Naive Bayes text classifiers: a locally weighted learning approach

Due to being fast, easy to implement and relatively effective, some state-of-the-art naive Bayes text classifiers with the strong assumption of conditional independence among attributes, such as multinomial naive Bayes, complement naive Bayes and the one-versus-all-but-one model, have received a great deal of attention from researchers in the domain of text classification. In this article, we revisit these naive Bayes text classifiers and empirically compare their classification performance on a large number of widely used text classification benchmark datasets. Then, we propose a locally weighted learning approach to these naive Bayes text classifiers. We call our new approach locally weighted naive Bayes text classifiers (LWNBTC). LWNBTC weakens the attribute conditional independence assumption made by these naive Bayes text classifiers by applying the locally weighted learning approach. The experimental results show that our locally weighted versions significantly outperform these state-of-the-art naive Bayes text classifiers in terms of classification accuracy.     

Using the self organizing map for clustering of text documents

An increasing number of computational and statistical approaches have been used for text classification, including nearest-neighbor classification, naïve Bayes classification, support vector machines, decision tree induction, rule induction, and artificial neural networks. Among these approaches, naïve Bayes classifiers have been widely used because of its simplicity. Due to the simplicity of the Bayes formula, the naïve Bayes classification algorithm requires a relatively small number of training data and shorter time in both the training and classification stages as compared to other classifiers. However, a major short coming of this technique is the fact that the classifier will pick the highest probability category as the one to which the document is annotated too. Doing this is tantamount to classifying using only one dimension of a multi-dimensional data set. The main aim of this work is to utilize the strengths of the self organizing map (SOM) to overcome the inadvertent dimensionality reduction resulting from using only the Bayes formula to classify. Combining the hybrid system with new ranking techniques further improves the performance of the proposed document classification approach. This work describes the implementation of an enhanced hybrid classification approach which affords a better classification accuracy through the utilization of two familiar algorithms, the naïve Bayes classification algorithm which is used to vectorize the document using a probability distribution and the self organizing map (SOM) clustering algorithm which is used as the multi-dimensional unsupervised classifier.     

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.     

Learning by extrapolation from marginal to full-multivariate probability distributions: decreasingly naive Bayesian classification

Averaged n-Dependence Estimators (AnDE) is an approach to probabilistic classification learning that learns by extrapolation from marginal to full-multivariate probability distributions. It utilizes a single parameter that transforms the approach between a low-variance high-bias learner (Naive Bayes) and a high-variance low-bias learner with Bayes optimal asymptotic error. It extends the underlying strategy of Averaged One-Dependence Estimators (AODE), which relaxes the Naive Bayes independence assumption while retaining many of Naive Bayes’ desirable computational and theoretical properties. AnDE further relaxes the independence assumption by generalizing AODE to higher-levels of dependence. Extensive experimental evaluation shows that the bias-variance trade-off for Averaged 2-Dependence Estimators results in strong predictive accuracy over a wide range of data sets. It has training time linear with respect to the number of examples, learns in a single pass through the training data, supports incremental learning, handles directly missing values, and is robust in the face of noise. Beyond the practical utility of its lower-dimensional variants, AnDE is of interest in that it demonstrates that it is possible to create low-bias high-variance generative learners and suggests strategies for developing even more powerful classifiers.     

On the combination of locally optimal pairwise classifiers

Classification methods generally rely on some idea about the data structure. If the specific assumptions are not met, a classifier may fail. In this paper, the possibility of combining classifiers in multi-class problems is investigated. Multi-class classification problems are split into two class problems. For each of the latter problems an optimal classifier is determined. The results of applying the optimal classifiers on the two class problems can be combined using a pairwise coupling algorithm.In this paper, exemplary situations are investigated where the respective assumptions of Naive Bayes or the classical Linear Discriminant Analysis (LDA) fail. It is investigated at which degree of violations of the assumptions it may be advantageous to use single methods or a classifier combination by pairwise coupling.     

Parameter estimation in bayesian networks from incomplete databases

Current methods to learn Bayesian Networks from incomplete databases share the common assumption that the unreported data are missing at random. This paper describes a method—called Bound and Collapse (BC)—to learn Bayesian Networks from incomplete databases which allows the analyst to efficiently integrate information provided by the observed data and exogenous knowledge about the pattern of missing data. BC starts by bounding the set of estimates consistent with the available information and then collapses the resulting set to a point estimate via a convex combination of the extreme points, with weights depending on the assumed pattern of missing data. Experiments comparing BC to Gibbs Sampling are provided.     

An intrusion detection and alert correlation approach based on revising probabilistic classifiers using expert knowledge

Bayesian networks are important knowledge representation tools for handling uncertain pieces of information. The success of these models is strongly related to their capacity to represent and handle dependence relations. Some forms of Bayesian networks have been successfully applied in many classification tasks. In particular, naive Bayes classifiers have been used for intrusion detection and alerts correlation. This paper analyses the advantage of adding expert knowledge to probabilistic classifiers in the context of intrusion detection and alerts correlation. As examples of probabilistic classifiers, we will consider the well-known Naive Bayes, Tree Augmented Naïve Bayes (TAN), Hidden Naive Bayes (HNB) and decision tree classifiers. Our approach can be applied for any classifier where the outcome is a probability distribution over a set of classes (or decisions). In particular, we study how additional expert knowledge such as “it is expected that 80 % of traffic will be normal” can be integrated in classification tasks. Our aim is to revise probabilistic classifiers’ outputs in order to fit expert knowledge. Experimental results show that our approach improves existing results on different benchmarks from intrusion detection and alert correlation areas.     

Case Based Imprecision Estimates for Bayes Classifiers with the Bayesian Bootstrap

This article outlines a Bayesian bootstrap method for case based imprecision estimates in Bayes classification. We argue that this approach is an important complement to methods such as k-fold cross validation that are based on overall error rates. It is shown how case based imprecision estimates may be used to improve Bayes classifiers under asymmetrical loss functions. In addition, other approaches to making use of case based imprecision estimates are discussed and illustrated on two real world data sets. Contrary to the common assumption, Bayesian bootstrap simulations indicate that the uncertainty associated with the output of a Bayes classifier is often far from normally distributed.     

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.     

Gait classification in children with cerebral palsy by Bayesian approach

Cerebral palsy (CP) is a non-progressive neuro-developmental condition that occurs in early childhood and is associated with a motor impairment, usually affecting mobility and posture. Automatic accurate identification of CP gait has many potential applications, for example, assistance in diagnosis, clinical decision-making and communication among the clinical professionals. In previous studies, support vector machine (SVM) and neural networks have been applied to classify CP gait patterns. However, one of the disadvantages of SVM and many neural network models is that given a gait sample, it only predicts a gait pattern class label without providing any estimate of the underlying probability, which is particularly important in computer aided diagnostics applications. The objective of this study is to first investigate different pattern classification paradigms in the automatic gait analysis and address the significance of Bayesian classifier model, and then give a comprehensive performances comparison. Bayesian classification is based on Bayes’ decision theory, which compute the probability of a given data point belonging to a class. Then among all classes, we choose the one that has the largest probability, and classify the data point as being of that class. Using a publicly available CP gait data set (68 normal healthy and 88 with spastic diplegia form of CP), different features including the two basic temporal-spatial gait parameters (stride length and cadence) have been experimented. Various hold-out and cross-validation testing show that the Bayesian model offers excellent classification performances compared with some popular classifiers such as random forest and multiple layer perceptron. With many advantages considered, Bayesian classifier model is very significant in establishing a clinical decision system for gait analysis.     

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.     

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。     

Learn.MF: A random subspace approach for the missing feature problem

We introduce Learn⁺⁺.MF, an ensemble-of-classifiers based algorithm that employs random subspace selection to address the missing feature problem in supervised classification. Unlike most established approaches, Learn⁺⁺.MF does not replace missing values with estimated ones, and hence does not need specific assumptions on the underlying data distribution. Instead, it trains an ensemble of classifiers, each on a random subset of the available features. Instances with missing values are classified by the majority voting of those classifiers whose training data did not include the missing features. We show that Learn⁺⁺.MF can accommodate substantial amount of missing data, and with only gradual decline in performance as the amount of missing data increases. We also analyze the effect of the cardinality of the random feature subsets, and the ensemble size on algorithm performance. Finally, we discuss the conditions under which the proposed approach is most effective.     

一种基于混合集成方法的数据流概念漂移检测方法

近年来,数据流分类问题研究受到了普遍关注,而漂移检测是其中一个重要的研究问题。已有的分类模型有单一集成模型和混合模型,其漂移检测机制多基于理想的分布假设。单一模型集成可能导致分类误差扩大,噪音环境下分类效果受到了一定影响,而混合集成模型多存在分类精度和时间性能难以两者兼顾的问题。为此,基于简单的WE集成框架,构建了基于决策树和bayes混合模型的集成分类方法 WE-DTB,并利用典型的概念漂移检测机制Hoeffding Bounds和μ检验来进行数据流环境下概念漂移的检测和分类。大量实验表明,WE-DTB能够有效检测概念漂移且具有较好的分类精度及时空性能。     

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.     

Learning accurate very fast decision trees from uncertain data streams

Most existing works on data stream classification assume the streaming data is precise and definite. Such assumption, however, does not always hold in practice, since data uncertainty is ubiquitous in data stream applications due to imprecise measurement, missing values, privacy protection, etc. The goal of this paper is to learn accurate decision tree models from uncertain data streams for classification analysis. On the basis of very fast decision tree (VFDT) algorithms, we proposed an algorithm for constructing an uncertain VFDT tree with classifiers at tree leaves (uVFDTc). The uVFDTc algorithm can exploit uncertain information effectively and efficiently in both the learning and the classification phases. In the learning phase, it uses Hoeffding bound theory to learn from uncertain data streams and yield fast and reasonable decision trees. In the classification phase, at tree leaves it uses uncertain naive Bayes (UNB) classifiers to improve the classification performance. Experimental results on both synthetic and real-life datasets demonstrate the strong ability of uVFDTc to classify uncertain data streams. The use of UNB at tree leaves has improved the performance of uVFDTc, especially the any-time property, the benefit of exploiting uncertain information, and the robustness against uncertainty.     

Bayesian Classifiers Programmed in SQL

The Bayesian classifier is a fundamental classification technique. In this work, we focus on programming Bayesian classifiers in SQL. We introduce two classifiers: Naive Bayes and a classifier based on class decomposition using K-means clustering. We consider two complementary tasks: model computation and scoring a data set. We study several layouts for tables and several indexing alternatives. We analyze how to transform equations into efficient SQL queries and introduce several query optimizations. We conduct experiments with real and synthetic data sets to evaluate classification accuracy, query optimizations, and scalability. Our Bayesian classifier is more accurate than Naive Bayes and decision trees. Distance computation is significantly accelerated with horizontal layout for tables, denormalization, and pivoting. We also compare Naive Bayes implementations in SQL and C++: SQL is about four times slower. Our Bayesian classifier in SQL achieves high classification accuracy, can efficiently analyze large data sets, and has linear scalability.