# Correcting Mode Proportion Bias in Generalized Bayesian Inference via a Weighted Kernel Stein Discrepancy

arXiv: https://arxiv.org/abs/2503.02108 · HTML: https://mlsanity.com/paper/2503.02108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [Measuring Sample Quality with Diffusions](https://mlsanity.com/paper/1611.06972/) (2016)
- [Random Feature Stein Discrepancies](https://mlsanity.com/paper/1806.07788/) (2018)
- [Testing Goodness of Fit of Conditional Density Models with Kernels](https://mlsanity.com/paper/2002.10271/) (2020)
- [Objective Bayesian inference with proper scoring rules](https://mlsanity.com/paper/1711.10819/) (2017)
- [Fisher Efficient Inference of Intractable Models](https://mlsanity.com/paper/1805.07454/) (2018)
- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy](https://mlsanity.com/paper/2304.14762/) (2023)

## Abstract (arXiv)

Generalized Bayesian Inference (GBI) provides a flexible framework for updating prior distributions using various loss functions instead of the traditional likelihoods, thereby enhancing the model robustness to model misspecification. However, GBI often suffers the problem associated with intractable likelihoods. Kernelized Stein Discrepancy (KSD), as utilized in a recent study, addresses this challenge by relying only on the gradient of the log-likelihood. Despite this innovation, KSD-Bayes suffers from critical pathologies, including insensitivity to well-separated modes in multimodal posteriors. To address this limitation, we propose a weighted KSD method that retains computational efficiency while effectively capturing multimodal structures. Our method improves the GBI framework for handling intractable multimodal posteriors while maintaining key theoretical properties such as posterior consistency and asymptotic normality. Experimental results demonstrate that our method substantially improves mode sensitivity compared to standard KSD-Bayes, while retaining robust performance in unimodal settings and in the presence of outliers.