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195
Wrappers for Feature Subset Selection
 AIJ SPECIAL ISSUE ON RELEVANCE
, 1997
"... In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a ..."
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Cited by 1133 (3 self)
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In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a feature subset selection method should consider how the algorithm and the training set interact. We explore the relation between optimal feature subset selection and relevance. Our wrapper method searches for an optimal feature subset tailored to a particular algorithm and a domain. We study the strengths and weaknesses of the wrapper approach andshow a series of improved designs. We compare the wrapper approach to induction without feature subset selection and to Relief, a filter approach to feature subset selection. Significant improvement in accuracy is achieved for some datasets for the two families of induction algorithms used: decision trees and NaiveBayes.
Boosting the margin: A new explanation for the effectiveness of voting methods
 In Proceedings International Conference on Machine Learning
, 1997
"... Abstract. One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show ..."
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Cited by 771 (51 self)
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Abstract. One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik’s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the biasvariance decomposition. 1
On the optimality of the simple Bayesian classifier under zeroone loss
 MACHINE LEARNING
, 1997
"... The simple Bayesian classifier is known to be optimal when attributes are independent given the class, but the question of whether other sufficient conditions for its optimality exist has so far not been explored. Empirical results showing that it performs surprisingly well in many domains containin ..."
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Cited by 645 (26 self)
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The simple Bayesian classifier is known to be optimal when attributes are independent given the class, but the question of whether other sufficient conditions for its optimality exist has so far not been explored. Empirical results showing that it performs surprisingly well in many domains containing clear attribute dependences suggest that the answer to this question may be positive. This article shows that, although the Bayesian classifier’s probability estimates are only optimal under quadratic loss if the independence assumption holds, the classifier itself can be optimal under zeroone loss (misclassification rate) even when this assumption is violated by a wide margin. The region of quadraticloss optimality of the Bayesian classifier is in fact a secondorder infinitesimal fraction of the region of zeroone optimality. This implies that the Bayesian classifier has a much greater range of applicability than previously thought. For example, in this article it is shown to be optimal for learning conjunctions and disjunctions, even though they violate the independence assumption. Further, studies in artificial domains show that it will often outperform more powerful classifiers for common training set sizes and numbers of attributes, even if its bias is a priori much less appropriate to the domain. This article’s results also imply that detecting attribute dependence is not necessarily the best way to extend the Bayesian classifier, and this is also verified empirically.
An Empirical Comparison of Voting Classification Algorithms: Bagging, Boosting, and Variants
 MACHINE LEARNING
, 1999
"... 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 realworld datasets. We review these algorithms and describe a large empirical study comparing several variants in co ..."
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Cited by 582 (2 self)
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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 realworld 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 NaiveBayes 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 Arcx4) reduced both the bias and
variance of unstable methods but increased the variance for NaiveBayes,
which was very stable. We observed that Arcx4 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 nopruning 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 meansquared error of voting methods to
nonvoting methods and show that the voting methods lead to large
and significant reductions in the meansquared 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.
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 562 (19 self)
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The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting algorithm for combining preferences called RankBoost. We also describe an efficient implementation of the algorithm for certain natural cases. We discuss two experiments we carried out to assess the performance of RankBoost. In the first experiment, we used the algorithm to combine different WWW search strategies, each of which is a query expansion for a given domain. For this task, we compare the performance of RankBoost to the individual search strategies. The second experiment is a collaborativefiltering task for making movie recommendations. Here, we present results comparing RankBoost to nearestneighbor and regression algorithms.
Arcing Classifiers
, 1998
"... Recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error. One of the more effective is bagging (Breiman [1996a] ) Here, modified training sets are formed by resampling from the original training set, classifiers con ..."
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Cited by 299 (6 self)
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Recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error. One of the more effective is bagging (Breiman [1996a] ) Here, modified training sets are formed by resampling from the original training set, classifiers constructed using these training sets and then combined by voting. Freund and Schapire [1995,1996] propose an algorithm the basis of which is to adaptively resample and combine (hence the acronymarcing) so that the weights in the resampling are increased for those cases most often misclassified and the combining is done by weighted voting. Arcing is more successful than bagging in test set error reduction. We explore two arcing algorithms, compare them to each other and to bagging, and try to understand how arcing works. We introduce the definitions of bias and variance for a classifier as components of the test set error. Unstable classifiers can have low bias on a large range of data sets....
On bias, variance, 0/1loss, and the curseofdimensionality
 Data Mining and Knowledge Discovery
, 1997
"... 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 classificat ..."
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Cited by 207 (1 self)
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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 curseofdimensionality on nearestneighbor 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.
Popular ensemble methods: an empirical study
 Journal of Artificial Intelligence Research
, 1999
"... An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Baggi ..."
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Cited by 206 (3 self)
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An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund & Schapire, 1996; Schapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier – especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble’s performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees. 1.
Mining ConceptDrifting Data Streams Using Ensemble Classifiers
, 2003
"... Recently, mining data streams with concept drifts for actionable insights has become an important and challenging task for a wide range of applications including credit card fraud protection, target marketing, network intrusion detection, etc. Conventional knowledge discovery tools are facing two ch ..."
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Cited by 192 (32 self)
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Recently, mining data streams with concept drifts for actionable insights has become an important and challenging task for a wide range of applications including credit card fraud protection, target marketing, network intrusion detection, etc. Conventional knowledge discovery tools are facing two challenges, the overwhelming volume of the streaming data, and the concept drifts. In this paper, we propose a general framework for mining conceptdrifting data streams using weighted ensemble classifiers. We train an ensemble of classification models, such as C4.5, RIPPER, naive Bayesian, etc., from sequential chunks of the data stream. The classifiers in the ensemble are judiciously weighted based on their expected classification accuracy on the test data under the timeevolving environment. Thus, the ensemble approach improves both the efficiency in learning the model and the accuracy in performing classification. Our empirical study shows that the proposed methods have substantial advantage over singleclassifier approaches in prediction accuracy, and the ensemble framework is effective for a variety of classification models.
Measures of Diversity in Classifier Ensembles and Their Relationship with the Ensemble Accuracy
, 2003
"... Diversity among the members of a team of classifiers is deemed to be a key issue in classifier combination. However, measuring diversity is not straightforward because there is no generally accepted formal definition. We have found and studied ten statistics which can measure diversity among binary ..."
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Cited by 150 (0 self)
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Diversity among the members of a team of classifiers is deemed to be a key issue in classifier combination. However, measuring diversity is not straightforward because there is no generally accepted formal definition. We have found and studied ten statistics which can measure diversity among binary classifier outputs (correct or incorrect vote for the class label): four averaged pairwise measures (the Q statistic, the correlation, the disagreement and the double fault) and six nonpairwise measures (the entropy of the votes, the difficulty index, the KohaviWolpert variance, the interrater agreement, the generalized diversity, and the coincident failure diversity). Four experiments have been designed to examine the relationship between the accuracy of the team and the measures of diversity, and among the measures themselves. Although there are proven connections between diversity and accuracy in some special cases, our results raise some doubts about the usefulness of diversity measures in building classifier ensembles in reallife pattern recognition problems.