# Robust probabilistic inference via a constrained transport metric

arXiv: https://arxiv.org/abs/2303.10085 · HTML: https://mlsanity.com/paper/2303.10085/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 78 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Robust Optimization for Fairness with Noisy Protected Groups](https://mlsanity.com/paper/2002.09343/) (2020)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Adversarially robust transfer learning](https://mlsanity.com/paper/1905.08232/) (2019)
- [On Formalizing Fairness in Prediction with Machine Learning](https://mlsanity.com/paper/1710.03184/) (2017)
- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Tree-Sliced Variants of Wasserstein Distances](https://mlsanity.com/paper/1902.00342/) (2019)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions](https://mlsanity.com/paper/1805.07594/) (2018)
- [Privacy-preserving parametric inference: a case for robust statistics](https://mlsanity.com/paper/1911.10167/) (2019)
- [A General Framework for Fair Regression](https://mlsanity.com/paper/1810.05041/) (2018)
- [Distributionally Robust Optimization for Sequential Decision Making](https://mlsanity.com/paper/1801.04745/) (2018)
- [Robust Fairness-aware Learning Under Sample Selection Bias](https://mlsanity.com/paper/2105.11570/) (2021)
- [Robust and Scalable Bayes via a Median of Subset Posterior Measures](https://mlsanity.com/paper/1403.2660/) (2014)
- [Fair quantile regression](https://mlsanity.com/paper/1907.08646/) (2019)
- [Finite mixture models do not reliably learn the number of components](https://mlsanity.com/paper/2007.04470/) (2020)
- [An MCMC Approach to Classical Estimation](https://mlsanity.com/paper/2301.07782/) (2023)
- [Bayesian Estimation and Comparison of Moment Condition Models](https://mlsanity.com/paper/1606.02931/) (2016)

## Built on by (most cited first, 1 of 1)

- [Constrained Reweighting of Distributions: an Optimal Transport Approach](https://mlsanity.com/paper/2310.12447/) (2023)

## Abstract (arXiv)

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted empirical likelihood carefully designed to concentrate near a parametric family of distributions of choice with respect to a novel variant of the Wasserstein metric, which is then combined with a prior distribution on model parameters to obtain a robustified posterior. The proposed approach finds applications in a wide variety of robust inference problems, where we intend to perform inference on the parameters associated with the centering distribution in presence of outliers. Our proposed transport metric enjoys great computational simplicity, exploiting the Sinkhorn regularization for discrete optimal transport problems, and being inherently parallelizable. We demonstrate superior performance of our methodology when compared against state-of-the-art robust Bayesian inference methods. We also demonstrate equivalence of our approach with a nonparametric Bayesian formulation under a suitable asymptotic framework, testifying to its flexibility. The constrained entropy maximization that sits at the heart of our likelihood formulation finds its utility beyond robust Bayesian inference; an illustration is provided in a trustworthy machine learning application.