Online Generalised Predictive Coding

TL;DR

This paper presents an online extension of generalised predictive coding, called ODEM, enabling real-time inference, learning, and uncertainty estimation in dynamic, potentially chaotic systems, inspired by neuro-mimetic principles.

Contribution

It specializes Dynamic Expectation Maximisation for online data assimilation, allowing slow parameter updates alongside fast state inference in a unified framework.

Findings

ODEM successfully tracks latent states in nonlinear, chaotic models.

The scheme demonstrates effective online inference and learning in dynamic environments.

It provides a biologically inspired approach to real-time uncertainty estimation.

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.