In an earlier paper, we introduced a new “boosting” algorithm called AdaBoost which, theoretically, can be used to significantly reduce the error of any learning algorithm that consistently generates classifiers whose performance is a little better than random guessing. We also introduced the related notion of a “pseudo-loss ” which is a method for forcing a learning algorithm of multi-label conceptsto concentrate on the labels that are hardest to discriminate. In this paper, we describe experiments we carried out to assess how well AdaBoost with and without pseudo-loss, performs on real learning problems. We performed two sets of experiments. The first set compared boosting to Breiman’s “bagging ” method when used to aggregate various classifiers (including decision trees and single attribute-value tests). We compared the performance of the two methods on a collection of machine-learning benchmarks. In the second set of experiments, we studied in more detail the performance of boosting using a nearest-neighbor classifier on an OCR problem.

Boosting (Freund & Schapire 1996, Schapire & Singer 1998) is one of the most important recent developments in classification methodology. The performance of many classification algorithms can often be dramatically improved by sequentially applying them to reweighted versions of the input data, and taking a weighted majority vote of the sequence of classifiers thereby produced. We show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles, namely additive modeling and maximum likelihood. For the two-class problem, boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum Bernoulli likelihood as a criterion. We develop more direct approximations and show that they exhibit nearly identical results to boosting. Direct multi-class generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multi-class generalizations of boosting in most...

We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small high-accuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using cross-validation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets.

Methods for voting classification algorithms, such as Bagging and AdaBoost, have been shown to be very successful in improving the accuracy of certain classifiers for artificial and real-world datasets. We review these algorithms and describe a large empirical study comparing several variants in conjunction with a decision tree inducer (three variants) and a Naive-Bayes inducer. The purpose of the study is to improve our understanding of why and when these algorithms, which use perturbation, reweighting, and combination techniques, affect classification error. We provide a bias and variance decomposition of the error to show how different methods and variants influence these two terms. This allowed us to determine that Bagging reduced variance of unstable methods, while boosting methods (AdaBoost and Arc-x4) reduced both the bias and variance of unstable methods but increased the variance for Naive-Bayes, which was very stable. We observed that Arc-x4 behaves differently than AdaBoost if reweighting is used instead of resampling, indicating a fundamental difference. Voting variants, some of which are introduced in this paper, include: pruning versus no pruning, use of probabilistic estimates, weight perturbations (Wagging), and backfitting of data. We found that Bagging improves when probabilistic estimates in conjunction with no-pruning are used, as well as when the data was backfit. We measure tree sizes and show an interesting positive correlation between the increase in the average tree size in AdaBoost trials and its success in reducing the error. We compare the mean-squared error of voting methods to non-voting methods and show that the voting methods lead to large and significant reductions in the mean-squared errors. Practical problems that arise in implementing boosting algorithms are explored, including numerical instabilities and underflows. We use scatterplots that graphically show how AdaBoost reweights instances, emphasizing not only "hard" areas but also outliers and noise.

In this survey, we review work in machine learning on methods for handling data sets containing large amounts of irrelevant information. We focus on two key issues: the problem of selecting relevant features, and the problem of selecting relevant examples. We describe the advances that have been made on these topics in both empirical and theoretical work in machine learning, and we present a general framework that we use to compare different methods. We close with some challenges for future work in this area.

Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify defining characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised discretization method, to entropy-based and purity-based methods, which are supervised algorithms. We found that the performance of the Naive-Bayes algorithm significantly improved when features were discretized using an entropy-based method. In fact, over the 16 tested datasets, the discretized version of Naive-Bayes slightly outperformed C4.5 on average. We also show that in some cases, the performance of the C4.5 induction algorithm significantly improved if features were discretized in advance; in our experiments, the performance never significantly degraded, an interesting phenomenon considering the fact that C4.5 is capable of locally discretizing features.

The simple Bayesian classifier (SBC) is commonly thought to assume that attributes are independent given the class, but this is apparently contradicted by the surprisingly good performance it exhibits in many domains that contain clear attribute dependences. No explanation for this has been proposed so far. In this paper we show that the SBC does not in fact assume attribute independence, and can be optimal even when this assumption is violated by a wide margin. The key to this finding lies in the distinction between classification and probability estimation: correct classification can be achieved even when the probability estimates used contain large errors. We show that the previously-assumed region of optimality of the SBC is a second-order infinitesimal fraction of the actual one. This is followed by the derivation of several necessary and several sufficient conditions for the optimality of the SBC. For example, the SBC is optimal for learning arbitrary conjunctions and disjunctions, even though they violate the independence assumption. The paper also reports empirical evidence of the SBC's competitive performance in domains containing substantial degrees of attribute dependence.

This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a decision tree. Oblique decision tree methods are tuned especially for domains in which the attributes are numeric, although they can be adapted to symbolic or mixed symbolic/numeric attributes. We present extensive empirical studies, using both real and artificial data, that analyze OC1's ability to construct oblique trees that are smaller and more accurate than their axis-parallel counterparts. We also examine the benefits of randomization for the construction of oblique decision trees. 1. Introduction Current data collection technology provides a unique challenge and opportunity for automated machine learning techniques. The advent of major scientific projects such as the Human Genome Project, the Hubble Space Telescope, and the human brain mappi...

In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that carries out a greedy search through the space of features. We hypothesize that this approach will improve asymptotic accuracy in domains that involve correlated features without reducing the rate of learning in ones that do not. We report experimental results on six natural domains, including comparisons with decision-tree induction, that support these hypotheses. In closing, we discuss other approaches to extending naive Bayesian classifiers and outline some directions for future research.

Abstract. The classification problem is considered in which an output variable y assumes discrete values with respective probabilities that depend upon the simultaneous values of a set of input variables x ={x1,...,xn}.At issue is how error in the estimates of these probabilities affects classification error when the estimates are used in a classification rule. These effects are seen to be somewhat counter intuitive in both their strength and nature. In particular the bias and variance components of the estimation error combine to influence classification in a very different way than with squared error on the probabilities themselves. Certain types of (very high) bias can be canceled by low variance to produce accurate classification. This can dramatically mitigate the effect of the bias associated with some simple estimators like “naive ” Bayes, and the bias induced by the curse-of-dimensionality on nearest-neighbor procedures. This helps explain why such simple methods are often competitive with and sometimes superior to more sophisticated ones for classification, and why “bagging/aggregating ” classifiers can often improve accuracy. These results also suggest simple modifications to these procedures that can (sometimes dramatically) further improve their classification performance.