Beyond Static Mini-Bucket: Towards Integrating with Iterative Cost-Shifting Based Dynamic Heuristics

We explore the use of iterative cost-shifting as a dynamic heuristic generator for solving MPE in graphical models via Branch and Bound. When mini-bucket elimination is limited by its memory budget, it may not provide good heuristics. This can happen often when the graphical model has a very high induced width with large variable domain sizes. In addition, we explore a hybrid setup where both MBE and the iterative cost-shifting bound are used in a combined heuristic. We compare these approaches with the most advanced statically generated heuristics.

[1]  Rina Dechter.  Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms , 2013, Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms.

[2]  William T. Freeman,et al.  Constructing free-energy approximations and generalized belief propagation algorithms , 2005, IEEE Transactions on Information Theory.

[3]  Martin C. Cooper,et al.  Optimal Soft Arc Consistency , 2007, IJCAI.

[4]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[5]  Simon de Givry,et al.  Computational protein design as an optimization problem , 2014, Artif. Intell..

[6]  Martin C. Cooper,et al.  Virtual Arc Consistency for Weighted CSP , 2008, AAAI.

[7]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[8]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

[9]  Thomas Schiex,et al.  Solving weighted CSP by maintaining arc consistency , 2004, Artif. Intell..

[10]  Tommi S. Jaakkola,et al.  Fixing Max-Product: Convergent Message Passing Algorithms for MAP LP-Relaxations , 2007, NIPS.

[11]  Lars Otten,et al.  Join-graph based cost-shifting schemes , 2012, UAI.

[12]  Rina Dechter,et al.  AND/OR search spaces for graphical models , 2007, Artif. Intell..

[13]  Ian McGraw,et al.  Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing , 2006, UAI.

[14]  Martin J. Wainwright,et al.  MAP estimation via agreement on trees: message-passing and linear programming , 2005, IEEE Transactions on Information Theory.

[15]  Tommi S. Jaakkola,et al.  Tightening LP Relaxations for MAP using Message Passing , 2008, UAI.

[16]  Rina Dechter,et al.  Mini-buckets: A general scheme for bounded inference , 2003, JACM.