Using and Learning GAI-Decompositions for Representing Ordinal Rankings

International audienceWe study the use of GAI-decomposable utility functions for representing ordinal rankings on combinatorial sets of objects. Considering only the relative order of objects leaves a lot of freedom for choosing a particular utility function, which allows one to get more compact representations. We focus on the problem of learning such representations, and give a polynomial PAC-learner for the case when a constant bound is known on the degree of the target representation. We also propose linear programming approaches for minimizing such representations

Laver's results and low-dimensional topology

In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications