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2016 | OriginalPaper | Chapter

Estimation of Edge Infection Probabilities in the Inverse Infection Problem

Authors : András Bóta, Miklós Krész, András Pluhár

Published in: Recent Advances in Computational Optimization

Publisher: Springer International Publishing

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Abstract

Several methods have been proposed recently to estimate the edge infection probabilities in infection or diffusion models. In this paper we will use the framework of the Generalized Cascade Model to define the Inverse Infection Problem—the problem of calculating these probabilities. We are going to show that the problem can be reduced to an optimization task and we will give a particle swarm based method as a solution. We will show, that direct estimation of the separate edge infection values is possible, although only on small graphs with a few thousand edges. To reduce the dimensionality of the task, the edge infection values can be considered as functions of known attributes on the vertices or edges of the graph, this way only the unknown coefficients of these functions have to be estimated. We are going to evaluate our method on artificially created infection scenarios. Our main points of interest are the accuracy and stability of the estimation.

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Footnotes
1
The BASEL II default probabilities were computed using vertex attributes.
 
2
Vertex attributes can be easily converted into edge attributes.
 
3
It is possible, that some of these attributes have no influence on the infection probability, but we expect the method to ignore the effect of these.
 
4
Each agent has four neighbors in a grid, connected to the upper, lower, left and right, while wrapping around the edges.
 
5
Again, these are the edge weights or the coefficients of the attribute function.
 
6
We have implemented the methods in JAVA, and we have used a computer with an Intel i7-2630QM processor, and 8 Gb of memory.
 
7
Note the sample sizes.
 
Literature
1.
go back to reference A. Bóta, A. Csernenszky, L. Győrffy, G. Kovács, M. Krész, A. Pluhár, Applications of the inverse infection problem on bank transaction networks. Cent. Eur. J. Oper. Res. 1–12 (2014) A. Bóta, A. Csernenszky, L. Győrffy, G. Kovács, M. Krész, A. Pluhár, Applications of the inverse infection problem on bank transaction networks. Cent. Eur. J. Oper. Res. 1–12 (2014)
2.
go back to reference A. Bóta, M. Krész, A. Pluhár, Approximations of the generalized cascade model. Acta Cybern. 21, 37–51 (2013) A. Bóta, M. Krész, A. Pluhár, Approximations of the generalized cascade model. Acta Cybern. 21, 37–51 (2013)
3.
go back to reference A. Bóta, M. Krész, A. Pluhár, Systematic learning of edge probabilities in the Domingos-Richardson model. Int. J. Complex Syst. Sci. 1(2), 115–118 (2011) A. Bóta, M. Krész, A. Pluhár, Systematic learning of edge probabilities in the Domingos-Richardson model. Int. J. Complex Syst. Sci. 1(2), 115–118 (2011)
5.
go back to reference A. Csernenszky, Gy. Kovács, M. Krész, A. Pluhár, T. Tóth, The use of infection models in accounting and crediting. Challenges for Analysis of the Economy, the Businesses, and Social Progress Szeged (2009), pp. 617–623 A. Csernenszky, Gy. Kovács, M. Krész, A. Pluhár, T. Tóth, The use of infection models in accounting and crediting. Challenges for Analysis of the Economy, the Businesses, and Social Progress Szeged (2009), pp. 617–623
6.
go back to reference T. Cao, X. Wu, T.X. Hu, S. Wang, Active learning of model parameters for influence maximization, in Machine Learning and Knowledge Discovery in Databases, Lecture Notes in Computer Science, ed. by D. Gunopulos, et al. (Springer, Berlin, 2011), pp. 280–295. doi:10.1007/978-3-642-23780-5_28 CrossRef T. Cao, X. Wu, T.X. Hu, S. Wang, Active learning of model parameters for influence maximization, in Machine Learning and Knowledge Discovery in Databases, Lecture Notes in Computer Science, ed. by D. Gunopulos, et al. (Springer, Berlin, 2011), pp. 280–295. doi:10.​1007/​978-3-642-23780-5_​28 CrossRef
7.
go back to reference W. Chen, Y. Yuan, L. Zhang, Scalable influence maximization in social networks under the linear threshold model, in Proceeding ICDM’10 Proceedings of the 2010 IEEE International Conference on Data Mining (IEEE Computer Society, 2010), pp. 88–97. doi:10.1109/ICDM.2010.118 W. Chen, Y. Yuan, L. Zhang, Scalable influence maximization in social networks under the linear threshold model, in Proceeding ICDM’10 Proceedings of the 2010 IEEE International Conference on Data Mining (IEEE Computer Society, 2010), pp. 88–97. doi:10.​1109/​ICDM.​2010.​118
8.
go back to reference W. Chen, C. Wang, Y, Wang, Scalable influence maximization for prevalent viral marketing in large-scale social networks, in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (ACM, 2010), pp. 1029–1038. http://doi.acm.org/10.1145/1835804.1835934 W. Chen, C. Wang, Y, Wang, Scalable influence maximization for prevalent viral marketing in large-scale social networks, in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (ACM, 2010), pp. 1029–1038. http://​doi.​acm.​org/​10.​1145/​1835804.​1835934
10.
go back to reference O. Diekmann, J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases, Model Building, Analysis and Interpretation (Wiley, Chichester, 2000) O. Diekmann, J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases, Model Building, Analysis and Interpretation (Wiley, Chichester, 2000)
15.
go back to reference J. Kennedy, R. Mendes, Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Trans. Syst. Man Cybern. Part C: Appl. Rev. 36(4), 515–519 (2006). doi:10.1109/TSMCC.2006.875410 J. Kennedy, R. Mendes, Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Trans. Syst. Man Cybern. Part C: Appl. Rev. 36(4), 515–519 (2006). doi:10.​1109/​TSMCC.​2006.​875410
17.
go back to reference D. Kempe, J. Kleinberg, E. Tardos, Influential nodes in a diffusion model for social networks, in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP) (Springer, 2005), pp. 1127–1138. doi:10.1007/11523468_91 D. Kempe, J. Kleinberg, E. Tardos, Influential nodes in a diffusion model for social networks, in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP) (Springer, 2005), pp. 1127–1138. doi:10.​1007/​11523468_​91
18.
go back to reference M. Kimura, K. Saito, Tractable models for information diffusion in social networks, Knowledge Discovery in Databases, Lecture Notes in Computer Science (Springer, Berlin, 2006), pp. 259–271. doi:10.1007/11871637_27 M. Kimura, K. Saito, Tractable models for information diffusion in social networks, Knowledge Discovery in Databases, Lecture Notes in Computer Science (Springer, Berlin, 2006), pp. 259–271. doi:10.​1007/​11871637_​27
19.
go back to reference J. Leskovec, J. Kleinberg, C. Faloutsos, Graphs over time: densification laws, shrinking diameters and possible explanations, in Proceedings of the 1st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (ACM, 2005), pp. 177–187. http://doi.acm.org/10.1145/1081870.1081893 J. Leskovec, J. Kleinberg, C. Faloutsos, Graphs over time: densification laws, shrinking diameters and possible explanations, in Proceedings of the 1st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (ACM, 2005), pp. 177–187. http://​doi.​acm.​org/​10.​1145/​1081870.​1081893
Metadata
Title
Estimation of Edge Infection Probabilities in the Inverse Infection Problem
Authors
András Bóta
Miklós Krész
András Pluhár
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-21133-6_2

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