Robustifying likelihoods by optimistically re-weighting data

Fuente: arXiv
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Autori principali: Dewaskar, Miheer, Tosh, Christopher, Knoblauch, Jeremias, Dunson, David B.
Natura: Preprint
Pubblicazione: 2023
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author Dewaskar, Miheer
Tosh, Christopher
Knoblauch, Jeremias
Dunson, David B.
author_facet Dewaskar, Miheer
Tosh, Christopher
Knoblauch, Jeremias
Dunson, David B.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2303_10525
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Robustifying likelihoods by optimistically re-weighting data
Dewaskar, Miheer
Tosh, Christopher
Knoblauch, Jeremias
Dunson, David B.
Methodology
Statistics Theory
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.
title Robustifying likelihoods by optimistically re-weighting data
topic Methodology
Statistics Theory
url https://arxiv.org/abs/2303.10525