title: Hierarchical models in the brain.
abstract: This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.
authors.affiliation: The Wellcome Trust Centre of Neuroimaging, University College London, London, United Kingdom. k.friston@fil.ion.ucl.ac.uk
authors.forename: Karl
authors.initials: K
authors.lastname: Friston
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000033:anatomy & histology / Q000502:physiology*; D006801:Humans; D016014:Linear Models; D008606:Mental Processes / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net / Q000033:anatomy & histology / Q000502:physiology; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D011336:Probability