Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation and, when the relaxation is tight, provably find the MAP

Abstract. We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Könemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation

We propose a new class of consistency constraints for Linear Programming (LP) relaxations for finding the most probable (MAP) configuration in graphical models. Usual cluster-based LP relaxations enforce joint consistency of the beliefs of a cluster of variables, with computational cost increasing

Abstract. Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions

the global maximum of a score over BN structures as an integer linear programming (ILP) problem. In this research report, extensions of characteristic imsets are considered which additionally encode chain graphs without flags equivalent to acyclic directed graphs. The main contribution is the LP relaxation

the variables. We present new approaches to approximate inference based on linear programming (LP) relaxations. Our algorithms optimize over the cycle relaxation of the marginal polytope, which we show to be closely related to the first lifting of the Sherali-Adams hierarchy, and is significantly tighter than

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Abstract. We discuss two formulations of the Pattern Minimization Problem: (1) introduced by Vanderbeck, and (2) obtained adding setup variables to the cutting stock formulation by Gilmore-Gomory. Let zLP i (u) be the bound given by the linear relaxation of (i) under a given vector u = (uk

We consider a linear programming relaxation of the MAP-inference problem. Its dual can be treated as an unconstrained, concave but non-smooth one. We utilize smoothing and coordinate descent algorithm (smoothed TRW-S) to deal with the smoothed problem. We propose a diminishing smoothing scheme

block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable parameters such as step size or tree weights. We also describe a generalization of the method to cluster based potentials. The new method is tested on synthetic and real-world problems, and compares