Online Generalised Predictive Coding

2026-05-04

AI Summary

This work addresses the challenge of simultaneously estimating hidden states, model parameters, and uncertainty in dynamic environments through a novel Online Dynamic Expectation Maximization (ODEM) method. ODEM uniquely integrates generalized predictive coding with a dynamic expectation maximization framework, employing multi-timescale optimization: rapid Bayesian updates for hidden states and slower adjustments for model parameters and precision. Grounded in variational inference and generalized filtering principles, the approach balances biological plausibility with engineering utility. Numerical experiments demonstrate that ODEM robustly tracks hidden states in nonlinear and even chaotic systems, maintaining strong performance despite structural mismatches in the generative model, thereby significantly enhancing online learning and data assimilation capabilities.

Abstract

This paper introduces an extension of generalised filtering for online applications. Generalised filtering refers to data assimilation schemes that jointly infer latent states, learn unknown model parameters, and estimate uncertainty in an integrated framework -- e.g., estimate state and observation noise -- at the same time (i.e., triple estimation). This framework appears across disciplines under different names, including variational Kalman-Bucy filtering in engineering, generalised predictive coding in neuroscience, and Dynamic Expectation Maximisation (DEM) in time-series analysis. Here, we specialise DEM for ``online'' data assimilation, through a separation of temporal scales. We describe the variational principles and procedures that allow one to assimilate data in a way that allows for a slow updating of parameters and precisions, which contextualise fast Bayesian belief updating about the dynamic hidden states. Using numerical studies, we demonstrate the validity of online DEM (ODEM) using a non-linear -- and potentially chaotic -- generative model, to show that the ODEM scheme can track the latent states of the generative process, even when its functional form differs fundamentally from the dynamics of the generative model. Framed from a neuro-mimetic predictive coding perspective, ODEM offers a biologically inspired solution to online inference, learning, and uncertainty estimation in dynamic environments.

Problem

• online data assimilation
• triple estimation
• latent states
• model parameters
• uncertainty estimation

Innovation

• online DEM
• generalised predictive coding
• triple estimation
• temporal scale separation
• variational inference