Related papers: A new approach to mutual information. II
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modelling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
The leading term for the mutual R\'enyi information is studied for two widely separated identical compound systems for free scalar fields in $(d+1)$ Euclidean space. The compound system consists of two identical spheres in contact, with a…
Given an equilibrium state $\mu$ for a continuous function $f$ on a shift of finite type $X$, the pressure of $f$ is the integral, with respect to $\mu$, of the sum of $f$ and the information function of $\mu$. We show that under certain…
This paper examines how an event from one random variable provides pointwise mutual information about an event from another variable via probability mass exclusions. We start by introducing probability mass diagrams, which provide a visual…
Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically…
We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second…
This paper develops a novel unified framework for testing mutual independence among random objects residing in possibly different metric spaces. The framework generalizes existing methodologies and introduces new measures of mutual…
Quantum coherence is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
In this paper, it is shown that the rank function of a matroid can be represented by a "mutual information function" if and only if the matroid is binary. The mutual information function considered is the one measuring the amount of…
We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.
We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper…
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of…
Sensor placement approaches in networks often involve using information-theoretic measures such as entropy and mutual information. We prove that mutual information abides by submodularity and is non-decreasing when considering the mutual…
Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture…
The channel capacity for the binary symmetric channel is investigated based on the symmetrized definition of the mutual information, which is arising from an attempt of extension of information content based on the nonadditivity. The…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
In \cite{Miller-Akin1999}, Miller and Akin investigated the invariant measures for correspondences, which are also known as upper semi-continuous set-valued maps. Recently, the variational principle and thermodynamic formalism for forward…