Version 1
: Received: 5 March 2024 / Approved: 5 March 2024 / Online: 6 March 2024 (07:22:09 CET)
Version 2
: Received: 22 April 2024 / Approved: 23 April 2024 / Online: 25 April 2024 (14:18:25 CEST)
How to cite:
Mages, T.; Anastasiadi, E.; Rohner, C. Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell Specific Information. Preprints2024, 2024030285. https://doi.org/10.20944/preprints202403.0285.v1
Mages, T.; Anastasiadi, E.; Rohner, C. Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell Specific Information. Preprints 2024, 2024030285. https://doi.org/10.20944/preprints202403.0285.v1
Mages, T.; Anastasiadi, E.; Rohner, C. Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell Specific Information. Preprints2024, 2024030285. https://doi.org/10.20944/preprints202403.0285.v1
APA Style
Mages, T., Anastasiadi, E., & Rohner, C. (2024). Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell Specific Information. Preprints. https://doi.org/10.20944/preprints202403.0285.v1
Chicago/Turabian Style
Mages, T., Elli Anastasiadi and Christian Rohner. 2024 "Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell Specific Information" Preprints. https://doi.org/10.20944/preprints202403.0285.v1
Abstract
Partial Information Decompositions (PIDs) aim to categorize how a set of source variables provide information about a target variable redundantly, uniquely, or synergetically. The original proposal for such an analysis used a lattice-based approach and gained significant attention. However, finding a suitable underlying decomposition measure is still an open research question, even at an arbitrary number of discrete random variables. This work proposes a solution to this case with a non-negative PID that satisfies an inclusion-exclusion relation for any f-information measure. The decomposition is constructed from a pointwise perspective of the target variable to take advantage of the equivalence between the Blackwell and zonogon order in this setting. We prove that the decomposition satisfies the axioms of the original decomposition framework and guarantees non-negative partial information results. We highlight that our decomposition behaves differently depending on the used information measure, which can be utilized for different applications. We additionally show how our proposal can be used to obtain a non-negative decomposition of Rényi-information at a transformed inclusion-exclusion relation, and for tracing partial information flows through Markov chains.
Keywords
partial information decomposition; redundancy; synergy; information flow analysis; f-information; rényi-information
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
