Self-adhesivity in lattices of abstract conditional independence models.

Abstract: In the first part of the talk, the concept of a self-adhesive polymatroid, introduced in 2007 by Matus, will be recalled. This concept can be viewed as the formalization of a method to derive non-Shannon information-theoretical inequalities, known in context of the so-called copy lemma. Then an abstraction of this method leads to the notion of a self-adhesive conditional independence (CI) model. These CI models will be defined relative to an abstract algebraic frame of CI models closed under three basic operations, called copying, marginalization, and intersection. Three examples of such abstract frames will be given. The application of this theory to the theme of entropic region delimitation will be mentioned in the end of the first part. Specifically, most of extreme rays of the 5-polymatroidal were computationally excluded from being almost entropic.

The second part of the talk will start with recalling certain basic facts from lattice theory and the formal concept analysis. Two basic ways to describe finite lattices in a condensed form will be presented. Particular attention will be devoted to the concept of a pseudo-closed set an implicational generator for a Moore family of sets. This leads to combinatorial algorithms to compute the so-called canonical implicational basis. The results of computational results on relevant families of CI models will be then presented, which results can be interpreted as the canonical "axiomatizations" for these CI families. The rest of the talk will be devoted other sensible operations with CI models, other conceivable abstract algebraic CI frames, and to open questions raised in this context.

The talk is based on a joint work with T. Boege and J.H. Bolt.

Computer scienceMathematics

Audience: researchers in the discipline

( paper )

---

Seminar on Algorithmic Aspects of Information Theory

Series comments: This online seminar is a follow up of the Dagstuhl Seminar 22301, www.dagstuhl.de/en/program/calendar/semhp/?semnr=22301.

---