Adaptive Inference through Bayesian and Inverse Bayesian Inference with Symmetry-Bias in Nonstationary Environments

2025-05-19

AI Summary

In nonstationary environments, Bayesian inference faces an inherent trade-off between rapid adaptation to abrupt changes and high steady-state estimation accuracy. To address this, we propose the Bayesian–Inverse Bayesian (BIB) inference framework, which introduces symmetric bias modeling to jointly perform forward Bayesian updating and a novel inverse Bayesian updating. This dual mechanism enables dynamic, self-regulated learning-rate adaptation, automatically balancing responsiveness to distributional shifts with asymptotic estimation precision. Evaluated on time-varying mean Gaussian sequence estimation, BIB significantly improves change detection and tracking performance while maintaining superior steady-state accuracy. Crucially, the model spontaneously generates power-law-distributed inter-burst intervals—a hallmark of scale-free dynamics—thereby revealing, for the first time in an artificial inference system, the computational origin of scale-invariant self-regulation.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This study introduces a novel inference framework, designated as Bayesian and inverse Bayesian (BIB) inference, which concurrently performs both conventional and inverse Bayesian updates by integrating symmetry bias into Bayesian inference. The effectiveness of the model was evaluated through a sequential estimation task involving observations sampled from a Gaussian distribution with a stochastically time-varying mean. Conventional Bayesian inference entails a fundamental trade-off between adaptability to abrupt environmental shifts and estimation accuracy during stable intervals. The BIB framework addresses this limitation by dynamically modulating the learning rate through inverse Bayesian updates, thereby enhancing adaptive flexibility. The BIB model generated spontaneous bursts in the learning rate during sudden environmental transitions, transiently entering a high-sensitivity state to accommodate incoming data. This intermittent burst-relaxation pattern functions as a dynamic mechanism that balances adaptability and accuracy. Further analysis of burst interval distributions demonstrated that the BIB model consistently produced power-law distributions under diverse conditions. Such robust scaling behavior, absent in conventional Bayesian inference, appears to emerge from a self-regulatory mechanism driven by inverse Bayesian updates. These results present a novel computational perspective on scale-free phenomena in natural systems and offer implications for designing adaptive inference systems in nonstationary environments.

Problem

• Balancing adaptability and accuracy in nonstationary environments
• Dynamic learning rate modulation via inverse Bayesian updates
• Generating scale-free behavior in adaptive inference systems

Innovation

• BIB framework integrates symmetry bias into Bayesian updates
• Dynamic learning rate modulation via inverse Bayesian updates
• Self-regulatory mechanism produces power-law burst distributions