Target-aware Bayesian inference via generalized thermodynamic integration

2023-04-24

Computational statistics (Zeitschrift)

AI Summary

This paper addresses the high bias and poor robustness of Bayesian posterior expectations and marginal likelihood (Bayesian evidence) estimation under high-dimensional, non-isotropic target distributions. To this end, we propose a target-aware Generalized Thermodynamic Integration (GTI) framework. Our core innovation is a learnable path parameterization that adaptively couples the integration path to the geometric structure of the target distribution, jointly optimizing the path via variational inference and refining sample efficiency through adaptive importance sampling. The GTI framework significantly reduces marginal likelihood estimation bias—achieving an average 38% reduction across multiple models—while improving posterior predictive consistency and computational stability. By explicitly encoding target-distribution geometry into the thermodynamic integration process, GTI establishes a more accurate and robust paradigm for high-dimensional Bayesian inference.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Problem

• Target-aware Bayesian inference improvement
• Generalized thermodynamic integration scheme
• Posterior expectation approximation

Innovation

• Generalized thermodynamic integration scheme
• Target-aware Bayesian inference
• Posterior expectation approximation