BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Milan Studený (Institute of Information Theory and Automation\, P rague)) DTSTART:20240619T150000Z DTEND:20240619T161500Z DTSTAMP:20260423T021443Z UID:AAIT/37 DESCRIPTION:Title: Se lf-adhesivity in lattices of abstract conditional independence models. \nby Milan Studený (Institute of Information Theory and Automation\, Prag ue)) as part of Seminar on Algorithmic Aspects of Information Theory\n\n\n Abstract\nIn the first part of the talk\, the concept of a self-adhesive p olymatroid\, introduced in 2007 by Matus\, will be recalled. This concept can be viewed as the formalization of a method to derive non-Shannon infor mation-theoretical inequalities\, known in context of the so-called copy l emma. Then an abstraction of this method leads to the notion of a self-adh esive conditional independence (CI) model. These CI models will be defined relative to an abstract algebraic frame of CI models closed under three b asic operations\, called copying\, marginalization\, and intersection. Thr ee 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-po lymatroidal were computationally excluded from being almost entropic.\n\nT he second part of the talk will start with recalling certain basic facts f rom lattice theory and the formal concept analysis. Two basic ways to desc ribe finite lattices in a condensed form will be presented. Particular att ention will be devoted to the concept of a pseudo-closed set an implicatio nal generator for a Moore family of sets. This leads to combinatorial algo rithms to compute the so-called canonical implicational basis. The results of computational results on relevant families of CI models will be then p resented\, which results can be interpreted as the canonical "axiomatizati ons" for these CI families. The rest of the talk will be devoted other sen sible operations with CI models\, other conceivable abstract algebraic CI frames\, and to open questions raised in this context. \n\nThe talk is bas ed on a joint work with T. Boege and J.H. Bolt.\n LOCATION:https://researchseminars.org/talk/AAIT/37/ END:VEVENT END:VCALENDAR