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Title: Optimistic distributionally robust optimization for nonparametric likelihood approximation
Authors: Nguyen, VA
Shafieezadeh-Abadeh, S
Yue, MC 
Kuhn, D
Wiesemann, W
Issue Date: 2019
Source: Advances in Neural Information Processing Systems 32 (NeurIPS 2019), 2019, v. 20, p. 15793-15803
Abstract: The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood that identifies a probability measure which lies in the neighborhood of the nominal measure and that maximizes the probability of observing the given sample point. We show that when the neighborhood is constructed by the Kullback-Leibler divergence, by moment conditions or by the Wasserstein distance, then our optimistic likelihood can be determined through the solution of a convex optimization problem, and it admits an analytical expression in particular cases. We also show that the posterior inference problem with our optimistic likelihood approximation enjoys strong theoretical performance guarantees, and it performs competitively in a probabilistic classification task.
Publisher: NeurIPS
ISBN: 978-1-7138-0793-3 (Print on Demand(PoD))
Description: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), 8-14 Dec 2019, Vancouver, Canada
Rights: Copyright © (2019) by individual authors and Neural Information Processing Systems Foundation Inc.
Posted with permission of the author.
Appears in Collections:Conference Paper

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