Related papers: Generalized informational functionals and new mono…
Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In…
Which combinatorial sequences correspond to moments of probability measures on the real line? We present a generating function, in the form of a continued fraction, for a fourteen-parameter family of such sequences and interpret these in…
We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the R\'{e}nyi entropy of a random vector in terms of the two…
We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or…
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…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…