Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation

Akshat Kumar and Shlomo Zilberstein. Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation. Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence (UAI), 428-435, Barcelona, Spain, 2011.

Abstract

Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concave-convex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A similar technique is used to derive a globally convergent algorithm for the convex QP relaxation of MAP. We also show that a recently developed expectation-maximization (EM) algorithm for the QP formulation of MAP can be derived from the CCCP perspective. Experiments on synthetic and real-world problems confirm that our new approach is competitive with max-product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation.

Bibtex entry:

@inproceedings{KZuai11,
  author	= {Akshat Kumar and Shlomo Zilberstein},
  title		= {Message-Passing Algorithms for Quadratic Programming 
                   Formulations of {MAP} Estimation},
  booktitle     = {Proceedings of the Twenty-Seventh Conference on Uncertainty in 
		   Artificial Intelligence},
  year		= {2011},
  pages		= {428-435},
  address       = {Barcelona, Spain},
  url		= {http://rbr.cs.umass.edu/shlomo/papers/KZuai11.html}
}

shlomo@cs.umass.edu