Abstract
Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related problem, that is, the problem of finding a set of sufficiently dissimilar, yet all plausible, explanations. Applications of this problem are, e.g., in search query results (you won’t want 10 results that all link to the same website) or in decision support systems. We show that the problem of finding a ‘good enough’ explanation that differs in structure from the best explanation is at least as hard as finding the best explanation itself.
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Notes
- 1.
An example of such a situation would be when \(m = 5\) and the solutions with binary encodings 000, 011, 101, 110, and 111 would be in \( optsol _{\mathcal {B}}^{1 \dots m}\), with \( optsol _{\mathcal {B}}= 000\).
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Kwisthout, J. (2019). Finding Dissimilar Explanations in Bayesian Networks: Complexity Results. In: Atzmueller, M., Duivesteijn, W. (eds) Artificial Intelligence. BNAIC 2018. Communications in Computer and Information Science, vol 1021. Springer, Cham. https://doi.org/10.1007/978-3-030-31978-6_6
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DOI: https://doi.org/10.1007/978-3-030-31978-6_6
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