混合高斯贝叶斯网络的推理

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摘要翻译：
本文的主要目的是描述一般混合贝叶斯网络（具有离散和连续机会变量的混合）的精确推理方法。我们的方法由混合高斯(MoG)BNS逼近一般混合贝叶斯网络组成。在MoG贝叶斯网络中，存在一种由Lauritzen-Jensen(LJ)提出的快速算法，用于精确推理，并有一个商业实现。然而，该算法只能用于MoG BNS。这类网络的一些限制如下。所有连续的机会变量必须具有条件线性高斯分布，离散的机会节点不能有连续的父节点。本文所描述的方法将使我们能够将LJ算法用于更大类的混合贝叶斯网络。这包括具有非高斯分布的连续机会节点的网络、对离散变量和连续变量拓扑结构没有限制的网络、具有条件确定性变量的网络、具有条件确定性变量的网络和具有条件确定性变量的网络。
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英文标题：
《Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians》
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作者：
Prakash P. Shenoy
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
--

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英文摘要：
  The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG Bayesian networks, and there exists a commercial implementation of this algorithm. However, this algorithm can only be used for MoG BNs. Some limitations of such networks are as follows. All continuous chance variables must have conditional linear Gaussian distributions, and discrete chance nodes cannot have continuous parents. The methods described in this paper will enable us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This includes networks with continuous chance nodes with non-Gaussian distributions, networks with no restrictions on the topology of discrete and continuous variables, networks with conditionally deterministic variables that are a nonlinear function of their continuous parents, and networks with continuous chance variables whose variances are functions of their parents.
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PDF链接：
https://arxiv.org/pdf/1206.6877

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关键词：贝叶斯网络 贝叶斯网 贝叶斯 distribution Restrictions 离散 MoG 节点 贝叶斯 商业