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A search problem in complex diagnostic Bayesian networks
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DOI：10.1016/j.knosys.2011.12.011.png)
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Abstract
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Inference in Bayesian networks (BNs) is NP-hard. We proposed the concept of a node set namely Maximum Quadruple-Constrained subset MQC(A,a - e) to improve the efficiency of exact inference in diagnostic Bayesian networks (DBNs). Here, A denotes a node set in a DBN and a - e represent five real numbers. The improvement in efficiency is achieved by computation sharing. That is, we divide inference in a DBN into the computation of eliminating MQC(A, a - e) and the subsequent computation. For certain complex DBNs and (A, a - e), the former computation covers a major part of the whole computation, and the latter one is highly efficient after sharing the former computation. Searching for MQC(A, a - e) is a combinatorial optimization problem. A backtracking-based exact algorithm Backtracking-Search (BS) was proposed, however the time complexity of BS is O(n(3)2(n)) (n = vertical bar A vertical bar). In this article, we propose the following algorithms for searching for MQC(A, a - e) especially in complex DBNs where vertical bar A vertical bar is large. (i) A divide-and-conquer algorithm Divide-and-Conquer (DC) for dividing the problem of searching for MQC(A, a - e) into sub-problems of searching for MQC(B-1, a - e), ...,MQC(B-m, a - e), where B-i subset of A(1 <= i m, 1 <= m <= vertical bar A vertical bar). (ii) A DC-based heuristic algorithm Heuristic-Search (HS) for searching for MQC(B-i, a - e). The time complexity of HS is O(n(6)) (n = vertical bar B-i vertical bar). Empirical results show that, HS outperforms BS over a range of networks.(C) 2011 Elsevier B.V. All rights reserved.
Keywords:
Diagnostic Bayesian networks
Exact inference
Computation sharing
Inference simplifying
Search
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