On Tightening the M-Best MAP Bounds

  • Qiang ChengEmail author
  • Li Chen
  • Yuanjian Xing
  • Yuhao Yang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 662)


We consider the problem of finding the M assignments with the maximum probabilities (or equivalently, the M-best MAP assignments) on a probabilistic graphical model. The covering graph approximation method provides an upper bound on each of the true M-best MAP costs. However, the tightness of these bounds is closely related to how to split the parameters of the duplicate nodes. We propose a monotonic algorithm to tighten the M-best MAP bounds by finding the optimal splitting of these parameters. Experimental results on synthetic and real problems show that our algorithm provides much tighter bounds than those provided by uniformly splitting the parameters.


M-best MAP inference Probabilistic graphical models Covering graph 


  1. 1.
    Batra, D., Yadollahpour, P., Shakhnarovich, G.: Diverse M-best solutions in MRFs. In: ECCV (2012)Google Scholar
  2. 2.
    Yanover, C., Weiss, Y.: Finding the M most probable configurations using loopy belief propagation. In: NIPS (2004)Google Scholar
  3. 3.
    Fromer, M., Yanover, C.: Accurate prediction for atomic-level protein design and its application in diversifying the near-optimal sequence space. Proteins Struct. Funct. Bioinform. 75, 682–705 (2008)CrossRefGoogle Scholar
  4. 4.
    Nilsson, D.: An efficient algorithm for finding the M most probable configurations in probabilistic expert systems. Stat. Comput. 8, 159–173 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fromer, M., Globerson, A.: An LP View of the M-best MAP problem. In: NIPS (2009)Google Scholar
  6. 6.
    Batra, D.: An efficient message passing algorithm for the M-best MAP problem. In: UAI (2012)Google Scholar
  7. 7.
    Flerova, N., Rollon, E., Dechter, R.: Bucket and mini-bucket schemes for M best solutions over graphical models. In: Croitoru, M., Rudolph, S., Wilson, N., Howse, J., Corby, O. (eds.) GKR 2011. LNCS, vol. 7205, pp. 91–118. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Yarkony, J., Fowlkes, C., Ihler, A.: Covering trees and lower-bounds on quadratic assignment. In: CVPR (2010)Google Scholar
  9. 9.
    Dechter, R., Rish, I.: Mini-buckets: a general scheme for bounded inference. J. ACM 50, 107–153 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  • Qiang Cheng
    • 1
    • 2
    Email author
  • Li Chen
    • 1
    • 2
  • Yuanjian Xing
    • 1
    • 2
  • Yuhao Yang
    • 1
    • 2
  1. 1.Nanjing Research Institute of Electronics TechnologyNanjingChina
  2. 2.Key Laboratory of IntelliSense Technology, CETCNanjingChina

Personalised recommendations