可分离贝叶斯网络的线性代数方法
Linear Algebra Approach to Separable Bayesian Networks
摘要：
可分离贝叶斯网络（英语：Separable Bayesian Networks），或称影响模型，是一种动态贝叶斯网络，其中条件概率分布可以被分离成仅是节点邻居的边缘分布的函数，而不是联合分布。在建模方面，可分离网络可以显着降低复杂性，因为状态空间在网络变量数量上仅是线性的，而典型的状态空间是指数的。本文用线性代数的方法描述了任意条件概率表（CPT）与可分系统之间的关系。给出了充分性与可分性等价性的另一种证明。我们提出了一个计算方法来测试是否一个给定的CPT是可分离的。
英文摘要：
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the joint distributions. In terms of modeling, separable networks has rendered possible siginificant reduction in complexity, as the state space is only linear in the number of variables on the network, in contrast to a typical state space which is exponential. In this work, We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an alternate proof on the equivalence of sufficiency and separability. We present a computational method for testing whether a given CPT is separable.
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