Abstract
We present a learning algorithm to construct a discriminative Conditional Random Fields cascade model. We decompose the original grid-structured graph model using a set of spanning trees which are learned and added into the cascade architecture iteratively one after another. A spanning tree at each cascade layer takes both outputs from the previous layer nodes as well as the observed variables, which are processed by all the layers. The structure of spanning trees is generated uniformly at random among all spanning trees of the original graph. The result of the learning is the number of cascade layers, the structure of the generated spanning trees, and the set of optimized parameters corresponding to the spanning trees. We performed the experimental validation on synthetic and real-world imagery datasets and demonstrated better performance of the cascade tree-based model over the original grid-structured CRF model with loopy belief propagation inference.
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References
Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: probabilistic models for segmenting and labeling sequence data. In: Proceedings of the 18th International Conference on Machine Learning (ICML) (2001)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1998)
Bach, F.R., Jordan, M.I.: Thin junction trees. In: Advances in Neural Information Processing Systems (NIPS) (2001)
Globerson, A., Jaakkola, T.: Approximate inference using planar graph decomposition. In: Advances in Neural Information Processing Systems (NIPS) (2006)
Batra, D., Gallagher, A.C., Rarikh, D., Chen, T.: Beyond trees: MRF inference via outer-panar decomposition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2010)
Kolmogorov, V., Zabih, R.: What energy functions can be optimized via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 147–159 (2004)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. on Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)
Shimony, S.E.: Finding MAPs for belief networks is NP-hard. Artificial Intelligence 68, 399–410 (1994)
Besag, J.: Statistical analysis of non-lattice data. The Statistician 24, 179–195 (1975)
Besag, J.: Efficiency of pseudo-likelihood estimation for simple gaussian fields. Biometrika 64(3), 616–618 (1977)
Sutton, C., McCallum, A.: Piecewise pseudolikelihood for efficient CRF training. In: Proceedings of the 24th International Conference on Machine Learning (ICML) (2007)
Sutton, C., McCallum, A.: Piecewise training for structured prediction. Machine Learning 77(2-3), 165–194 (2009)
Wainwright, M., Jaakkola, T., Willsky, A.: MAP estimation via agreement on (hyper)trees: message-passing and linear programming approaches. IEEE Transactions on Information Theory 51(11), 3697–3717 (2005)
Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(10), 1568–1583 (2006)
Pletscher, P., Ong, C.S., Buhmann, J.M.: Spanning tree approximations for conditional random fields. In: Proceedings of the 12th International Conference on Artificial Intelligence and Statistics, (AISTATS) (2009)
Wilson, D.B.: Generating random spanning trees more quickly than the cover time. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC) (1996)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization methods. Mathematical Programming 45, 503–528 (1989)
Kumar, S., Hebert, M.: Discriminative fields for modeling spatial dependencies in natural images. In: Advances in Neural Information Processing Systems (NIPS) (2003)
Kumar, S., Hebert, M.: Discriminative random fields. International Journal of Computer Vision 68(2), 179–201 (2006)
Skurikhin, A.N.: Learning tree-structured approximations for conditional random fields. In: Proc. IEEE Applied Imagery Pattern Recognition Workshop (AIPR) (2014)
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Skurikhin, A.N. (2014). Hierarchical Spanning Tree-Structured Approximation for Conditional Random Fields: An Empirical Study. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2014. Lecture Notes in Computer Science, vol 8888. Springer, Cham. https://doi.org/10.1007/978-3-319-14364-4_9
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DOI: https://doi.org/10.1007/978-3-319-14364-4_9
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