optimistic likelihood – Optimization Online

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Published: 2019/10/23

Stochastic Programming kullback-leibler divergence, moment ambiguity set, nonparametric bayesian statistics, optimistic likelihood, wasserstein distance

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 … Read more

Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

Published: 2019/10/21

Daniel Kuhn

Viet Anh Nguyen

Soroosh Shafieezadeh-Abadeh

Wolfram Wiesemann

Man-Chung Yue

Generalized Convexity/Monoticity, Semi-definite Programming, Stochastic Programming fisher-rao distance, geodesic convex, kullback-leibler divergence, optimistic likelihood

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 … Read more