The Lazy Flipper: Efficient Depth-Limited Exhaustive Search in Discrete Graphical Models

  • Bjoern Andres
  • Jörg H. Kappes
  • Thorsten Beier
  • Ullrich Köthe
  • Fred A. Hamprecht
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7578)


We propose a new exhaustive search algorithm for optimization in discrete graphical models. When pursued to the full search depth (typically intractable), it is guaranteed to converge to a global optimum, passing through a series of monotonously improving local optima that are guaranteed to be optimal within a given and increasing Hamming distance. For a search depth of 1, it specializes to ICM. Between these extremes, a tradeoff between approximation quality and runtime is established. We show this experimentally by improving approximations for the non-submodular models in the MRF benchmark [1] and Decision Tree Fields [2].


  1. 1.
    Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields with smoothness-based priors. TPAMI 30, 1068–1080 (2008)CrossRefGoogle Scholar
  2. 2.
    Nowozin, S., Rother, C., Bagon, S., Sharp, T., Yao, B., Kohli, P.: Decision tree fields. In: ICCV (2011)Google Scholar
  3. 3.
    Koller, D., Friedman, N.: Probabilistic Graphical Models. MIT Press (2009)Google Scholar
  4. 4.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Francisco (1988)Google Scholar
  5. 5.
    Lauritzen, S.L.: Graphical Models. Statistical Science. Oxford (1996)Google Scholar
  6. 6.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. TPAMI 23, 1222–1239 (2001)CrossRefGoogle Scholar
  7. 7.
    Kolmogorov, V., Zabin, R.: What energy functions can be minimized via graph cuts? TPAMI 26, 147–159 (2004)CrossRefGoogle Scholar
  8. 8.
    Schlesinger, D.: Exact Solution of Permuted Submodular MinSum Problems. In: Yuille, A.L., Zhu, S.-C., Cremers, D., Wang, Y. (eds.) EMMCVPR 2007. LNCS, vol. 4679, pp. 28–38. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Shimony, S.E.: Finding MAPs for belief networks is NP-hard. Artificial Intelligence 68, 399–410 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Batra, D., Nowozin, S., Kohli, P.: Tighter relaxations for MAP-MRF inference: A local primal-dual gap based separation algorithm. JMLR (Proceedings Track) 15, 146–154 (2011)Google Scholar
  11. 11.
    Komodakis, N., Paragios, N., Tziritas, G.: MRF energy minimization and beyond via Dual Decomposition. TPAMI 33, 531–552 (2011)CrossRefGoogle Scholar
  12. 12.
    Sontag, D., Meltzer, T., Globerson, A., Jaakkola, T., Weiss, Y.: Tightening LP relaxations for MAP using message passing. In: UAI (2008)Google Scholar
  13. 13.
    Wainwright, M.J., Jordan, M.I.: Graphical Models, Exponential Families, and Variational Inference. Now Publishers Inc., Hanover (2008)Google Scholar
  14. 14.
    Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. TPAMI 28, 1568–1583 (2006)CrossRefGoogle Scholar
  15. 15.
    Wainwright, M.J., Jaakkola, T., Willsky, A.S.: MAP estimation via agreement on trees: message-passing and linear programming. Transactions on Information Theory 51, 3697–3717 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Komodakis, N., Paragios, N., Tziritas, G.: MRF energy minimization and beyond via dual decomposition. TPAMI 33, 531–552 (2011)CrossRefGoogle Scholar
  17. 17.
    Besag, J.: On the statisical analysis of dirty pictures. J. of the Royal Statistical Society B 48, 259–302 (1986)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Frey, B.J., Jojic, N.: A comparison of algorithms for inference and learning in probabilistic graphical models. TPAMI 27, 1392–1416 (2005)CrossRefGoogle Scholar
  19. 19.
    Jung, K., Kohli, P., Shah, D.: Local rules for global MAP: When do they work? In: NIPS (2009)Google Scholar
  20. 20.
    Swendsen, R.H., Wang, J.S.: Nonuniversal critical dynamics in monte carlo simulations. Physical Review Letters 58, 86–88 (1987)CrossRefGoogle Scholar
  21. 21.
    Avis, D., Fukuda, K.: Reverse search for enumeration. Discrete Appl. Math. 65, 21–46 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Moerkotte, G., Neumann, T.: Analysis of two existing and one new dynamic programming algorithm for the generation of optimal bushy join trees without cross products. In: Proc. of the 32nd Int. Conf. on Very Large Data Bases (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bjoern Andres
    • 1
  • Jörg H. Kappes
    • 1
  • Thorsten Beier
    • 1
  • Ullrich Köthe
    • 1
  • Fred A. Hamprecht
    • 1
  1. 1.HCI, University of HeidelbergGermany

Personalised recommendations