Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Man Chung Yue, Daniel Kuhn, Wolfram Wiesemann

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review


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. We thus propose to replace each nominal distribution with an ambiguity set containing all distributions in its vicinity and to evaluate an optimistic likelihood, that is, the maximum of the likelihood over all distributions in the ambiguity set. When the proximity of distributions is quantified by the Fisher-Rao distance or the Kullback-Leibler divergence, the emerging optimistic likelihoods can be computed efficiently using either geodesic or standard convex optimization techniques. We showcase the advantages of working with optimistic likelihoods on a classification problem using synthetic as well as empirical data.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 32 (NIPS 2019)
Number of pages21
Publication statusPublished - Oct 2019
EventThirty-third Conference on Neural Information Processing Systems - Vancouver Convention Center, Vancouver, Canada
Duration: 8 Dec 201914 Dec 2019


ConferenceThirty-third Conference on Neural Information Processing Systems
Abbreviated titleNeurIPS 2019


  • Distributionally Robust Optimization
  • Manifold Optimization
  • Geodesic Convexity
  • Quadratic Discriminant Analysis
  • Projected Gradient Descent
  • Fisher-Rao Distance


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