Minimum cross-entropy distributions on Wasserstein balls and their applications

2021/06/06 by Luis Felipe Vargas, Vargas, Luis Felipe, Mauricio Velasco +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Point processes and geometric inequalities #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2106.03226

openalex publication_date 2021/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a prior probability density p on a compact set K we characterize the probability distribution q_δ^* on K contained in a Wasserstein ball B_δ(μ) centered in a given discrete measure μ for which the relative-entropy H(q,p) achieves its minimum. This characterization gives us an algorithm for computing such distributions efficiently

Citations

• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

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