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Cycle structure of permutation functions over finite fields and their applications
Computation of cross-moments using message passing over factor graphs
1. | Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Beograd, Serbia |
2. | University of Niš, Faculty of Occupational Safety, Čarnojevića 10a, 18000 Niš, Serbia, Serbia |
References:
[1] |
S. Aji and R. McEliece, The generalized distributive law, IEEE Trans. Inform. Theory, 46 (2000), 325-343.
doi: 10.1109/18.825794. |
[2] |
A. Azuma and Y. Matsumoto, A generalization of forward-backward algorithm, in "Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I,'' Springer-Verlag, Berlin, Heidelberg, (2009), 99-114.
doi: 10.1007/978-3-642-04180-8_24. |
[3] |
C. M. Bishop, "Pattern Recognition and Machine Learning (Information Science and Statistics),'' Springer-Verlag, New York, 2006. |
[4] |
C. Cortes, M. Mohri, A. Rastogi and M. Riley, On the computation of the relative entropy of probabilistic automata, Int. J. Found. Comput. Sci., 19 (2008), 219-242. |
[5] |
R. G. Cowell, P. A. Dawid, S. L. Lauritzen and D. J. Spiegelhalter, "Probabilistic Networks and Expert Systems (Information Science and Statistics),'' Springer, New York, 2003. |
[6] |
R. Gallager, Low-density parity-check codes, IRE Trans. Inform. Theory, 8 (1962), 21-28.
doi: 10.1109/TIT.1962.1057683. |
[7] |
S. Golomb, The information generating function of a probability distribution (corresp.), IEEE Trans. Inform. Theory, 12 (1966), 75-77.
doi: 10.1109/TIT.1966.1053843. |
[8] |
A. Heim, V. Sidorenko and U. Sorger, Computation of distributions and their moments in the trellis, Adv. Math. Commun., 2 (2008), 373-391.
doi: 10.3934/amc.2008.2.373. |
[9] |
V. M. Ilic, M. S. Stankovic and B. T. Todorovic, Entropy message passing, IEEE Trans. Inform. Theory, 57 (2011), 219-242.
doi: 10.1109/TIT.2010.2090235. |
[10] |
F. Kschischang, B. Frey and H.-A. Loeliger, Factor graphs and the sum-product algorithm, IEEE Trans. Inform. Theory, 47 (2001), 498-519.
doi: 10.1109/18.910572. |
[11] |
A. Kulesza and B. Taskar, Structured determinantal point processes, in "Advances in Neural Information Processing Systems 23,'' 2011. |
[12] |
Z. Li and J. Eisner, First- and second-order expectation semirings with applications to minimum-risk training on translation forests, in "Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 1 - Volume 1,'' Association for Computational Linguistics, Stroudsburg, PA, (2009), 40-51. |
[13] |
D. MacKay, Good error-correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, 45 (1999), 399-431.
doi: 10.1109/18.748992. |
[14] |
D. J. C. MacKay, "Information Theory, Inference, and Learning Algorithms,'' Cambridge University Press, 2003. |
[15] |
K. P. Murphy, Y. Weiss and M. I. Jordan, Loopy belief propagation for approximate inference: an empirical study, in "Proceedings of Uncertainty in AI,'' (1999), 467-475. |
[16] |
M. Protter, "Basic Elements of Real Analysis,'' Springer, New York, 1998. |
[17] |
T. Richardson and R. Urbanke, "Modern Coding Theory,'' Cambridge University Press, 2008.
doi: 10.1017/CBO9780511791338. |
[18] |
Y. Weiss, Correctness of local probability propagation in graphical models with loops, Neural Computation, 12 (2000), 1-41.
doi: 10.1162/089976600300015880. |
[19] |
J. Yedidia, W. Freeman and Y. Weiss, Constructing free-energy approximations and generalized belief propagation algorithms, IEEE Trans. Inform. Theory, 51 (2005), 2282-2312.
doi: 10.1109/TIT.2005.850085. |
show all references
References:
[1] |
S. Aji and R. McEliece, The generalized distributive law, IEEE Trans. Inform. Theory, 46 (2000), 325-343.
doi: 10.1109/18.825794. |
[2] |
A. Azuma and Y. Matsumoto, A generalization of forward-backward algorithm, in "Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I,'' Springer-Verlag, Berlin, Heidelberg, (2009), 99-114.
doi: 10.1007/978-3-642-04180-8_24. |
[3] |
C. M. Bishop, "Pattern Recognition and Machine Learning (Information Science and Statistics),'' Springer-Verlag, New York, 2006. |
[4] |
C. Cortes, M. Mohri, A. Rastogi and M. Riley, On the computation of the relative entropy of probabilistic automata, Int. J. Found. Comput. Sci., 19 (2008), 219-242. |
[5] |
R. G. Cowell, P. A. Dawid, S. L. Lauritzen and D. J. Spiegelhalter, "Probabilistic Networks and Expert Systems (Information Science and Statistics),'' Springer, New York, 2003. |
[6] |
R. Gallager, Low-density parity-check codes, IRE Trans. Inform. Theory, 8 (1962), 21-28.
doi: 10.1109/TIT.1962.1057683. |
[7] |
S. Golomb, The information generating function of a probability distribution (corresp.), IEEE Trans. Inform. Theory, 12 (1966), 75-77.
doi: 10.1109/TIT.1966.1053843. |
[8] |
A. Heim, V. Sidorenko and U. Sorger, Computation of distributions and their moments in the trellis, Adv. Math. Commun., 2 (2008), 373-391.
doi: 10.3934/amc.2008.2.373. |
[9] |
V. M. Ilic, M. S. Stankovic and B. T. Todorovic, Entropy message passing, IEEE Trans. Inform. Theory, 57 (2011), 219-242.
doi: 10.1109/TIT.2010.2090235. |
[10] |
F. Kschischang, B. Frey and H.-A. Loeliger, Factor graphs and the sum-product algorithm, IEEE Trans. Inform. Theory, 47 (2001), 498-519.
doi: 10.1109/18.910572. |
[11] |
A. Kulesza and B. Taskar, Structured determinantal point processes, in "Advances in Neural Information Processing Systems 23,'' 2011. |
[12] |
Z. Li and J. Eisner, First- and second-order expectation semirings with applications to minimum-risk training on translation forests, in "Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 1 - Volume 1,'' Association for Computational Linguistics, Stroudsburg, PA, (2009), 40-51. |
[13] |
D. MacKay, Good error-correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, 45 (1999), 399-431.
doi: 10.1109/18.748992. |
[14] |
D. J. C. MacKay, "Information Theory, Inference, and Learning Algorithms,'' Cambridge University Press, 2003. |
[15] |
K. P. Murphy, Y. Weiss and M. I. Jordan, Loopy belief propagation for approximate inference: an empirical study, in "Proceedings of Uncertainty in AI,'' (1999), 467-475. |
[16] |
M. Protter, "Basic Elements of Real Analysis,'' Springer, New York, 1998. |
[17] |
T. Richardson and R. Urbanke, "Modern Coding Theory,'' Cambridge University Press, 2008.
doi: 10.1017/CBO9780511791338. |
[18] |
Y. Weiss, Correctness of local probability propagation in graphical models with loops, Neural Computation, 12 (2000), 1-41.
doi: 10.1162/089976600300015880. |
[19] |
J. Yedidia, W. Freeman and Y. Weiss, Constructing free-energy approximations and generalized belief propagation algorithms, IEEE Trans. Inform. Theory, 51 (2005), 2282-2312.
doi: 10.1109/TIT.2005.850085. |
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