Cumulants of multiinformation density in the case of a multivariate normal distribution

TL;DR

This paper generalizes information density to multiple subvectors in multivariate normal distributions, deriving cumulant-generating functions and cumulants based on regression coefficients.

Contribution

It introduces a novel approach to analyze multivariate information density through cumulants linked to regression coefficients.

Findings

Cumulant-generating function expressed in terms of regression coefficients

Cumulants depend solely on regression coefficients in multivariate normal case

Provides analytical tools for multivariate information analysis

Abstract

We consider a generalization of information density to a partitioning into $N \geq 2$ subvectors. We calculate its cumulant-generating function and its cumulants, showing that these quantities are only a function of all the regression coefficients associated with the partitioning.