Related papers: Infinite Divisibility of Information
Let $Z$ be a standard normal random variable (r.v.). It is shown that the distribution of the r.v. $\ln|Z|$ is infinitely divisible; equivalently, the standard normal distribution considered as the distribution on the multiplicative group…
Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit…
We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is…
Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of…
The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have…
We establish a quantitative bound on the entropy jump associated to the sum of independent, identically distributed (IID) radially symmetric random vectors having dimension greater than one. Following the usual approach, we first consider…
Any unconstrained information inequality in three or fewer random variables can be written as a linear combination of instances of Shannon's inequality I(A;B|C) >= 0 . Such inequalities are sometimes referred to as "Shannon" inequalities.…
Let $X $ be a square integrable random variable with basic probability space $(\O, \A, \P)$, taking values in a lattice $\mathcal L(v_0,1)=\big\{v_k=v_0+ k,k\in \Z\big\}$ and such that $\t_X =\sum_{k\in \Z}\P\{X=v_k\}\wedge…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…
We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution…
We propose two new measures for extracting the unique information in $X$ and not $Y$ about a message $M$, when $X, Y$ and $M$ are joint random variables with a given joint distribution. We take a Markov based approach, motivated by…
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…
The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
Given two relations containing multiple measurements - possibly with uncertainties - our objective is to find which sets of attributes from the first have a corresponding set on the second, using exclusively a sample of the data. This…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…