Hierarchical Gaussian Filtering of Sufficient Statistic Time Series for Active Inference
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Under fairly general assumptions (for all probability distributions from the exponential family), belief updates in hierarchical Bayesian models rest on precision-weighted prediction errors.
“under fairly general assumptions (i.e., for all probability distributions from the exponential family, Mathys, 2016; Mathys & Weber, 2020), these belief updates rest on (precision-weighted) prediction errors (PEs)”
From The generalized Hierarchical Gaussian Filter (2026) · cites this paper as Mathys & Weber, 2020
The generalized HGF can accommodate beliefs about any type of state governed by an exponential family distribution by filtering that distribution's sufficient statistics.
“However, the generalized HGF can also accommodate beliefs about any type of state governed by an exponential family distribution by filtering this distribution’s sufficient statistics Mathys & Weber (2020).”
From The generalized Hierarchical Gaussian Filter (2026) · cites this paper as Mathys & Weber (2020)
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Human inference reflects a normative balance of complexity and accuracy
Tavoni, G., Doi, T., Pizzica, C., Balasubramanian, V., & Gold, J. I. (2022) · Nature Human Behaviour · doi:10.1038/s41562-022-01357-z · Cited by 35 · see citing works
The generalized Hierarchical Gaussian Filter
Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., & Mathys, C. (2026) · eLife · doi:10.7554/elife.110174
Self-citation
- Authors
- Mathys, C., & Weber, L.
- Affiliations
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- University of Zurich (CH)
- Corresponding author
- Mathys, Christoph
- Venue
- Communications in Computer and Information Science
- Publisher
- Springer International Publishing
- Published
- 2020
- Pages
- 52-58
- ISSN
- 1865-0929 (ISSN-L)
- 1865-0937
- OpenAlex
- W3112274343
- Cited by
- 8
- References
- 0
- Citations by year
- 2026: 3 · 2025: 1 · 2022: 2 · 2021: 2
- FWCI
- 1.30
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Communications in computer and information science (publishedVersion)
- SDL (submittedVersion)
- Scopus (Elsevier) (submittedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Embodied and Extended Cognition
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Target Tracking and Data Fusion in Sensor Networks
- Keywords
- active inference, hierarchical Gaussian filter, sufficient statistics, time series filtering, surprise minimization, Bayesian inference, state-space model, exponential family
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