CSH Talk by Velimir Ilic “On generalized mutual information, channel capacity, and statistical complexity measures”

Velimir Ilic (Serbian Academy of Sciences and Arts) will present a talk on Wednesday, June 28th, 2023 at 3 PM in Room 201.

Title: On generalized mutual information, channel capacity, and statistical complexity measures

Abstract: In this talk, we will consider axiomatic approaches for the characterization of information transmission and statistical complexity measures which are built from the strongly pseudo-additive (SPA) entropies, such as the super-exponential entropy and the Sharma-Mittal entropy, including instances such as the Rényi, the Tsallis and Landsberg-Verdral entropies. First, we propose Sharma-Mittal information transfer measures named the α-q-mutual information and the α-q-capacity, which, unlike the previous approaches, do not manifest non-physical behaviors such as sub-capacitance or super-capacitance. After that, we provide a general treatment of the statistical complexity measures so that the statistical complexity measure of a discrete system is required to be a non-negative composition of a SPA entropy, which serves as a measure of disorder, and of a generalized certainty measure, which serves as a measure of an order, and we derived the unique class of measures which satisfies introduced set of axioms. In particular, we analyze the class of statistical complexity measures built from super-exponential entropy and their properties.

Bio: Velimir Ilić is a Research Associate at the Mathematical Institute of the Serbian Academy of Sciences and Arts. His research is focused on generalized entropies, which are beyond the Boltzmann-Gibbs one, on probabilistic graphical models for complex systems modeling, as well as on efficient information procession schemes, for the computation of information-theoretic and thermodynamic quantities of systems.