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Fast Möbius transform: an algebraic approach to information decomposition
File(s)
32sq-z2jf.pdf (1.97 MB)
Published version
OA Location
Author(s)
Jansma, Abel
Mediano, Pedro AM
Rosas, Fernando E
Type
Journal Article
Abstract
The partial information decomposition (PID) and its extension integrated information decomposition (Φ⁢ID) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these approaches is the high computational cost involved in their calculation. Here we leverage fundamental algebraic properties of these decompositions to enable a computationally-efficient method to estimate them, which we call the fast Möbius transform. Our approach is based on a formula for estimating the Möbius function that circumvents important computational bottlenecks and can in some cases offer a double-exponential speedup. We showcase the capabilities of this approach by presenting two analyses that would be unfeasible without this method: decomposing the information that neural activity at different frequency bands yields about the brain's macroscopic functional organization and identifying distinctive dynamical properties of the interactions between multiple voices in baroque music. Overall, our proposed approach illuminates the value of algebraic facets of information decomposition and opens the way to a wide range of future analyses.
Date Issued
2025-07-11
Date Acceptance
2025-06-16
Citation
Physical Review Research, 2025, 7 (3)
URI
URL
DOI
ISSN
2643-1564
Publisher
American Physical Society
Journal / Book Title
Physical Review Research
Volume
7
Issue
3
Copyright Statement
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by Max Planck Society
License URL
Subjects
Physical Sciences
Physics
Physics, Multidisciplinary
Science & Technology
Publication Status
Published
Article Number
033049
Date Publish Online
2025-07-11