Learning compositional structure from data

Abstract: We introduce the neighbourhood lattice decomposition of a distribution, which is a compact, non-graphical representation of conditional independence that is valid in the absence of a faithful graphical representation. The idea is to view the set of neighbourhoods of a variable as a subset lattice, and partition this lattice into convex sublattices, each of which directly encodes a collection of conditional independence relations. We show that this decomposition exists in any compositional graphoid and can be computed consistently in high-dimensions without the curse of dimensionality. In particular, this gives a way to learn from data all of the independence relations implied by any graphical model and thus in particular its structure.

Computer scienceMathematics

Audience: researchers in the discipline

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.