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Uncertainty in perception and the Hierarchical Gaussian Filter.

Mathys, CD; Lomakina, EI; Daunizeau, J; Iglesias, S; Brodersen, KH; Friston, KJ; Stephan, KE; (2014) Uncertainty in perception and the Hierarchical Gaussian Filter. Front Hum Neurosci , 8 , Article 825. 10.3389/fnhum.2014.00825. Green open access

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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.

Type: Article
Title: Uncertainty in perception and the Hierarchical Gaussian Filter.
Location: Switzerland
Open access status: An open access version is available from UCL Discovery
DOI: 10.3389/fnhum.2014.00825
Publisher version: http://dx.doi.org/10.3389/fnhum.2014.00825
Language: English
Additional information: © 2014 Mathys, Lomakina, Daunizeau, Iglesias, Brodersen, Friston and Stephan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Keywords: Bayesian inference, decision-making, filtering, free energy, hierarchical modeling, learning, uncertainty, volatility
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Imaging Neuroscience
URI: https://discovery.ucl.ac.uk/id/eprint/1458365
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