具有隐藏变量的贝叶斯网络结构学习

目前,学习具有隐藏变量的贝叶斯网络结构主要采用结合EM算法的打分-搜索方法,其效率和可靠性低.本文针对此问题建立一种新的具有隐藏变量贝叶斯网络结构学习方法.该方法首先依据变量之间基本依赖关系、基本结构和依赖分析思想进行不考虑隐藏变量的贝叶斯网络结构学习,然后利用贝叶斯网络道德图中的Cliques发现隐藏变量的位置,最后基于依赖结构、Gibbs sampling和MDL标准确定隐藏变量的取值、维数和局部结构.该方法能够避免标准Gibbs sampling的指数复杂性问题和现有学习方法存在的主要问题.实验结果表明,该方法能够有效进行具有隐藏变量的贝叶斯网络结构学习.     

马尔科夫网络中的隐藏变量学习

吗尔科夫网络中的隐藏变量学习是一个重要而困难的研究课题．关于隐藏变量需要解决三个问题，它们是隐藏变量的位置，维数和取值，局部结构．根据马尔科夫网络中的Clique确定隐藏变量的位置；然后基于依赖结构和Gibbs sampling确定隐藏变量的取值和维数；最后利用MDL标准进行局部打分确定局部结构．试验结果表明，该方法能够有效地进行马尔科夫网络的隐藏变量学习．     

用于因果分析的混合贝叶斯网络结构学习

目前主要结合扩展的熵离散化方法和打分一搜索方法进行混合贝叶斯网络结构学习，算法效率和可靠性低，而且易于陷入局部最优结构。针对问题建立了一种新的混合贝叶斯网络结构迭代学习方法．在迭代中，基于父结点结构和Gibbs sampling进行混合数据聚类，实现对连续变量的离散化，再结合贝叶斯网络结构优化调整，使贝叶斯网络结构序列逐渐趋于稳定，可避免使用扩展的熵离散化和打分——搜索所带来的主要问题．     

基于推理信息量的BN参数学习变量离散化方法

提出推理信息量的概念,将其作为贝叶斯网络连续变量离散化评价标准。在连续变量离散化的过程中,采用遗传算法寻求最优解,设计个体编码方式、交叉算子和变异算子,将推理信息量作为衡量个体适应度的标准。实例分析证明,通过该方法对变量进行离散化后学习得到的贝叶斯网络在推理时能得到更大的推理信息量。     

基于局部解释能力的贝叶斯网络隐藏变量学习

目前,在贝叶斯网络中插入隐藏变量的主要目的是简化贝叶斯网络结构,从而提高推理效率,但隐藏变量使用不当会降低推理的可靠性.本文以提高贝叶斯网络的局部最优解释推理能力为标准插入隐藏变量,并将最优解释、星形结构和Gibbs抽样相结合来确定隐藏变量的位置、取值和维数,因此,通过隐藏变量的引入,在能够提高推理效率的同时,还可改进推理的可靠性.     

基于遗传算法的Bayesian网中连续变量离散化的研究

文中如何从含有离散变量和连续变量的混合数据中学习Bayesian网进行了研究，提出了一种基于遗传算法的连续变量散化算法，在该处中给出了兼顾离散模型准确度和复杂度的适应度函数；并基于对离散化的实质性分析，定义了离散策略等价的概念，由此制定了离散策略的编码方案；进一步设计了变换离散策略的遗传算法。算法不存在局部极值问题，且不需要事先给定变量序关系，模拟实验结果表明，该算法能有效地对连续变量散化，从而使得从混合数据中学到的Bayesian网具有较好性能。     

扩展的树增强朴素贝叶斯分类器

树增强朴素贝叶斯分类器继承了朴素贝叶斯分类器计算简单和鲁棒性的特点,同时分类性能常常优于朴素贝叶斯分类器,然而在有连续变量的情况下要求必须进行预离散化.为了更好地表达数据的分布,减少信息损失,有必要考虑混合数据的情况.本文推导混合数据的极大似然函数,提出扩展的树增强朴素贝叶斯分类器,突破必须对连续变量进行预离散化的限制,能够在树增强朴素贝叶斯分类器的框架内处理混合变量的情况.实验测试证明其具有良好的分类精度.     

贝叶斯网参数学习中连续变量离散化方法研究

连续变量离散化是贝叶斯网络参数学习中面临的一个重要问题,它的好坏将直接影响到贝叶斯网络的推理效果。目前缺少一种有效的手段用于评价连续变量离散化的好坏,通过研究,提出了推理信息量的概念,并采用作为衡量连续变量离散化好坏的标准。在连续变量离散化的过程中,采用遗传算法通过迭代的方式寻求最优解,其中,推理信息量作为衡量个体适应度的标准。实例分析证明,推理信息量大的推理效果好要优于推理信息量小的推理效果。     

因果图向信度网转化的方法研究

在因果图理论中，采用了图形化和直接因果强度来表达知识和因果关系，它克服了贝叶斯网的一些不足，已经发展成了一个能够处理离散变量和连续变量的混合模型。但已有的因果图的推理算法还不能完全适应实际问题的需要，这大大地限制了因果图推广和使用，然而信度网研究已比较成熟，已有许多现成的算法和实用的推理软件。文中给出了从因果图向信度网转化的一般方法，包括因果图的连接强度向信度网的条件概率表转化和因果图的结构向信度网的结构转化，从而可以利用信度网的这些成果。     

混合多元回归学习模型的改进

研究统计方法分析问题,针对在实际应用外特性模型的输入普遍为混合变量,既包括连续随机变量,也包括离散随机变量.目前已有混合多元回归学习模型大多只处理连续随机变量,且有着多重共线性的缺陷.针对上述问题,研究了基于贝叶斯网络的回归树学习模型.基于贝叶斯网络的回归树学习模型的研究方法建立在朴素贝叶斯网络模型基础上,采用分而治之的原则构造决策树,以朴素贝叶斯取代叶节点.在2个UCI机器学习数据集上的仿真实验结果表明模型性能良好.基于贝叶斯网络的回归树学习模型可以有效减小预测误差.     

Hierarchical hybrid fuzzy-neural networks for approximation with mixed input variables

Real-world systems usually involve both continuous and discrete input variables. However, in existing learning algorithms of both neural networks and fuzzy systems, these mixed variables are usually treated as continuous without taking into account the special features of discrete variables. It is inefficient to represent each discrete input variable having only a few fixed values by one input neuron with full connection to the hidden layer. This paper proposes a novel hierarchical hybrid fuzzy neural network to represent systems with mixed input variables. The proposed model consists of two levels: the lower level are fuzzy sub-systems each of which aggregates several discrete input variables into an intermediate variable as its output; the higher level is a neural network whose input variables consist of continuous input variables and intermediate variables. For systems or function approximations with mixed variables, it is shown that the proposed hierarchical hybrid fuzzy neural networks outperform standard neural networks in accuracy with fewer parameters, and both provide greater transparency and preserve the universal approximation property (i.e., they can approximate any function with mixed input variables to any degree of accuracy).     

基于预测能力的连续贝叶斯网络结构学习

通过对连续随机变量之间预测能力及其计算方法的讨论,提出基于预测能力的连续贝叶斯网络结构学习方法。该方法包括两个步骤,每个步骤都伴随环路检验。首先建立初始贝叶斯网络结构,其次调整初始贝叶斯网络结构,包括增加丢失的弧、删除多余的弧及调整弧的方向,并使用模拟数据进行了对比实验,结果表明该方法非常有致。     

基于人工鱼群算法的贝叶斯网络参数学习方法

研究算法改进,提高计算性能,贝叶斯网络是解决不确定性问题的一种有效方法,在很多领域得到了广泛应用。参数学习是贝叶斯网络构建的重要环节,但含隐变量、连续变量的参数学习是非常困难的。为解决上述问题,提出了一种人工鱼群算法的贝叶斯网络参数学习方法,并进一步通过调整人工鱼随机移动速度的方法提高了算法的收敛性能和速度。最后,将参数学习方法在由Noisy-Or和Noisy-And节点组成的贝叶斯网络中进行了仿真,仿真结果表明了参数学习方法,特别是改进后方法的可行性和优越性。     

Upper bound for variational free energy of Bayesian networks

In recent years, variational Bayesian learning has been used as an approximation of Bayesian learning. In spite of the computational tractability and good generalization in many applications, its statistical properties have yet to be clarified. In this paper, we focus on variational Bayesian learning of Bayesian networks which are widely used in information processing and uncertain artificial intelligence. We derive upper bounds for asymptotic variational free energy or stochastic complexities of bipartite Bayesian networks with discrete hidden variables. Our result theoretically supports the effectiveness of variational Bayesian learning as an approximation of Bayesian learning.     

Model gene network by semi-fixed Bayesian network

Gene networks describe functional pathways in a given cell or tissue, representing processes such as metabolism, gene expression regulation, and protein or RNA transport. Thus, learning gene network is a crucial problem in the post genome era. Most existing works learn gene networks by assuming one gene provokes the expression of another gene directly leading to an over-simplified model. In this paper, we show that the gene regulation is a complex problem with many hidden variables. We propose a semi-fixed model to represent the gene network as a Bayesian network with hidden variables. In addition, an effective algorithm based on semi-fixed structure learning is proposed to learn the model. Experimental results and comparison with the-state-of-the-art learning algorithms on artificial and real-life datasets confirm the effectiveness of our approach.     

A heuristic method for learning Bayesian networks using discrete particle swarm optimization

Bayesian networks are a powerful approach for representing and reasoning under conditions of uncertainty. Many researchers aim to find good algorithms for learning Bayesian networks from data. And the heuristic search algorithm is one of the most effective algorithms. Because the number of possible structures grows exponentially with the number of variables, learning the model structure from data by considering all possible structures exhaustively is infeasible. PSO (particle swarm optimization), a powerful optimal heuristic search algorithm, has been applied in various fields. Unfortunately, the classical PSO algorithm only operates in continuous and real-valued space, and the problem of Bayesian networks learning is in discrete space. In this paper, two modifications of updating rules for velocity and position are introduced and a Bayesian networks learning based on binary PSO is proposed. Experimental results show that it is more efficient because only fewer generations are needed to obtain optimal Bayesian networks structures. In the comparison, this method outperforms other heuristic methods such as GA (genetic algorithm) and classical binary PSO.     

A Bayesian method for learning belief networks that contain hidden variables

This paper presents a Bayesian method for computing the probability of a Bayesian belief-network structure from a database. In particular, the paper focuses on computing the probability of a belief-network structure that contains a hidden (latent) variable. A hidden variable represents a postulated entity that has not been directly measured. After reviewing related techniques, which previously were reported, this paper presents a new, more efficient method for handling hidden variables in belief networks.