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63
A DecisionTheoretic Generalization of onLine Learning and an Application to Boosting
, 1997
"... In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worstcase online framework. The model we study can be interpreted as a broad, abstract extension of the wellstudied online prediction model to a general decisiontheoretic set ..."
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Cited by 2307 (59 self)
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In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worstcase online framework. The model we study can be interpreted as a broad, abstract extension of the wellstudied online prediction model to a general decisiontheoretic setting. We show that the multiplicative weightupdate rule of Littlestone and Warmuth [20] can be adapted to this model yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multipleoutcome prediction, repeated games and prediction of points in R n . In the second part of the paper we apply the multiplicative weightupdate technique to derive a new boosting algorithm. This boosting algorithm does not require any prior knowledge about the performance of the weak learning algorithm. We also study generalizations of...
Experiments with a New Boosting Algorithm
, 1996
"... 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 relate ..."
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Cited by 1625 (21 self)
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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 “pseudoloss ” which is a method for forcing a learning algorithm of multilabel 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 pseudoloss, 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 attributevalue tests). We compared the performance of the two methods on a collection of machinelearning benchmarks. In the second set of experiments, we studied in more detail the performance of boosting using a nearestneighbor classifier on an OCR problem.
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 721 (52 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
Improved Boosting Algorithms Using Confidencerated Predictions
 MACHINE LEARNING
, 1999
"... We describe several improvements to Freund and Schapire’s AdaBoost boosting algorithm, particularly in a setting in which hypotheses may assign confidences to each of their predictions. We give a simplified analysis of AdaBoost in this setting, and we show how this analysis can be used to find impr ..."
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Cited by 698 (26 self)
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We describe several improvements to Freund and Schapire’s AdaBoost boosting algorithm, particularly in a setting in which hypotheses may assign confidences to each of their predictions. We give a simplified analysis of AdaBoost in this setting, and we show how this analysis can be used to find improved parameter settings as well as a refined criterion for training weak hypotheses. We give a specific method for assigning confidences to the predictions of decision trees, a method closely related to one used by Quinlan. This method also suggests a technique for growing decision trees which turns out to be identical to one proposed by Kearns and Mansour. We focus next on how to apply the new boosting algorithms to multiclass classification problems, particularly to the multilabel case in which each example may belong to more than one class. We give two boosting methods for this problem, plus a third method based on output coding. One of these leads to a new method for handling the singlelabel case which is simpler but as effective as techniques suggested by Freund and Schapire. Finally, we give some experimental results comparing a few of the algorithms discussed in this paper.
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 539 (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 515 (18 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.
BoosTexter: A Boostingbased System for Text Categorization
 MACHINE LEARNING
, 2000
"... This work focuses on algorithms which learn from examples to perform multiclass text and speech categorization tasks. Our approach is based on a new and improved family of boosting algorithms. We describe in detail an implementation, called BoosTexter, of the new boosting algorithms for text categor ..."
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Cited by 485 (21 self)
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This work focuses on algorithms which learn from examples to perform multiclass text and speech categorization tasks. Our approach is based on a new and improved family of boosting algorithms. We describe in detail an implementation, called BoosTexter, of the new boosting algorithms for text categorization tasks. We present results comparing the performance of BoosTexter and a number of other textcategorization algorithms on a variety of tasks. We conclude by describing the application of our system to automatic calltype identification from unconstrained spoken customer responses.
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 277 (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....
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 181 (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.