Project description
Advanced algebraic approaches to nonlinear information theory problems
Information theory, which blends statistics, engineering and computer science, is a key theoretical pillar of data science. Computational problems in this field are highly nonlinear. Funded by the Marie Skłodowska-Curie Actions programme, the ALGETIQ project plans to apply cutting-edge computational nonlinear algebra methods to information theory. The goal is to study the inherent algebraic complexity of information theory problems and provide practical tools for solving them. The focus will be on the practical computation of information quantities using numerical and differential algebraic geometry and identify the algebraic complexity in instances of general interest. Another objective is to uncover fundamental laws and limits of data science imposed by nonlinear inequalities constraining the entropic region, providing universal bounds for many optimisation problems in information theory.
Objective
Information theory is a discipline at the intersection of statistics, engineering and computer science. As the study of information quantities, such as compression or communication capacities, information content or measures of statistical dependency, it is one of the theoretical underpinnings of data science.
Computational problems in information theory are highly non-linear. The goal of this project is to transfer state-of-the-art methods of computational non-linear algebra to information theory, to study the inherent algebraic complexity of information-theoretical problems and to provide tools for solving them in practice. The algebraic point of view has proven to be fruitful in seemingly unrelated areas, as witnessed by a surge of recent work in algebraic statistics, in particular on likelihood geometry. However, maximizing the likelihood function is the same as minimizing relative entropy — a specific information quantity. Hence, this project also aims at generalizing the techniques developed in likelihood geometry.
One focus is on the practical computation of information quantities using numerical and differential algebraic geometry. Such quantities are defined via non-linear optimization problems and we aim to pinpoint the algebraic complexity of these problems in instances of general interest, such as common information measures. The final objective is finding fundamental laws and limits of data science imposed by non-linear inequalities constraining the entropic region. These inequalities provide, by duality, universal bounds for many of the optimization problems studied in information theory.
Fields of science
Keywords
Programme(s)
- HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA) Main Programme
Funding Scheme
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European FellowshipsCoordinator
9019 Tromso
Norway