Calculating optimistic likelihoods using (geodesically) convex optimization
File(s)
Accepted version
Author(s)
Nguyen, Viet Anh
Shafieezadeh-Abadeh, Soroosh
Yue, Man Chung
Kuhn, Daniel
Wiesemann, Wolfram
Type
Conference Paper
Abstract
A fundamental problem arising in many areas of machine learning is the evaluationof the likelihood of a given observation under different nominal distributions.Frequently, these nominal distributions are themselves estimated from data, whichmakes them susceptible to estimation errors. We thus propose to replace eachnominal distribution with an ambiguity set containing all distributions in its vicinityand to evaluate anoptimistic likelihood, that is, the maximum of the likelihoodover all distributions in the ambiguity set. When the proximity of distributionsis quantified by the Fisher-Rao distance or the Kullback-Leibler divergence, theemerging optimistic likelihoods can be computed efficiently using either geodesicor standard convex optimization techniques. We showcase the advantages ofworking with optimistic likelihoods on a classification problem using synthetic aswell as empirical data.
Date Issued
2019-12-08
Date Acceptance
2019-09-03
Citation
Advances in Neural Information Processing Systems 32 (NIPS 2019), 2019, 32
ISSN
1049-5258
Publisher
Neural Information Processing Systems Foundation, Inc.
Journal / Book Title
Advances in Neural Information Processing Systems 32 (NIPS 2019)
Volume
32
Copyright Statement
© 2019 Neural Information Processing Systems Foundation, Inc.
Source
33rd Conference on Neural Information Processing Systems (NeurIPS)
Subjects
Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science
SPACE
MATRICES
1701 Psychology
1702 Cognitive Sciences
Publication Status
Published
Start Date
2019-12-08
Finish Date
2019-12-14
Coverage Spatial
Vancouver, Canada