Restricted Bayesian classification networks

Bayesian networks are graphical models that describe dependency relationships between variables, and are powerful tools for studying probability classifiers. At present, the causal Bayesian network learning method is used in constructing Bayesian network classifiers while the contribution of attribute to class is over-looked. In this paper, a Bayesian network specifically for classification-restricted Bayesian classification networks is proposed. Combining dependency analysis between variables, classification accuracy evaluation criteria and a search algorithm, a learning method for restricted Bayesian classification networks is presented. Experiments and analysis are done using data sets from UCI machine learning repository. The results show that the restricted Bayesian classification network is more accurate than other well-known classifiers.     

Distributed support vector machines

A truly distributed (as opposed to parallelized) support vector machine (SVM) algorithm is presented. Training data are assumed to come from the same distribution and are locally stored in a number of different locations with processing capabilities (nodes). In several examples, it has been found that a reasonably small amount of information is interchanged among nodes to obtain an SVM solution, which is better than that obtained when classifiers are trained only with the local data and comparable (although a little bit worse) to that of the centralized approach (obtained when all the training data are available at the same place). We propose and analyze two distributed schemes: a "na/spl inodot//spl uml/ve" distributed chunking approach, where raw data (support vectors) are communicated, and the more elaborated distributed semiparametric SVM, which aims at further reducing the total amount of information passed between nodes while providing a privacy-preserving mechanism for information sharing. We show the feasibility of our proposal by evaluating the performance of the algorithms in benchmarks with both synthetic and real-world datasets.     

Maximum margin Bayesian network classifiers

We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.     

Boosted Bayesian network classifiers

The use of Bayesian networks for classification problems has received a significant amount of recent attention. Although computationally efficient, the standard maximum likelihood learning method tends to be suboptimal due to the mismatch between its optimization criteria (data likelihood) and the actual goal of classification (label prediction accuracy). Recent approaches to optimizing classification performance during parameter or structure learning show promise, but lack the favorable computational properties of maximum likelihood learning. In this paper we present boosted Bayesian network classifiers, a framework to combine discriminative data-weighting with generative training of intermediate models. We show that boosted Bayesian network classifiers encompass the basic generative models in isolation, but improve their classification performance when the model structure is suboptimal. We also demonstrate that structure learning is beneficial in the construction of boosted Bayesian network classifiers. On a large suite of benchmark data-sets, this approach outperforms generative graphical models such as naive Bayes and TAN in classification accuracy. Boosted Bayesian network classifiers have comparable or better performance in comparison to other discriminatively trained graphical models including ELR and BNC. Furthermore, boosted Bayesian networks require significantly less training time than the ELR and BNC algorithms.     

Bayesian Network Classifiers

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state-of-the-art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.     

Bayesian network classifiers based on Gaussian kernel density

For learning a Bayesian network classifier, continuous attributes usually need to be discretized. But the discretization of continuous attributes may bring information missing, noise and less sensitivity to the changing of the attributes towards class variables. In this paper, we use the Gaussian kernel function with smoothing parameter to estimate the density of attributes. Bayesian network classifier with continuous attributes is established by the dependency extension of Naive Bayes classifiers. We also analyze the information provided to a class for each attributes as a basis for the dependency extension of Naive Bayes classifiers. Experimental studies on UCI data sets show that Bayesian network classifiers using Gaussian kernel function provide good classification accuracy comparing to other approaches when dealing with continuous attributes.     

一种基于多进化神经网络的分类方法

分类问题是目前数据挖掘和机器学习领域的重要内容.提出了一种基于多进化神经网络的分类方法CABEN(classification approach based on evolutionary neural networks).利用改进的进化策略和Levenberg-Marquardt方法对多个三层前馈神经网络同时进行训练.训练好各个分类模型以后,将待识别数据分别输入,最后根据绝对多数投票法决定最终分类结果.实验结果表明,该方法可以较好地进行数据分类,而且与传统的神经网络方法以及贝叶斯方法和决策树方法相比,在     

Graphical model construction based on evolutionary algorithms

1 Introduction Evolutionary algorithms(EAs) [1～5] are stochastic search and optimization techniques, which were inspired by the analogy of evolution and population genetics. They have been demonstrated to be effective and robust in searching very large, varied, spaces in a wide range of applications, including classification, machine learning, ecological, so- cial systems and so on. However, most of the common evo- lutionary algorithms using simple operators are incapable of learning the reg…     

具有丢失数据的贝叶斯网络结构学习研究

目前主要基于EM算法和打分-搜索方法进行具有丢失数据的贝叶斯网络结构学习,算法效率较低,而且易于陷入局部最优结构.针对这些问题,建立了一种新的具有丢失数据的贝叶斯网络结构学习方法.首先随机初始化未观察到的数据,得到完整的数据集,并利用完整数据集建立最大似然树作为初始贝叶斯网络结构,然后进行迭代学习.在每一次迭代中,结合贝叶斯网络结构和Gibbs sampling修正未观察到的数据,在新的完整数据集的基础上,基于变量之间的基本依赖关系和依赖分析思想调整贝叶斯网络结构,直到结构趋于稳定.该方法既解决了标准Gi     

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.     

Detection of surface defects on raw steel blocks using Bayesian network classifiers

This paper proposes an approach that detects surface defects with three-dimensional characteristics on scale-covered steel blocks. The surface reflection properties of the flawless surface changes strongly. Light sectioning is used to acquire the surface range data of the steel block. These sections are arbitrarily located within a range of a few millimeters due to vibrations of the steel block on the conveyor. After the recovery of the depth map, segments of the surface are classified according to a set of extracted features by means of Bayesian network classifiers. For establishing the structure of the Bayesian network, a floating search algorithm is applied, which achieves a good tradeoff between classification performance and computational efficiency for structure learning. This search algorithm enables conditional exclusions of previously added attributes and/or arcs from the network. The experiments show that the selective unrestricted Bayesian network classifier outperforms the naïve Bayes and the tree-augmented naïve Bayes decision rules concerning the classification rate. More than 98% of the surface segments have been classified correctly.     

用于风险管理的贝叶斯网络学习

结合专家知识和数据进行贝叶斯网络学习.首先利用专家知识建立初始贝叶斯网络结构和参数;然后基于变量之间基本依赖关系、基本结构和依赖分析方法,对初始贝叶斯网络结构进行修正和调整,得到新的贝叶斯网络结构;最后将由专家和数据确定的参数合成为新的参数,得到融合专家知识和数据的贝叶斯网络.该方法可避免现有的贝叶斯网络学习过于依赖数据、对数据的数量和质量要求过高等问题.     

Evolving a Bayesian Classifier for ECG-based Age Classification in Medical Applications

ObjectiveTo classify patients by age based upon information extracted from their electrocardiograms (ECGs). To develop and compare the performance of Bayesian classifiers.Methods and materialWe present a methodology for classifying patients according to statistical features extracted from their ECG signals using a genetically evolved Bayesian network classifier. Continuous signal feature variables are converted to a discrete symbolic form by thresholding, to lower the dimensionality of the signal. This simplifies calculation of conditional probability tables for the classifier, and makes the tables smaller. Two methods of network discovery from data were developed and compared: the first using a greedy hill-climb search and the second employed evolutionary computing using a genetic algorithm (GA).Results and conclusionsThe evolved Bayesian network performed better (86.25% AUC) than both the one developed using the greedy algorithm (65% AUC) and the naïve Bayesian classifier (84.75% AUC). The methodology for evolving the Bayesian classifier can be used to evolve Bayesian networks in general thereby identifying the dependencies among the variables of interest. Those dependencies are assumed to be non-existent by naïve Bayesian classifiers. Such a classifier can then be used for medical applications for diagnosis and prediction purposes.     

基于结点排序的贝叶斯网络结构学习

给出了变量之间k阶分类能力的概念及计算方法,并证明了k阶分类能力就是k阶分类正确率,以及k阶分类能力和条件独立性的等价性,在此基础上构造出基于分类能力的贝叶斯网络结构打分函数,同时结合依赖分析方法和打分-搜索方法建立了有效的贝叶斯网络结构学习方法,实验结果显示该方法能够有效地进行贝叶斯网络结构学习,并使学习得到的结构倾向于简单化。     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

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.     

一种基于决策图贝叶斯网络的强度Pareto进化算法

提出了一种基于决策图贝叶斯网络的强度Pareto进化算法,该算法把贝叶斯概率模型结合到多目标进化算法中,通过构造和学习网络来替代传统进化算法中的交叉重组和变异等遗传操作,避免对大量参数的人工设置和重要构造块的破坏．求解多目标背包问题的仿真结果表明,所提算法可以快速收敛到较好的Pareto前沿,有很强的鲁棒性．     

基于条件互信息和概率突跳机制的贝叶斯网络结构学习算法

贝叶斯网络分类器的精确构造是NP难问题,使用K2算法可以有效地缩减搜索空间,提高学习效率。然而K2算法需要初始的节点次序作为输入,这在缺少先验信息的情况下很难确定;另一方面,K2算法采用贪婪的搜索策略,容易陷入局部最优解。提出了一种基于条件互信息和概率突跳机制的贝叶斯网络结构学习算法(CMI-PK2算法),该算法首先利用条件互信息生成有效的节点次序作为K2算法的输入,然后利用概率突跳机制改进K2算法的搜索过程来提高算法的全局寻优能力,学习较为理想的网络结构。在两个基准网络Asia和Alarm上进行了实验验证,结果表明CMI-PK2算法具有更高的分类精度和数据拟合程度。     

EBNO: Evolution of cost-sensitive Bayesian networks

The last decade has seen an increase in the attention paid to the development of cost-sensitive learning algorithms that aim to minimize misclassification costs while still maintaining accuracy. Most of this attention has been on cost-sensitive decision tree learning, whereas relatively little attention has been paid to assess if it is possible to develop better cost-sensitive classifiers based on Bayesian networks. Hence, this paper presents EBNO, an algorithm that utilizes Genetic algorithms to learn cost-sensitive Bayesian networks, where genes are utilized to represent the links between the nodes in Bayesian networks and the expected cost is used as a fitness function. An empirical comparison of the new algorithm has been carried out with respect to (a) an algorithm that induces cost-insensitive Bayesian networks to provide a base line, (b) ICET, a well-known algorithm that uses Genetic algorithms to induce cost-sensitive decision trees, (c) use of MetaCost to induce cost-sensitive Bayesian networks via bagging (d) use of AdaBoost to induce cost-sensitive Bayesian networks, and (e) use of XGBoost, a gradient boosting algorithm, to induce cost-sensitive decision trees. An empirical evaluation on 28 data sets reveals that EBNO performs well in comparison with the algorithms that produce single interpretable models and performs just as well as algorithms that use bagging and boosting methods.     

Structure learning of Bayesian networks by genetic algorithms: aperformance analysis of control parameters

We present a new approach to structure learning in the field of Bayesian networks. We tackle the problem of the search for the best Bayesian network structure, given a database of cases, using the genetic algorithm philosophy for searching among alternative structures. We start by assuming an ordering between the nodes of the network structures. This assumption is necessary to guarantee that the networks that are created by the genetic algorithms are legal Bayesian network structures. Next, we release the ordering assumption by using a “repair operator” which converts illegal structures into legal ones. We present empirical results and analyze them statistically. The best results are obtained with an elitist genetic algorithm that contains a local optimizer