相关论文: Metric and probabilistic information associated wi…
Parasupersymmetric quantum mechanics is exploited to introduce a topological invariant associated with a pair of parameter dependent Fredholm (respectively elliptic differential) operators satisfying two compatibility conditions. An…
Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI)…
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…
This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give…
In this paper we outline some mathematical questions that emerge from trying to "turn the scientific method into math". Specifically, we consider the problem of experiment planning (choosing the best experiment to do next) in explicit…
This paper explores the solution of Fredholm-like equations with infinite dimensional solution spaces. We set out to find a method for determining a particular solution to a Fredholm-like equation subject to a given constraint. The…
The probability that an interval $I$ is free of eigenvalues in a matrix ensemble with unitary symmetry is given by a Fredholm determinant. When the weight function in the matrix ensemble is a classical weight function, and the interval $I$…
In this paper we delve into some important properties of probability distributions of the power type in order to provide some answers to questions recently raised in the literature. More precisely, we focus on the properties of maximizers…
By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in…
Does the asymptotic variance of the maximum composite likelihood estimator of a parameter of interest always decrease when the nuisance parameters are known? Will a composite likelihood necessarily become more efficient by incorporating…
We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between…