嵌入式贝叶斯网络是否代表概率模型的检验
On Testing Whether an Embedded Bayesian Network Represents a Probability Model
摘要：
测试包含不可测（隐藏）变量的概率模型的有效性被证明是一项艰巨的任务。我们证明了，测试模型是否与手头的数据在结构上不兼容的任务，需要指数数量的独立性评估，每个评估的形式是：“X有条件地独立于Y，给定Z。相比之下，测试标准贝叶斯网络需要线性数量的此类评估（每个顶点一个）。在积极的一面，我们表明，如果一个网络的隐变量G有一个树骨架，检查G是否代表一个给定的概率模型P需要多项式的独立性评估。此外，我们提供了一种算法，有效地构建一个树结构的贝叶斯网络（隐变量），代表P，如果这样的网络存在，并进一步认识到，当这样的网络不存在。
英文摘要：
Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential number of independence evaluations, each of the form: "X is conditionally independent of Y, given Z." In contrast, a linear number of such evaluations is required to test a standard Bayesian network (one per vertex). On the positive side, we show that if a network with hidden variables G has a tree skeleton, checking whether G represents a given probability model P requires the polynomial number of such independence evaluations. Moreover, we provide an algorithm that efficiently constructs a tree-structured Bayesian network (with hidden variables) that represents P if such a network exists, and further recognizes when such a network does not exist.
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