Dynamic bayesian networks: representation, inference and learning
Dynamic bayesian networks: representation, inference and learning
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发表时间：
2002
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通讯作者：
Kevin P. Murphy;Stuart J. Russell
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作者：
Kevin P. Murphy;Stuart J. Russell
动态贝叶斯网络：表示、推理和学习Kevin帕特里克墨菲计算机科学哲学博士加州大学伯克利分校教授Stuart Russell，主席建模序列数据在科学和工程的许多领域都很重要。隐马尔可夫模型（Hidden Markov Models，简称HMF）和卡尔曼滤波模型（Kalman Filter Models，简称KFM）是一种简单而灵活的模型。例如，HMF已被用于语音识别和生物序列分析，KFM已被用于从跟踪飞机和导弹到预测经济的问题。然而，障碍和KFM在其“表达能力”方面是有限的。动态贝叶斯网络（DBN）通过允许状态空间以因子形式表示，而不是作为单个离散随机变量来推广Hyndrome。DBN通过允许任意概率分布而不仅仅是（单峰）线性高斯分布来推广KFM。在这篇论文中，我将讨论如何用DBN来表示各种不同类型的模型，如何在DBN中执行精确和近似推理，以及如何从序列数据中学习DBN模型。本文的主要创新之处在于：提出了一种用DBN表示层次HNN的方法，使得推理时间由O（T）缩短为O（T），其中T是序列的长度;提出了一种精确的平滑算法，其时间复杂度由O（T）缩短为O（log T）;提出了一种简单的使用联合树算法进行DBN在线推理的方法;提出了一种新的DBN精确在线推理的复杂度界限;一种新的确定性近似推理算法，称为因子边界;分析了BK算法和循环置信传播之间的关系;将Rao-Blackwellised粒子滤波应用于DBN的方法，以及SLAM（同时定位和映射）问题;将结构EM算法扩展到DBN的方式;以及DBN的各种不同应用。然而，也许这篇论文的主要价值在于它对序列数据建模领域的全面介绍。
Dynamic Bayesian Networks: Representation, Inference and Learning by Kevin Patrick Murphy Doctor of Philosophy in Computer Science University of California, Berkeley Professor Stuart Russell, Chair Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T ) time instead of O(T ), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T ) space instead of O(T ); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.