Learning Maximum Weighted (k+1)-Order Decomposable Graphs by Integer Linear Programming

Aritz Pérez, Christian Blum, José Antonio Lozano

Abstract: This work is focused on learning maximum weighted graphs subject to three structural constraints: (1) the graph is decomposable, (2) it has a maximum clique size of k + 1, and (3) it is coarser than a given maximum k-order decomposable graph. After proving that the problem is NP-hard we give a formulation of the problem based on integer linear programming. The approach has shown competitive experimental results in artificial domains. The proposed formulation has important applications in the field of probabilistic graphical models, such as learning decomposable models based on decomposable scores (e.g. log-likelihood, BDe, MDL, just to name a few).