Boolean Network (BN) and its extension Probabilistic Boolean Network (PBN) are popular mathematical models for studying genetic regulatory networks. BNs and PBNs are also applied to model manufacturing systems, financial risk and healthcare service systems. In this paper, we propose a novel Greedy Entry Removal (GER) algorithm for constructing sparse PBNs. We derive theoretical upper bounds for both existing algorithms and the GER algorithm. Furthermore, we are the first to study the lower bound problem of the construction of sparse PBNs, and to derive a series of related theoretical results. In our numerical experiments based on both synthetic and practical data, GER gives the best performance among state-of-the-art sparse PBN construction algorithms and outputs sparsest possible decompositions on most of the transition probability matrices being tested.

翻译：布尔网络（Boolean Network, BN）及其扩展形式概率布尔网络（Probabilistic Boolean Network, PBN）是研究基因调控网络的常用数学模型。BN与PBN亦被应用于建模制造系统、金融风险与医疗服务系统。本文提出一种新颖的贪心项移除（Greedy Entry Removal, GER）算法用于构建稀疏PBN。我们推导了现有算法及GER算法的理论上界。此外，我们首次研究了稀疏PBN构建的下界问题，并推导出一系列相关理论结果。在基于合成数据与实际数据的数值实验中，GER在现有先进稀疏PBN构建算法中表现最佳，并在大多数测试的转移概率矩阵上输出了可能的最稀疏分解。