Uncertainty in perception and the Hierarchical Gaussian Filter

Area of Science:

• Computational Neuroscience
• Cognitive Science
• Bayesian Inference

Background:

• Perception relies on agents' internal models of sensory input and probabilistic inference.
• Inherent uncertainty in perceptual inferences necessitates robust computational frameworks.
• The Hierarchical Gaussian Filter (HGF) offers a Bayesian approach to modeling perceptual uncertainty.

Purpose of the Study:

• To generalize and extend the Hierarchical Gaussian Filter (HGF) for modeling perceptual uncertainty.
• To integrate the HGF with decision-making models and explore computational methods for inversion.
• To evaluate the performance of different optimization techniques for HGF/decision model inversion.

Main Methods:

• Explicit formulation of the HGF hierarchy for arbitrary levels.
• Explanation of uncertainty accommodation via variational free energy minimization.
• Combination of HGF with decision models and demonstration of inversion.
• Comparative simulation study of four optimization methods (Nelder-Mead, Gaussian Processes, Variational Bayes, MCMC).

Main Results:

• The generalized HGF effectively accommodates various forms of perceptual uncertainty.
• Variational Bayes demonstrated superior efficiency and informativeness for inverting the HGF/decision model combination.
• All tested optimization methods performed well, even under significant noise levels.
• The HGF framework proved flexible and computationally efficient for online state estimation.

Conclusions:

• The Hierarchical Gaussian Filter offers a principled, flexible, and intuitive framework for resolving perceptual uncertainty in agents.
• The HGF's integration with decision models and robust inversion methods facilitate applications in computational neuroscience and cognitive science.
• This work advances the understanding and computational modeling of perception and decision-making under uncertainty.