Modelling Multivariate Ranking Functions with Min-Sum Networks.

Spohnian ranking functions are a qualitative abstraction of probability functions, and they have been applied to knowledge representation and reasoning that involve uncertainty. However, how to represent a ranking function which has a size that is exponential in the number of variables still remains insufficiently explored. In this work we introduce min-sum networks (MSNs) for a compact representation of ranking functions for multiple variables. This representation allows for exact inference with linear cost in the size of the number of nodes .