Hierarchical Models in the Brain

• Published in: PLoS computational biology Vol. 4; no. 11; p. e1000211
• Main Author: Friston, Karl
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.11.2008; Public Library of Science (PLoS)
• Subjects: Algorithms; Anatomy & physiology; Animals; Brain - anatomy & histology; Brain - physiology; Economic models; Humans; Linear Models; Mathematics/Statistics; Mental Processes - physiology; Models, Neurological; Nerve Net - anatomy & histology; Nerve Net - physiology; Neural Networks, Computer; Neuroscience; Neuroscience/Theoretical Neuroscience; Nonlinear Dynamics; Probability; Studies; Mental Processes; Brain; Algorithms; Animals; Humans; Nerve Net; Probability; Linear Models; Models, Neurological; Nonlinear Dynamics; Neural Networks (Computer)
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1000211

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.