Work

A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation

Year: 2026

Type: preprint

Abstract: We study strictly positive multivariate binary distributions by separating one-body marginals from dependence. Local positive reweighting defines a dependence nucleus, completely characterized by the higher-order Walsh log-linear coefficients $J_S$, $|S|\ge2$. Any such nucleus and any strictly positive one-body marginals determine a unique joint distribution. In finite-spin Gibbs systems, these coefficients are the many-body interaction couplings.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12805

Author: Lin, Yi-Yu

Institutions: Fudan University, Shanghai Institute for Mathematics and Interdisciplinary Sciences

Language: English

Topic: Bayesian Modeling and Causal Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7221526990

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