贝叶斯网络的混合逼近
Mixture Approximations to Bayesian Networks
摘要：
贝叶斯网络中的结构和参数唯一地指定了建模域的概率分布。结构和概率信息的局部性是贝叶斯网络的最大优点，并且要求建模者仅指定局部信息。另一方面，这种信息的局部性可能会阻止建模者（甚至其他任何人）获得域中重要关系的总体概述。本文提出的工作的目标是提供一个“替代”的观点编码的贝叶斯网络的知识，这可能有时是非常有帮助的，提供深入了解的基础域。基本思想是计算贝叶斯网络表示的概率分布的混合近似。混合物组分密度可以被认为是代表贝叶斯模型所暗示的典型场景，提供关于基本关系的直觉。作为一个额外的好处，在近似模型中执行推理非常简单和直观，并且可以提供额外的见解。混合近似计算的计算复杂性主要取决于定义由贝叶斯网络表示的概率分布与近似分布之间的距离的度量。KL-发散和后向KL-发散都会导致算法效率低下。顺便说一句，后者是用在最近的工作混合物的平均场的解决方案，这里提出的工作是密切相关的。然而，我们表明，使用均方误差成本函数导致更新方程，可以使用连接树算法来解决。我们的结论是，均方误差成本函数可以用于贝叶斯网络中的推理的连接树的基础上是听话的。然而，对于大型网络，人们可能不得不依赖平均场近似。
英文摘要：
Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the modeler to only specify local information. On the other hand this locality of information might prevent the modeler - and even more any other person - from obtaining a general overview of the important relationships within the domain. The goal of the work presented in this paper is to provide an "alternative" view on the knowledge encoded in a Bayesian network which might sometimes be very helpful for providing insights into the underlying domain. The basic idea is to calculate a mixture approximation to the probability distribution represented by the Bayesian network. The mixture component densities can be thought of as representing typical scenarios implied by the Bayesian model, providing intuition about the basic relationships. As an additional benefit, performing inference in the approximate model is very simple and intuitive and can provide additional insights. The computational complexity for the calculation of the mixture approximations criticaly depends on the measure which defines the distance between the probability distribution represented by the Bayesian network and the approximate distribution. Both the KL-divergence and the backward KL-divergence lead to inefficient algorithms. Incidentally, the latter is used in recent work on mixtures of mean field solutions to which the work presented here is closely related. We show, however, that using a mean squared error cost function leads to update equations which can be solved using the junction tree algorithm. We conclude that the mean squared error cost function can be used for Bayesian networks in which inference based on the junction tree is tractable. For large networks, however, one may have to rely on mean field approximations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
