Abstract
The paper considers algorithms for global structures generation in algebraic Bayesian networks. A decremental algorithm for constructing a secondary structure after deleting vertex from the adjacency graph is proposed supplemented by a listing of the algorithm code and by the proof of its correctness. The results of the statistical tests for decremental algorithm are proposed graphically together with a comparative analysis of the results. Moreover, the description of incremental algorithm for adding vertex in tertiary structure is provided supplemented by a listing of the algorithm code and proof of its correctness.
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
References
Cano, A., Gomez-Olmedo, M., Moral, S.: Binary probability trees for bayesian networks inference. Symbo. Quant. Approaches Reasoning uncertainty Proc. 5590, 180–191 (2009)
Flores, M., Gamez, J., Olesen, K.: Incremental compilation of bayesian networks based on maximal prime subgraphs. Int. J. Uncertainty Fuzziness knowl.-Based Syst. 19(2), 155–191 (2011)
Leonelli, M., Smith, J.: Bayesian decision support for complex systems with many distributed experts. Ann. Oper. Res. 235(1) (2015)
Nepomniaschaya, A.: Efficient parallel implementation of the ramalingam decremental algorithm for updating the shortest paths subgraph. Comput. Inform. 32(2), 331–354 (2013)
Oparin, V.V., Filchenkov, A.A., Sirotkin, A.V., Tulupyev, A.L.: Matroidal representation for the adjacency graphs family built on a set of knowledge patterns. Sci. Tech. J. Inf. Technol. Mech. Opt. (4), 73–76 (2009). http://ntv.ifmo.ru/file/article/697.pdf (In Russian)
Oparin, V.V., Tulupyev, A.L.: Synthesis of a joint graph with minimal number of edges: an algorithm formalization and a proof of correctness. Tr. SPIIRAN (11), 142–157 (2009).http://mi.mathnet.ru/trspy52 (In Russian)
Tulupyev, A.L.: Join tree with conjunctions ideals as an acyclic algebraic bayesian network. Tr. SPIIRAN (3), 198–227 (2006). http://mi.mathnet.ru/trspy222 (In Russian)
Tulupyev, A.L.: Algebraic bayesian networks: global probabilistic-logic inference in adjacent tree (2007) (In Russian)
Tulupyev, A.L., Nikolenko, S.I., Sirotkin, A.V.: Bayesian Networks: a Probabilistic-logic Approach. SPb: Nauka (2006) (In Russian)
Tulupyev, A.L., Sirotkin, A.V., Nikolenko, S.I.: Bayesian Belief Networks. SPb: SPbSU Press (2009) (In Russian)
Yue, K., Fang, Q., Wang, X., Li, J., Liu, W.: A parallel and incremental approach for data-intensive learning of bayesian networks. IEEE Trans. Cybern. 45(12) (2015)
Zhu, M., Liu, S.: A decomposition algorithm for learning bayesian networks based on scoring function. J. Appl. Math.
Zotov, M.A., Tulupyev, A.L., Sirotkin, A.V.: Complexity statistical estimates of straightforward and greedy algorithms for algebraic Bayesian networks syntesis. Nechetkie Sistemy i Myagkie Vychisleniya [Fuzzy Systems and Soft Computing] 10(1), 75–91 (2015) (In Russian)
Zotov, M., Levenets, D., Tulupyev, A., Zolotin, A.: Synthesis of the secondary structure of algebraic bayesian networks: an incremental algorithm and statistical estimation of its complexity. Tr. SPIIRAN 16(1), 122–132 (2016) (In Russian)
Zotov, M., Tulupyev, A.: Secondary structure synthesis in algebraic bayesian networks: a statistical technique for complexity estimates and comparative analysis of greedy and straightforward algorithms. Comput. Tools Educ. 1, 3–18 (2015) (In Russian)
The paper presents results of the project partially supported with RFBR grant 15-01-09,001-a “Combined Probabilistic-Logic Graphical Approach to Representation and Processing of Unsertain Knowledge Systems: Algebraical Bayesian Networks and Related Models”, and partially supported by the Government of the Russian Federation, Grant 074-U01.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Levenets, D.G., Zotov, M.A., Romanov, A.V., Tulupyev, A.L., Zolotin, A.A., Filchenkov, A.A. (2016). Decremental and Incremental Reshaping of Algebraic Bayesian Networks Global Structures. In: Abraham, A., Kovalev, S., Tarassov, V., Snášel, V. (eds) Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’16). Advances in Intelligent Systems and Computing, vol 451. Springer, Cham. https://doi.org/10.1007/978-3-319-33816-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-33816-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33815-6
Online ISBN: 978-3-319-33816-3
eBook Packages: EngineeringEngineering (R0)