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VE dimension induced by Bayesian networks over the boolean domain

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Abstract

In this paper, we focus on the concept classes \({\mathcal {C}}_{{\mathcal{N}}}\) induced by Bayesian networks. The relationship between two-dimensional values induced by these concept classes is studied, one of which is the VC-dimension of the concept class \({\mathcal {C}}_{\cal {N}},\) denoted as \(VCdim({\mathcal {N}}), \) and other is the smallest dimensional of Euclidean spaces into which \({\mathcal {C}}_{{\mathcal {N}}}\) can be embedded, denoted as \(Edim({\mathcal {N}}). \) As a main result, we show that the two-dimensional values are equal for the Bayesian networks with n ≤ 4 variables, called the VE-dimension for that Bayesian networks.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (61075055). We would like to thank the anonymous reviewers for their valuable comments and suggestions.

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  1. Department of Mathematics, Xidian University, Xi’an, 710071, People’s Republic of China

    Youlong Yang & Yan Wu

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  1. Youlong Yang
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  2. Yan Wu
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Correspondence to Youlong Yang.

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Yang, Y., Wu, Y. VE dimension induced by Bayesian networks over the boolean domain. Pattern Anal Applic 17, 799–807 (2014). https://doi.org/10.1007/s10044-013-0320-3

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