Gaussian BROJA Partial Information Decomposition in Closed Form
Abstract
The BROJA partial information decomposition provides an operationally motivated way to separate the information that two sources carry about a target into unique, redundant, and synergistic components. For continuous and high-dimensional variables, however, computing the BROJA decomposition requires solving a difficult optimization problem. Previous work showed that, when each source-target pair is jointly Gaussian, the problem can be reduced to finite-dimensional numerical optimization. Here, we derive a closed-form solution to this optimization problem, enabling direct computation of the BROJA decomposition in the general multivariate Gaussian setting. The resulting closed-form expression enables speedups exceeding two orders of magnitude for high-dimensional Gaussian BROJA PID. Code is available at https://github.com/brainsandmachines/Eigen_PID.
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BibTeX
@misc{sheelo2026gaussian,
title = {{Gaussian BROJA Partial Information Decomposition in Closed Form}},
author = {Ohad Sheelo and Tal Golan and Ari Pakman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13464},
eprint = {2610.13464},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13464},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gaussian BROJA Partial Information Decomposition in Closed Form
AU - Ohad Sheelo
AU - Tal Golan
AU - Ari Pakman
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13464
UR - https://arxiv.org/abs/2610.13464
AB - The BROJA partial information decomposition provides an operationally motivated way to separate the information that two sources carry about a target into unique, redundant, and synergistic components. For continuous and high-dimensional variables, however, computing the BROJA decomposition requires solving a difficult optimization problem. Previous work showed that, when each source-target pair is jointly Gaussian, the problem can be reduced to finite-dimensional numerical optimization. Here, we derive a closed-form solution to this optimization problem, enabling direct computation of the BROJA decomposition in the general multivariate Gaussian setting. The resulting closed-form expression enables speedups exceeding two orders of magnitude for high-dimensional Gaussian BROJA PID. Code is available at https://github.com/brainsandmachines/Eigen_PID.
ER -