贝叶斯网等价类学习算法

贝叶斯网用一种紧凑的形式表示联合概率分布,具有完备的语义和坚实的理论基础,目前已成为人工智能领域处理不确定性问题的最佳方法之一。贝叶斯网学习是其关键问题,传统学习方法存在如下不足：（1）随节点数增多非法结构以指数级增加,影响学习效率;（2）在等价结构之间进行打分搜索,影响收敛速度;（3）假设每个结构具有相同的先验概率,造成等价类中包含结构越多则先验概率越高。本文提出一种学习马尔科夫等价类算法,该算法基于骨架空间进行状态转换,利用从骨架空间到等价类空间的映 映射关系实现学习贝叶斯网等价类。实验数据证明,该方法可有效缩小搜索空间规模,相对于在有向图空间搜索的算法加快了算法的收敛速度,提高了执行效率。     

一种混合的贝叶斯网结构学习算法

贝叶斯网是人工智能中一个重要的理论模型,也是现实世界中不确定性问题建模的重要工具.针对贝叶斯网的结构学习问题,提出了一种将约束满足、蚁群优化和模拟退火策略相结合的混合算法.新算法首先利用阈值自调整的条件测试来动态地压缩搜索空间,在加速搜索过程的同时保证学习的求解质量;然后在基于MDL的蚁群随机搜索中引入模拟退火的优化调节机制,改进了算法的优化效率.实验结果验证了所提策略的有效性,与最新的同类算法相比,新算法在保持较快收敛速度的前提下具有更好的求解质量.     

贝叶斯网学习算法模型及参数学习算法

1 引言近年来,贝叶斯网(又称随机信息网)作为处理人工智能中不确定性问题的建模工具受到学术界的广泛关注,并成功地应用在医学诊断、模式识别、故障诊断各个方面。作为一种有向图表示的建模方法,贝叶斯网由于其表达方式自然、紧凑,深受知识工程师喜受,已广泛地用于知识获取和表示。但是,利用专家知识构造贝叶斯网是一件烦琐的工作,特别是网络节点数很大时更是这样。因此,利用数据例子,通过学习自动生成贝叶斯网的方法日益受到重视,有一些学习     

学习信度网的结构

一、等价的信度网结构学习信度网的结构,就是通过分析实例数据库,建立能够表达实例数据所包含信息的信度网的结构。任何一个由所有的结点(变量)构成的有向无环图都可能作为信度网的结构。如对图1(d)所示的关于吸烟、性别及肺癌的实例数据库,其三种可能的信度网结构如图1     

基于演化序搜索的混合贝叶斯网络结构学习方法

贝叶斯网络是一种不确定性知识表示与推理的有效工具,学习其结构是利用这一工具进行推理的基础。现有的贝叶斯网络结构学习算法,在智能教育等应用场景中往往面临着难以权衡有效性与高效性的问题。一方面,评分搜索类方法能搜索到高质量的解,但面临着算法复杂度高的挑战。另一方面,混合类方法效率高,但所找到的解的质量不尽如人意。针对上述问题,提出了一种基于演化序搜索的混合贝叶斯网络结构学习方法(EvOS)。该方法首先通过约束类算法构建无向图骨架,然后利用演化算法搜索最优节点序,最后使用该节点序指导贪婪搜索得到贝叶斯网络结构。基于常用基准数据集以及教育知识结构发现任务,验证了所提方法的有效性与高效性。实验结果表明,所提方法相较于评分搜索类方法,能够在保持相仿精度的情况下最高加速百倍,且有效性显著高于混合类方法。     

基于结构继承的贝叶斯网结构学习优化设计

采用遗传算法建立贝叶斯网络的优化学习结构,一直是贝叶斯网络研究倍受关注的课题.传统遗传算法的个体设计存在需要反复进行无环性检验的问题,降低了进化效率.针对这个问题,提出一种新的个体编码方式.考虑到进化过程中家族得分的可继承性,提出基于家族继承的结构评分改进算法,进而设计相应的改进遗传算法.实验结果表明,改进算法在BN建网精度与效率上都得到明显提升.     

贝叶斯网络结构学习综述

贝叶斯网络是一种有效的不确定性知识表达和推理工具,在数据挖掘等领域得到了较好的应用,而结构学习是其重要研究内容之一.经过二十多年的发展,已经出现了一些比较成熟的贝叶斯网络结构学习算法,对迄今为止的贝叶斯网络结构学习方法进行了综述.现阶段获得的用于结构学习的观测数据都比较复杂,这些数据分为完备数据和不完备数据两种类型.针对完备数据,分别从基于依赖统计分析的方法、基于评分搜索的方法和混合搜索方法三个方面对已有的算法进行分析.对于不完备数据,给出了数据不完备情况下网络结构的学习框架.在此基础上归纳总结了贝叶斯网络结构学习各个方向的研究进展,给出了贝叶斯网络结构学习未来可能的研究方向.     

贝叶斯网络结构学习分析

贝叶斯网络结构学习(以下简称结构学习)的目标是寻找对先验知识和数据拟合得最好的网络结构。结构学习有两种方式,一种是模型选择,即选择一个最好的网络结构;另一种是选择性的模型平均,即选择合适数量的网络结构,以这些网络结构代表所有的网络结构。我们从限定的结构学习与非限定的结构学习两类     

贝叶斯网模型的学习、推理和应用

近年来在人工智能领域,不确定性问题一直成为人们关注和研究的焦点。贝叶斯网是用来表示不确定变量集合联合概率分布的图形模式,它反映了变量间潜在的依赖关系。使用贝叶斯网建模已成为解决许多不确定性问题的强有力工具。基于国内外最新的研究成果对贝叶斯网模型的学习、推理和应用情况进行了综述,并对未来的发展方向进行了展望。     

基于遗传禁忌算法的贝叶斯网边定向方法

针对贝叶斯网边定向过程中存在的问题,提出一种基于遗传禁忌算法的贝叶斯网边定向方法,该方法将禁忌搜索的＂多样化＂引入遗传算法的交叉算子和变异算子中,生成禁忌交叉算子和禁忌变异算子,并对航班离港延误骨架模型进行定向,仿真实验结果表明,该方法是有效可行的。     

基于Jaya的贝叶斯网络结构学习算法研究

基于评分搜索的贝叶斯网络结构学习算法通常需要调参,导致计算量增大且不当的参数易使算法陷入局部最优。针对这一问题,将无需调参的Jaya算法应用于贝叶斯网络结构学习。在Jaya算法的框架下,结合遗传算法的交叉变异思想重新设计了个体更新策略,使Jaya算法能够应用于结构学习这一离散优化问题,并结合马尔科夫链的相关理论讨论了所提算法的敛散性。实验结果表明,该算法能有效应用于贝叶斯网络结构学习。     

Parameter Learning in Object-Oriented Bayesian Networks

This paper describes a method for parameter learning in Object-Oriented Bayesian Networks (OOBNs). We propose a methodology for learning parameters in OOBNs, and prove that maintaining the object orientation imposed by the prior model will increase the learning speed in object-oriented domains. We also propose a method to efficiently estimate the probability parameters in domains that are not strictly object oriented. Finally, we attack type uncertainty, a special case of model uncertainty typical to object-oriented domains.     

一种基于随机抽样的贝叶斯网络结构学习算法

针对贝叶斯网络的结构学习问题,基于并行随机抽样的思想提出了结构学习算法PCMHS,构建多条并行的收敛于Boltzmann分布的马尔可夫链.首先基于节点之间的互信息,进行所有马尔可夫链的初始化,在其迭代过程中,基于并行的MHS抽样总体得到产生下一代个体的建议分布,并通过对网络中弧和子结构的抽样产生下一代个体.算法FCMHS收敛于平稳分布,具有良好的学习精度,而该算法又通过使其初始分布和建议分布近似于其平稳分布,有效提高了马尔可夫链的收敛速度.在标准数据集上的实验结果验证了算法PCMHS的学习效率和学习精度明显优于经典算法MHS和PopMCMC.     

基于小生境遗传算法的贝叶斯网络结构学习算法研究*

在数据缺失的情况下讨论一种贝叶斯网络的结构学习算法.该算法结合了小生境遗传算法和EM算法,最后通过试验说明了该算法的有效性.     

Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption of likelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—a prior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at most k = 1 parent. For the general case (k > 1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.     

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior landscape. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.     

The Sample Complexity of Learning Fixed-Structure Bayesian Networks

We consider the problem of PAC learning probabilistic networks in the case where the structure of the net is specified beforehand. We allow the conditional probabilities to be represented in any manner (as tables or specialized functions) and obtain sample complexity bounds for learning nets with and without hidden nodes.     

Learning Bayesian Network Classifiers: Searching in a Space of Partially Directed Acyclic Graphs

There is a commonly held opinion that the algorithms for learning unrestricted types of Bayesian networks, especially those based on the score+search paradigm, are not suitable for building competitive Bayesian network-based classifiers. Several specialized algorithms that carry out the search into different types of directed acyclic graph (DAG) topologies have since been developed, most of these being extensions (using augmenting arcs) or modifications of the Naive Bayes basic topology. In this paper, we present a new algorithm to induce classifiers based on Bayesian networks which obtains excellent results even when standard scoring functions are used. The method performs a simple local search in a space unlike unrestricted or augmented DAGs. Our search space consists of a type of partially directed acyclic graph (PDAG) which combines two concepts of DAG equivalence: classification equivalence and independence equivalence. The results of exhaustive experimentation indicate that the proposed method can compete with state-of-the-art algorithms for classification.Editors: Pedro Larrañaga, Jose A. Lozano, Jose M. Peña and Iñaki Inza