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)

Abstract

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].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)MathSciNetMATHCrossRefGoogle 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)MathSciNetMATHGoogle 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)MathSciNetMATHCrossRefGoogle 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