Exploiting tensor rank-one decomposition in probabilistic inference

Kybernetika

Volumn 43, Issue 5, 2007, Pages 747-764

  Savicky, Petr ^a   Vomlel, Jiří ^b  

^a INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^b INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Graphical probabilistic models; Probabilistic inference; Tensor rank

Indexed keywords

EID: 43649104508     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. M. Chavira and A. Darwiche: Compiling Bayesian networks with local structure. In: Proc. 19th Internat. Joint Conference on Artificial Intelligence (IJCAI), Edinburgh 2005, pp. 1306-1312.
2. A. Darwiche: A differential approach to inference in Bayesian networks. J. Assoc. Comput. Mach. 50 (2003), 3, 280-305.
3. L. De Lathauwer and B. De Moor: From matrix to tensor: multilinear algebra and signal processing. In: 4th Internat. Conference on Mathematics in Signal Processing, Part I, IMA Conference Series, Warwick 1996, pp. 1-11.
4. N) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21 (2000), 4, 1324-1342.
5. F. J. Diez and S. F. Galán: An efficient factorization for the noisy MAX. Internat. J. Intell. Systems 18 (2003), 2, 165-177.
6. G. H. Golub and C. F. Van Loan: Matrix Computations. Third edition. Johns Hopkins University Press, Baltimore 1996.
7. D. Heckerman: A tractable inference algorithm for diagnosing multiple diseases. In: Proc. Fifth Annual Conference on Uncertainty in AI (M. Henrion, R. D. Shachter, L.N. Kanal, and J. F. Lemmer, eds.), August 18-21, 1989, Windsor, ON, pp. 163-171.
8. D. Heckerman: Causal independence for knowledge acquisition and inference. In: Proc. Ninth Conference on Uncertainty in AI (D. Heckerman and A. Mamdani, eds.), July 9-11, 1993, Washington, D.C., pp. 122-127.
9. D. Heckerman and J. S. Breese: A new look at causal independence. In: Proc. Tenth Conference on Uncertainty in AI (R. Lopez de Mantaras and D. Poole, eds.), July 29-31, 1994, Seattle, WA, pp. 286-292.
10. J. Hastad: Tensor Rank is NP-complete. J. Algorithms 11 (1990), 644-654.
11. F. V. Jensen: Bayesian Networks and Decision Graphs. (Statistics for Engineering and Information Science.) Springer-Verlag, New York - Berlin - Heidelberg 2001.
12. F. V. Jensen, S. L. Lauritzen, and K. G. Olesen: Bayesian updating in recursive graphical models by local computation. Computat. Statist. Quart. 4 (1990), 269-282.
13. S. L. Lauritzen: Graphical Models. Clarendon Press, Oxford 1996.
14. K. G. Olesen, U. Kjaerulff, F. Jensen, F. V. Jensen, B. Falck, S. Andreassen and S. K. Andersen: A MUNIN network for the median nerve - a case study on loops. Appl. Artif. Intell., Special issue: Towards Causal AI Models in Practice 3 (1989), 384-403.
15. E. Polak: Computational Methods in Optimization: A Unified Approach. Academic Press, New York 1971.
16. M. Takikawa and B. D'Ambrosio: Multiplicative factorization of noisy-max. In: Proc. Fifteenth Conference on Uncertainty in AI (K. B. Laskey and H. Prade, eds.), July 30-August 1, 1999, Stockholm, pp. 622-630.
17. J. Vomlel: Exploiting functional dependence in Bayesian network inference. In: Proc. Eighteenth Conference on Uncertainty in AI (UAI) - Edmonton (Canada), Morgan Kaufmann, San Francisco 2002, pp. 528-535.
18. N. L. Zhang and D. Poole: Exploiting causal independence in Bayesian network inference. J. Artif. Intell. Res. 5 (1996), 301-328.