In particular, we prove generalization bounds that involve the covering number properties of the original ERM problem. As an illustrative example, we provide generalization guarantees for transport-based domain adaptation problems where the Wasserstein distance between the source and target domain distributions can be reliably estimated from unlabeled samples.
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M3 - Conference article
AN - SCOPUS:85064814555
SN - 1049-5258
VL - 2018-December
SP - 2687
EP - 2696
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018
Y2 - 2 December 2018 through 8 December 2018
ER -