2019/10/23 by Viet Anh Nguyen, Soroosh Shafieezadeh-Abadeh, Nguyen, Viet Anh +8 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1910.10583
openalex publication_date 2019/10/23 · openalex created_date 2019/11/01 · openalex updated_date 2026/07/28
The likelihood function is a fundamental component in Bayesian statistics.\nHowever, evaluating the likelihood of an observation is computationally\nintractable in many applications. In this paper, we propose a non-parametric\napproximation of the likelihood that identifies a probability measure which\nlies in the neighborhood of the nominal measure and that maximizes the\nprobability of observing the given sample point. We show that when the\nneighborhood is constructed by the Kullback-Leibler divergence, by moment\nconditions or by the Wasserstein distance, then our \optimistic\nlikelihood can be determined through the solution of a convex optimization\nproblem, and it admits an analytical expression in particular cases. We also\nshow that the posterior inference problem with our optimistic likelihood\napproximation enjoys strong theoretical performance guarantees, and it performs\ncompetitively in a probabilistic classification task.\n