Adaptive Inference through Bayesian and Inverse Bayesian Inference with Symmetry-Bias in Nonstationary Environments (2505.12796v3)

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.