A rapid algorithm to calculate joint probability matrices for joint entropies of arbitrary order

TL;DR

This paper introduces a fast algorithm for computing joint probability matrices of any order using only first-order entropy calculations, simplifying the process of analyzing complex signals.

Contribution

The paper presents a novel rapid method to derive joint probability matrices for arbitrary order entropies from first-order entropy data, reducing computational complexity.

Findings

Enables quick calculation of joint probabilities for higher-order entropies.

Reduces reliance on computationally intensive search algorithms.

Facilitates analysis of complex signals with minimal entropy calculations.

Abstract

There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive the underlying probabilities through search algorithms. These become more computationally expensive as entropies of higher orders are investigated. In this paper, a method to calculate a joint probability matrix based on the entropy for any order is elaborated. With this method, only first order entropies need to be successfully calculated while the others are derived via multiplicative cascades.