Properties of unique information

Rauh, Johannes, Schünemann, Maik, and Jost, Jürgen. "Properties of unique information." Kybernetika 57.3 (2021): 383-403. <http://eudml.org/doc/297757>.

@article{Rauh2021,
abstract = {We study the unique information function $UI(T:X\setminus Y)$ defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of $UI$. We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of $T$, $X$ and $Y$. Our results are based on a reformulation of the first order conditions on the objective function as rank constraints on a matrix of conditional probabilities. These results help to speed up the computation of $UI(T:X\setminus Y)$, most notably when $T$ is binary. Optima in the relative interior of the optimization domain are solutions of linear equations if $T$ is binary. In the all binary case, we obtain a complete picture of where the optimizing probability distributions lie.},
author = {Rauh, Johannes, Schünemann, Maik, Jost, Jürgen},
journal = {Kybernetika},
keywords = {information decomposition; unique information},
language = {eng},
number = {3},
pages = {383-403},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Properties of unique information},
url = {http://eudml.org/doc/297757},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Rauh, Johannes
AU - Schünemann, Maik
AU - Jost, Jürgen
TI - Properties of unique information
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 3
SP - 383
EP - 403
AB - We study the unique information function $UI(T:X\setminus Y)$ defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of $UI$. We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of $T$, $X$ and $Y$. Our results are based on a reformulation of the first order conditions on the objective function as rank constraints on a matrix of conditional probabilities. These results help to speed up the computation of $UI(T:X\setminus Y)$, most notably when $T$ is binary. Optima in the relative interior of the optimization domain are solutions of linear equations if $T$ is binary. In the all binary case, we obtain a complete picture of where the optimizing probability distributions lie.
LA - eng
KW - information decomposition; unique information
UR - http://eudml.org/doc/297757
ER -