# Robustifying likelihoods by optimistically re-weighting data

arXiv: https://arxiv.org/abs/2303.10525 · HTML: https://mlsanity.com/paper/2303.10525/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2023.

## Built on by (most cited first, 6 of 6)

- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [Proxy-informed Bayesian transfer learning with unknown sources](https://mlsanity.com/paper/2411.03263/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Efficient first-order algorithms for large-scale, non-smooth maximum entropy models with application to wildfire science](https://mlsanity.com/paper/2403.06816/) (2024)
- [Joint Model and Data Sparsification via the Marginal Likelihood](https://mlsanity.com/paper/2605.29908/) (2026)

## Abstract (arXiv)

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.