Robustifying likelihoods by optimistically re-weighting data

Autor:	Dewaskar, Miheer, Tosh, Christopher, Knoblauch, Jeremias, Dunson, David B.
Rok vydání:	2023
Předmět:	Statistics - Methodology Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification: outliers, data contamination or inappropriate parametric assumptions such as Gaussianity mean that most models are at best rough approximations of reality. A significant practical concern is that for certain inferences, even small amounts of model misspecification may have a substantial impact; a problem we refer to as brittleness. This article attempts to address the brittleness problem in likelihood-based inferences by choosing the most model friendly data generating process in a distance-based neighborhood of the empirical measure. This leads to a new Optimistically Weighted Likelihood (OWL), which robustifies the original likelihood by formally accounting for a small amount of model misspecification. Focusing on total variation (TV) neighborhoods, we study theoretical properties, develop estimation algorithms and illustrate the methodology in applications to mixture models and regression. Comment: Python code available at https://github.com/cjtosh/owl
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.10525 Zobrazit plný text záznamu View this record from Arxiv