Not So Naive Bayes: Aggregating One-Dependence Estimators

Of numerous proposals to improve the accuracy of naive Bayes by weakening its attribute independence assumption, both LBR and Super-Parent TAN have demonstrated remarkable error performance. However, both techniques obtain this outcome at a considerable computational cost. We present a new approach to weakening the attribute independence assumption by averaging all of a constrained class of classifiers. In extensive experiments this technique delivers comparable prediction accuracy to LBR and Super-Parent TAN with substantially improved computational efficiency at test time relative to the former and at training time relative to the latter. The new algorithm is shown to have low variance and is suited to incremental learning.     

Technical Note: Naive Bayes for Regression

Despite its simplicity, the naive Bayes learning scheme performs well on most classification tasks, and is often significantly more accurate than more sophisticated methods. Although the probability estimates that it produces can be inaccurate, it often assigns maximum probability to the correct class. This suggests that its good performance might be restricted to situations where the output is categorical. It is therefore interesting to see how it performs in domains where the predicted value is numeric, because in this case, predictions are more sensitive to inaccurate probability estimates.This paper shows how to apply the naive Bayes methodology to numeric prediction (i.e., regression) tasks by modeling the probability distribution of the target value with kernel density estimators, and compares it to linear regression, locally weighted linear regression, and a method that produces model trees—decision trees with linear regression functions at the leaves. Although we exhibit an artificial dataset for which naive Bayes is the method of choice, on real-world datasets it is almost uniformly worse than locally weighted linear regression and model trees. The comparison with linear regression depends on the error measure: for one measure naive Bayes performs similarly, while for another it is worse. We also show that standard naive Bayes applied to regression problems by discretizing the target value performs similarly badly. We then present empirical evidence that isolates naive Bayes' independence assumption as the culprit for its poor performance in the regression setting. These results indicate that the simplistic statistical assumption that naive Bayes makes is indeed more restrictive for regression than for classification.     

Learning Bayesian classifiers from positive and unlabeled examples

The positive unlabeled learning term refers to the binary classification problem in the absence of negative examples. When only positive and unlabeled instances are available, semi-supervised classification algorithms cannot be directly applied, and thus new algorithms are required. One of these positive unlabeled learning algorithms is the positive naive Bayes (PNB), which is an adaptation of the naive Bayes induction algorithm that does not require negative instances. In this work we propose two ways of enhancing this algorithm. On one hand, we have taken the concept behind PNB one step further, proposing a procedure to build more complex Bayesian classifiers in the absence of negative instances. We present a new algorithm (named positive tree augmented naive Bayes, PTAN) to obtain tree augmented naive Bayes models in the positive unlabeled domain. On the other hand, we propose a new Bayesian approach to deal with the a priori probability of the positive class that models the uncertainty over this parameter by means of a Beta distribution. This approach is applied to both PNB and PTAN, resulting in two new algorithms. The four algorithms are empirically compared in positive unlabeled learning problems based on real and synthetic databases. The results obtained in these comparisons suggest that, when the predicting variables are not conditionally independent given the class, the extension of PNB to more complex networks increases the classification performance. They also show that our Bayesian approach to the a priori probability of the positive class can improve the results obtained by PNB and PTAN.     

一种限定性的双层贝叶斯分类模型

朴素贝叶斯分类模型是一种简单而有效的分类方法,但它的属性独立性假设使其无法表达属性变量间存在的依赖关系,影响了它的分类性能.通过分析贝叶斯分类模型的分类原则以及贝叶斯定理的变异形式,提出了一种基于贝叶斯定理的新的分类模型DLBAN(double-level Bayesian network augmented naive Bayes).该模型通过选择关键属性建立属性之间的依赖关系.将该分类方法与朴素贝叶斯分类器和TAN(tree augmented naive Bayes)分类器进行实验比较.实验结果表明,在大多数数据集上,DLBAN分类方法具有较高的分类正确率.     

基于朴素Bayes组合的简易集成分类器

朴素Bayes分类器是一种简单有效的机器学习工具.本文用朴素Bayes分类器的原理推导出"朴素Bayes组合"公式,并构造相应的分类器.经过测试,该分类器有较好的分类性能和实用性,克服了朴素Bayes分类器精确度差的缺点,并且比其他分类器更加快速而不会显著丧失精确度.     

Some Effective Techniques for Naive Bayes Text Classification

While naive Bayes is quite effective in various data mining tasks, it shows a disappointing result in the automatic text classification problem. Based on the observation of naive Bayes for the natural language text, we found a serious problem in the parameter estimation process, which causes poor results in text classification domain. In this paper, we propose two empirical heuristics: per-document text normalization and feature weighting method. While these are somewhat ad hoc methods, our proposed naive Bayes text classifier performs very well in the standard benchmark collections, competing with state-of-the-art text classifiers based on a highly complex learning method such as SVM     

基于Naive Bayes的CLIF-NB 文本分类学习方法

针对Naive Bayes方法中条件独立性假设常常与实际相违背的情况，提出了CLIF_NB文本分类学习方法，利用互信息理论，计算特征属性之间的最大相关性概率，用变量集组合替代线性不可分属性，改善条件独立性假设的限制，并通过学习一系列分类器，缩小训练集中的分类错误，综合得出分类准确率较高的CLIF_NB分类器．     

基于Rough Set的加权朴素贝叶斯分类算法

朴素贝叶斯算法是一种简单而高效的分类算法,但其条件独立性假设并不符合客观实际,这在某种程度上影响了它的分类性能。加权朴素贝叶斯是对它的一种扩展。基于Rough Set的属性重要性理论,提出了基于Rough Set的加权朴素贝叶斯分类方法,并分别从代数观、信息观及综合代数观和信息观的角度给出了属性权值的求解方法。通过在UCI数据集上的仿真实验,验证了该方法的有效性。     

一种基于强属性限定的贝叶斯分类模型

朴素贝叶斯分类模型一种简单而高效的分类模型,但它的条件独立性假设使其无法将属性间的依赖表达出来,影响了它分类的正确率。属性间的依赖关系与属性本身的特性有关,有些属性的特性决定了其他属性必然依赖于它,即强属性。文中通过分析属性相关性的度量和贝叶斯定理的变形公式,介绍了强属性的选择方法,通过在强弱属性之间添加增强弧以弱化朴素贝叶斯的独立性假设,扩展了朴素贝叶斯分类模型的结构。在此基础上提出一种基于强属性限定的贝叶斯分类模型SANBC。实验结果表明,与朴素贝叶斯分类模型相比,SANBC分类模型具有较高的分类正确率。     

分布式朴素贝叶斯算法在文本分类中的应用

传统串行贝叶斯算法在对大规模数据进行分类时,性能较低下.为此,在TFIDF(词频-逆向文件频率)特征加权基础上,提出ICF(逆类别因子)类别加权因子,对传统贝叶斯分类模型进行改进.利用MapReduce并行计算框架在处理海量数据方面的优势,设计并实现了一种对TFIDF改进的分布式朴素贝叶斯文本分类算法.实验结果表明,与传统分布式朴素贝叶斯算法和TFIDF加权的分布式朴素贝叶斯算法相比,改进后的分类算法在查准率、查全率、F-measure等方面都有了较大提高.     

基于贝叶斯学习的集成流量分类方法

NB方法条件独立性假设和BAN方法小训练集难以建模。为此,提出一种基于贝叶斯学习的集成流量分类方法。构造单独的NB和BAN分类器,在此基础上利用验证集得到各分类器的权重,通过加权平均组合各分类器的输出,实现网络流量分类。以Moore数据集为实验数据,并与NB方法和BAN方法相比较,结果表明,该方法具有更高的分类准确率和稳定性。     

基于朴素贝叶斯与ID3算法的决策树分类

v在朴素贝叶斯算法和ID3算法的基础上,提出一种改进的决策树分类算法。引入客观属性重要度参数,给出弱化的朴素贝叶斯条件独立性假设,并采用加权独立信息熵作为分类属性的选取标准。理论分析和实验结果表明,改进算法能在一定程度上克服ID3算法的多值偏向问题,并且具有较高的执行效率和分类准确度。     

Classification using Hierarchical Naïve Bayes models

Classification problems have a long history in the machine learning literature. One of the simplest, and yet most consistently well-performing set of classifiers is the Naïve Bayes models. However, an inherent problem with these classifiers is the assumption that all attributes used to describe an instance are conditionally independent given the class of that instance. When this assumption is violated (which is often the case in practice) it can reduce classification accuracy due to “information double-counting” and interaction omission. In this paper we focus on a relatively new set of models, termed Hierarchical Naïve Bayes models. Hierarchical Naïve Bayes models extend the modeling flexibility of Naïve Bayes models by introducing latent variables to relax some of the independence statements in these models. We propose a simple algorithm for learning Hierarchical Naïve Bayes models in the context of classification. Experimental results show that the learned models can significantly improve classification accuracy as compared to other frameworks.     

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.     

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.     

一种属性相关性的加权贝叶斯分类算法研究

根据RoughSet属性重要度理论,构建了基于互信息的属性子集重要度,提出属性相关性的加权朴素贝叶斯分类算法,该算法同时放宽了朴素贝叶斯算法属性独立性、属性重要性相同的假设。通过在UCI部分数据集上进行仿真实验,与基于属性相关性分析的贝叶斯(CB)和加权朴素贝叶斯(WNB)两种算法做比较,证明了该算法的有效性。     

An attribute value frequency-based instance weighting filter for naive Bayes

Due to its simplicity, efficiency and efficacy, naive Bayes (NB) continues to be one of the top 10 data mining algorithms. A mass of improved approaches to NB have been proposed to weaken its conditional independence assumption. However, there has been little work, up to the present, on instance weighting filter approaches to NB. In this paper, we propose a simple, efficient, and effective instance weighting filter approach to NB. We call it attribute (feature) value frequency-based instance weighting and denote the resulting improved model as attribute value frequency weighted naive Bayes (AVFWNB). In AVFWNB, the weight of each training instance is defined as the inner product of its attribute value frequency vector and the attribute value number vector. The experimental results on 36 widely used classification problems show that AVFWNB significantly outperforms NB, yet at the same time maintains the computational simplicity that characterizes NB.     

操作风险等级预测的朴素贝叶斯方法研究

操作风险数据积累比较困难,而且往往不完整,朴素贝叶斯分类器是目前进行小样本分类最优秀的分类器之一,适合于操作风险等级预测。在对具有完整数据朴素贝叶斯分类器学习和分类的基础上,提出了基于星形结构和Gibbs sampling的具有丢失数据朴素贝叶斯分类器学习方法,能够避免目前常用的处理丢失数据方法所带来的局部最优、信息丢失和冗余等方面的问题。     

基于特征加权的朴素贝叶斯分类器

朴素贝叶斯分类器是一种广泛使用的分类算法,其计算效率和分类效果均十分理想。但是,由于其基础假设“朴素贝叶斯假设”与现实存在一定的差异,因此在某些数据上可能导致较差的分类结果。现在存在多种方法试图通过放松朴素贝叶斯假设来增强贝叶斯分类器的分类效果,但是通常会导致计算代价大幅提高。该文利用特征加权技术来增强朴素贝叶斯分类器。特征加权参数直接从数据导出,可以看作是计算某个类别的后验概率时,某个属性对于该计算的影响程度。数值实验表明,特征加权朴素贝叶斯分类器（FWNB）的效果与其他的一些常用分类算法,例如树扩展朴素贝叶斯（TAN）和朴素贝叶斯树（NBTree）等的分类效果相当,其平均错误率都在17％左右;在计算速度上,FWNB接近于NB,比TAN和NBTree快至少一个数量级。