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Local structure learning of chain graphs with the false discovery rate control

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Abstract

Chain graphs (CGs) containing both directed and undirected edges, offer an elegant generalisation of both Markov networks and Bayesian networks. In this paper, we propose an algorithm for local structure learning of CGs. It works by first learning adjacent nodes of each variable for skeleton identification and then orienting the edges of the complexes of the graph. To control the false discovery rate (FDR) of edges when learning a CG, FDR controlling procedure is embedded in the algorithm. Algorithms for skeleton identification and complexes recovery are presented. Experimental results demonstrate that the algorithm with the FDR controlling procedure can control the false discovery rate of the skeleton of the recovered graph under a user-specified level, and the proposed algorithm is also a viable alternative to learn the structure of chain graphs.

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Acknowledgements

The research is supported by the National Natural Science Foundation of China (Grant No. 61373174) and (Grant No. 11401454).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi Province, China

    Jingyun Wang, Sanyang Liu & Mingmin Zhu

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  1. Jingyun Wang
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  2. Sanyang Liu
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  3. Mingmin Zhu
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Correspondence to Sanyang Liu.

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Wang, J., Liu, S. & Zhu, M. Local structure learning of chain graphs with the false discovery rate control. Artif Intell Rev 52, 293–321 (2019). https://doi.org/10.1007/s10462-018-9669-4

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