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

2025-03-03

AI Summary

This work addresses estimation bias in generalized Bayesian inference (GBI) under multimodal posteriors, arising from kernelized Stein discrepancy’s (KSD) insensitivity to inter-modal separation and relative mass. We propose a weighted KSD (wKSD) framework that introduces, for the first time, a data-dependent weighting scheme to explicitly correct KSD’s imbalanced sensitivity to well-separated modes, jointly accounting for modal locations and relative weights. Theoretically, wKSD preserves computational efficiency while guaranteeing posterior consistency and asymptotic normality. Empirically, it significantly improves mode sensitivity and accuracy in estimating modal proportions under multimodality, and maintains robustness in unimodal settings and in the presence of outliers. Thus, wKSD establishes a new paradigm for likelihood-free, gradient-driven robust inference.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Addresses mode proportion bias in Generalized Bayesian Inference.
• Improves sensitivity to multimodal posteriors using weighted KSD.
• Maintains computational efficiency and theoretical properties in GBI.

Innovation

• Weighted KSD enhances mode sensitivity.
• Retains computational efficiency in GBI.
• Improves handling of intractable multimodal posteriors.