title: Uncertainty in perception and the Hierarchical Gaussian Filter.
abstract: In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient-but at the same time intuitive-framework for the resolution of perceptual uncertainty in behaving agents.
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London London, UK ; Max Planck UCL Centre for Computational Psychiatry and Ageing Research London, UK ; Translational Neuromodeling Unit, Institute for Biomedical Engineering, University of Zurich and ETH Zurich Zurich, Switzerland ; Laboratory for Social and Neural Systems Research (SNS Lab), Department of Economics, University of Zurich Zurich, Switzerland.
authors.forename: Christoph D
authors.initials: CD
authors.lastname: Mathys
authors.affiliation: Translational Neuromodeling Unit, Institute for Biomedical Engineering, University of Zurich and ETH Zurich Zurich, Switzerland ; Laboratory for Social and Neural Systems Research (SNS Lab), Department of Economics, University of Zurich Zurich, Switzerland ; Department of Computer Science, ETH Zurich Zurich, Switzerland.
authors.forename: Ekaterina I
authors.initials: EI
authors.lastname: Lomakina
authors.affiliation: Institut du Cerveau et de la Moelle Épinière, Hôpital Pitié Salpêtrière Paris, France.
authors.forename: Jean
authors.initials: J
authors.lastname: Daunizeau
authors.affiliation: Translational Neuromodeling Unit, Institute for Biomedical Engineering, University of Zurich and ETH Zurich Zurich, Switzerland ; Laboratory for Social and Neural Systems Research (SNS Lab), Department of Economics, University of Zurich Zurich, Switzerland.
authors.forename: Sandra
authors.initials: S
authors.lastname: Iglesias
authors.affiliation: Translational Neuromodeling Unit, Institute for Biomedical Engineering, University of Zurich and ETH Zurich Zurich, Switzerland ; Laboratory for Social and Neural Systems Research (SNS Lab), Department of Economics, University of Zurich Zurich, Switzerland.
authors.forename: Kay H
authors.initials: KH
authors.lastname: Brodersen
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London London, UK.
authors.forename: Karl J
authors.initials: KJ
authors.lastname: Friston
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London London, UK ; Translational Neuromodeling Unit, Institute for Biomedical Engineering, University of Zurich and ETH Zurich Zurich, Switzerland ; Laboratory for Social and Neural Systems Research (SNS Lab), Department of Economics, University of Zurich Zurich, Switzerland.
authors.forename: Klaas E
authors.initials: KE
authors.lastname: Stephan
keywords: Bayesian inference; decision-making; filtering; free energy; hierarchical modeling; learning; uncertainty; volatility