Skip to main content
SpringerLink
Log in

A Novel Tree Block-Coordinate Method for MAP Inference

  • Conference paper
  • First Online:
Pattern Recognition (DAGM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9358))

Included in the following conference series:

  • 2084 Accesses

Abstract

Block-coordinate methods inspired by belief propagation are among the most successful methods for approximate MAP inference in graphical models. The set of unknowns optimally updated in such block-coordinate methods is typically very small and spans only single edges or shallow trees. We derive a method that optimally updates sets of unknowns spanned by an arbitrary tree that is different from one reported in the literature. It provides some insight why “tree block-coordinate” methods are not as useful as expected, and enables a simple technique to makes these tree updates more effective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    Since the unknowns \((\rho _s)_{s \in \mathcal V}\) play only the role of auxiliary variables, we drop them as argument to \(E^*_{\text {MAP}}\) to simplify the notation.

References

  1. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)

    Article  Google Scholar 

  2. Domke, J.: Parameter learning with truncated message-passing. In: Proceedings of the CVPR, pp. 2937–2943 (2011)

    Google Scholar 

  3. Drory, A., Haubold, C., Avidan, S., Hamprecht, F.A.: Semi-global matching: a principled derivation in terms of message passing. In: Jiang, X., Hornegger, J., Koch, R. (eds.) GCPR 2014. LNCS, vol. 8753, pp. 43–53. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  4. Globerson, A., Jaakkola, T.: Fixing max-product: convergent message passing algorithms for MAP LP-relaxations. In: NIPS (2007)

    Google Scholar 

  5. Hazan, T., Shashua, A.: Norm-prodcut belief propagtion: primal-dual message-passing for LP-relaxation and approximate-inference. IEEE Trans. Inf. Theory 56(12), 6294–6316 (2010)

    Article  Google Scholar 

  6. Hirschmüller, H.: Accurate and efficient stereo processing by semi-global matching and mutual information. In: Proceedings CVPR, pp. 807–814 (2005)

    Google Scholar 

  7. Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Trans. Pattern Anal. Mach. Intell. 28(10), 1568–1583 (2006)

    Article  Google Scholar 

  8. Lempitsky, V., Rother, C., Roth, S., Blake, A.: Fusion moves for Markov random field optimization. IEEE Trans. Pattern Anal. Mach. Intell. 32(8), 1392–1405 (2010)

    Article  Google Scholar 

  9. Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, Mountain view (1988)

    Google Scholar 

  10. Scharstein, D., Szeliski, R.: High-accuracy stereo depth maps using structured light. In: Proceedings of the CVPR, pp. 195–202 (2003)

    Google Scholar 

  11. Sontag, D., Globerson, A., Jaakkola, T.: Optimization for machine learning. In: Introduction to Dual Decomposition for Inference. MIT Press (2011)

    Google Scholar 

  12. Sontag, D., Jaakkola, T.: Tree block coordinate descent for MAP in graphical models. J. Mach. Learn. Res. 5, 544–551 (2009)

    Google Scholar 

  13. Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1, 1–305 (2008)

    Article  Google Scholar 

  14. Wainwright, M.J., Jaakkola, T.S., Willsky, A.S.: MAP estimation via agreement on trees: message-passing and linear programming. IEEE Trans. Inf. Theory 51(11), 3697–3717 (2005)

    Article  MathSciNet  Google Scholar 

  15. Weiss, Y., Yanover, C., Meltzer, T.: MAP estimation, linear programming and belief propagation with convex free energies. In: UAI (2007)

    Google Scholar 

  16. Werner, T.: A linear programming approach to max-sum problem: a review. IEEE Trans. Pattern Anal. Mach. Intell. 29(7), 1165–1179 (2007)

    Article  Google Scholar 

  17. Zach, C.: A principled approach for coarse-to-fine MAP inference. In: Proceedings of the CVPR, pp. 1330–1337 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Toshiba Research Europe, Cambridge, UK

    Christopher Zach

Authors
  1. Christopher Zach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher Zach .

Editor information

Editors and Affiliations

  1. Institute of Computer Science III, University of Bonn, Bonn, Germany

    Juergen Gall

  2. MPI for Intelligent Systems, University of Tübingen, Tübingen, Germany

    Peter Gehler

  3. Computer Vision Group, Visual Computing Institute, RWTH Aachen, Aachen, Germany

    Bastian Leibe

1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 678 KB)

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Zach, C. (2015). A Novel Tree Block-Coordinate Method for MAP Inference. In: Gall, J., Gehler, P., Leibe, B. (eds) Pattern Recognition. DAGM 2015. Lecture Notes in Computer Science(), vol 9358. Springer, Cham. https://doi.org/10.1007/978-3-319-24947-6_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24947-6_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24946-9

  • Online ISBN: 978-3-319-24947-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation