Abstract
Among the graph structures underlying Probabilistic Graphical Models, trees are valuable tools for modeling several interesting problems, such as linguistic parsing, phylogenetic analysis, and music harmony analysis. In this paper we introduce CDoT, a novel exact algorithm for answering Maximum a Posteriori queries on tree structures. We discuss its properties and study its asymptotic complexity; we also provide an empirical assessment of its performances, showing that the proposed algorithm substantially improves over a dynamic programming based competitor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)
Heckerman, D., Horvitz, E., Nathwani, B.: Toward normative expert systems: The Pathfinder project. Knowledge Systems Laboratory, Stanford University (1992)
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. IEEE Trans. Pattern Anal. Mach. Intell. 30(6), 1068–1080 (2008)
Sun, Y., Deng, H., Han, J.: Probabilistic models for text mining. In: Aggarwal, C.C., Zhai, C. (eds.) Mining Text Data, pp. 259–295. Springer (2012)
Johnson, M., Griffiths, T., Goldwater, S.: Bayesian inference for PCFGs via Markov Chain Monte Carlo. In: Human Language Technologies 2007, pp. 139–146 (2007)
Csűrös, M., Miklós, I.: Streamlining and large ancestral genomes in archaea inferred with a phylogenetic birth-and-death model. Mol. Bio. Evol. 26(9) (2009)
Paiement, J.F., Eck, D., Bengio, S.: A Probabilistic Model for Chord Progressions. In: Proc. of the 6th Int. Conf. on Music Information Retrieval, London (2005)
Viterbi, A.J.: Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans. Inf. Theory 13, 260–269 (1967)
Esposito, R., Radicioni, D.P.: CarpeDiem: Optimizing the Viterbi Algorithm and Applications to Supervised Sequential Learning. JMLR 10, 1851–1880 (2009)
Belanger, D., Passos, A., Riedel, S., McCallum, A.: Speeding up MAP with Column Generation and Block Regularization. In: Proc. of the ICML Workshop on Inferning: Interactions Between Inference and Learning. Omnipress (2012)
Murphy, K., Weiss, Y., Jordan, M.: Loopy belief propagation for approximate inference: An empirical study. In: Proc. of the 15th Conf. on Uncertainty in Art. Intell., pp. 467–475 (1999)
Wainwright, M., Jaakkola, T., Willsky, A.: Map estimation via agreement on trees: message-passing and linear programming. IEEE Trans. Inf. Theory 51(11), 3697–3717 (2005)
Marinescu, R., Kask, K., Dechter, R.: Systematic vs. non-systematic algorithms for solving the mpe task. In: Proc. of the 9th Conf. on Uncertainty in Artificial Intelligence, pp. 394–402. Morgan Kaufmann Publishers Inc. (2002)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)
Zhang, N., Poole, D.: Exploiting causal independence in bayesian network inference. JAIR 5, 301–328 (1996)
Weiss, Y., Freeman, W.: On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. IEEE Trans. Inf. Theory 47(2), 736–744 (2001)
Kaji, N., Fujiwara, Y., Yoshinaga, N., Kitsuregawa, M.: Efficient staggered decoding for sequence labeling. In: Proc. of the 48th Meeting of the ACL, pp. 485–494 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Esposito, R., Radicioni, D.P., Visconti, A. (2013). CDoT: Optimizing MAP Queries on Trees. In: Baldoni, M., Baroglio, C., Boella, G., Micalizio, R. (eds) AI*IA 2013: Advances in Artificial Intelligence. AI*IA 2013. Lecture Notes in Computer Science(), vol 8249. Springer, Cham. https://doi.org/10.1007/978-3-319-03524-6_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-03524-6_41
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03523-9
Online ISBN: 978-3-319-03524-6
eBook Packages: Computer ScienceComputer Science (R0)