Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors that are preserved or even amplified by the likelihood estimation. To alleviate this issue, we propose to replace the nominal distributions with ambiguity sets containing all distributions that are sufficiently close to the nominal distributions. When this proximity is measured by the Fisher-Rao distance or the Kullback-Leibler divergence, the emerging \emph{optimistic likelihoods} can be calculated efficiently using either geodesic or standard convex optimization techniques. We showcase the advantages of our optimistic likelihoods on a classification problem using artificially generated as well as standard benchmark instances.

Published in:
[Advances in Neural Information Processing Systems 33 (NIPS 2019)]
Presented at:
NeurIPS 2019 : Thirty-third Conference on Neural Information Processing Systems, Vancouver, Canada, December 8-14, 2019

 Record created 2019-09-03, last modified 2019-09-04

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