Naive Bayes classifier

About: Naive Bayes classifier is a research topic. Over the lifetime, 16207 publications have been published within this topic receiving 386597 citations. The topic is also known as: Naive Bayes.

The Optimality of Naive Bayes.

Abstract: Naive Bayes is one of the most efficient and effective inductive learning algorithms for machine learning and data mining. Its competitive performance in classification is surprising, because the conditional independence assumption on which it is based, is rarely true in realworld applications. An open question is: what is the true reason for the surprisingly good performance of naive Bayes in classification? In this paper, we propose a novel explanation on the superb classification performance of naive Bayes. We show that, essentially, the dependence distribution; i.e., how the local dependence of a node distributes in each class, evenly or unevenly, and how the local dependencies of all nodes work together, consistently (supporting a certain classification) or inconsistently (canceling each other out), plays a crucial role. Therefore, no matter how strong the dependences among attributes are, naive Bayes can still be optimal if the dependences distribute evenly in classes, or if the dependences cancel each other out. We propose and prove a sufficient and necessary conditions for the optimality of naive Bayes. Further, we investigate the optimality of naive Bayes under the Gaussian distribution. We present and prove a sufficient condition for the optimality of naive Bayes, in which the dependence between attributes do exist. This provides evidence that dependence among attributes may cancel out each other. In addition, we explore when naive Bayes works well. Naive Bayes and Augmented Naive Bayes Classification is a fundamental issue in machine learning and data mining. In classification, the goal of a learning algorithm is to construct a classifier given a set of training examples with class labels. Typically, an example E is represented by a tuple of attribute values (x1, x2, , · · · , xn), where xi is the value of attribute Xi. Let C represent the classification variable, and let c be the value of C. In this paper, we assume that there are only two classes: + (the positive class) or − (the negative class). A classifier is a function that assigns a class label to an example. From the probability perspective, according to Bayes Copyright c © 2004, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. Rule, the probability of an example E = (x1, x2, · · · , xn) being class c is p(c|E) = p(E|c)p(c) p(E) . E is classified as the class C = + if and only if fb(E) = p(C = +|E) p(C = −|E) ≥ 1, (1) where fb(E) is called a Bayesian classifier. Assume that all attributes are independent given the value of the class variable; that is, p(E|c) = p(x1, x2, · · · , xn|c) = n ∏

Using AUC and accuracy in evaluating learning algorithms

Abstract: The area under the ROC (receiver operating characteristics) curve, or simply AUC, has been traditionally used in medical diagnosis since the 1970s. It has recently been proposed as an alternative single-number measure for evaluating the predictive ability of learning algorithms. However, no formal arguments were given as to why AUC should be preferred over accuracy. We establish formal criteria for comparing two different measures for learning algorithms and we show theoretically and empirically that AUC is a better measure (defined precisely) than accuracy. We then reevaluate well-established claims in machine learning based on accuracy using AUC and obtain interesting and surprising new results. For example, it has been well-established and accepted that Naive Bayes and decision trees are very similar in predictive accuracy. We show, however, that Naive Bayes is significantly better than decision trees in AUC. The conclusions drawn in this paper may make a significant impact on machine learning and data mining applications.

Correlation-based Feature Selection for Discrete and Numeric Class Machine Learning

Abstract: Algorithms for feature selection fall into two broad categories: wrappers that use the learning algorithm itself to evaluate the usefulness of features and filters that evaluate features according to heuristics based on general characteristics of the data. For application to large databases, filters have proven to be more practical than wrappers because they are much faster. However, most existing filter algorithms only work with discrete classification problems. This paper describes a fast, correlation-based filter algorithm that can be applied to continuous and discrete problems. The algorithm often outperforms the well-known ReliefF attribute estimator when used as a preprocessing step for naive Bayes, instance-based learning, decision trees, locally weighted regression, and model trees. It performs more feature selection than ReliefF does—reducing the data dimensionality by fifty percent in most cases. Also, decision and model trees built from the preprocessed data are often significantly smaller.

A Probabilistic Analysis of the Rocchio Algorithm with TFIDF for Text Categorization

Abstract: : A probabilistic analysis of the Rocchio relevance feedback algorithm, one of the most popular learning methods from information retrieval, is presented in a text categorization framework. The analysis results in a probabilistic version of the Rocchio classifier and offers an explanation for the TFIDF word weighting heuristic. The Rocchio classifier, its probabilistic variant and a standard naive Bayes classifier are compared on three text categorization tasks. The results suggest that the probabilistic algorithms are preferable to the heuristic Rocchio classifier.

Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification

Abstract: We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and two-dimensional Gabor wavelet transform responses taken at multiple scales. The Gabor wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The method's performance is evaluated on publicly available DRIVE (Staal et al.,2004) and STARE (Hoover et al.,2000) databases of manually labeled images. On the DRIVE database, it achieves an area under the receiver operating characteristic curve of 0.9614, being slightly superior than that presented by state-of-the-art approaches. We are making our implementation available as open source MATLAB scripts for researchers interested in implementation details, evaluation, or development of methods