Learning and inference in the brain

Karl Friston

Abstract

There are several architectural principles of functional brain anatomy that have emerged from careful anatomic and physiologic studies over the past century.  These principles are considered in the light of representational learning to see if they could have been predicted a priori on the basis of purely theoretical considerations.  Specifically, I will focus on hierarchical dynamic models (HDMs) and expectation maximisation (EM) schemes for their estimation.  These models are very general in the sense that they subsume many simpler variants, such as independent component analysis, through to generalised nonlinear convolution models.  The generality of HDMs renders their EM a useful framework that covers procedures ranging from variance component estimation, in classical linear observation models, to blind deconvolution, using exactly the same formalism and operational equations.  Critically, they may provide heuristics that inform our understanding of neuronal processing.  For example, the central role of hierarchies in empirical Bayesian formulations of representational learning may provide an understanding of why sensory cortices in the brain are arranged hierarchically.  A second example is the need for explicit generative and recognition models in the context of noninvertible processes generating auditory data.  This dichotomy may be useful in understanding asymmetries between forward and backward connections of the brain in the context of predictive coding.   The notion that the brain may use empirical Bayes for inference about its sensory input, given the hierarchical organisation of cortical systems, is compelling.  Although it is fairly easy to develop this in the context of static observation models, it would be interesting to generalise the same idea to cover dynamical systems. This would enable us to model and understand evoked brain responses in a much more functionally informed fashion.  Here predictive coding takes on a dual meaning in the sense that the prediction may involve, not only minimising prediction error (to provide conditional estimators), but also a component of forecasting, to pursue conditional trajectories of dynamically evolving states.