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427
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 1522 (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.
A Study of CrossValidation and Bootstrap for Accuracy Estimation and Model Selection
 INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1995
"... We review accuracy estimation methods and compare the two most common methods: crossvalidation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), te ..."
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Cited by 1248 (12 self)
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We review accuracy estimation methods and compare the two most common methods: crossvalidation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), tenfold crossvalidation may be better than the more expensive leaveoneout crossvalidation. We report on a largescale experiment  over half a million runs of C4.5 and a NaiveBayes algorithm  to estimate the effects of different parameters on these algorithms on realworld datasets. For crossvalidation, we vary the number of folds and whether the folds are stratified or not; for bootstrap, we vary the number of bootstrap samples. Our results indicate that for realword datasets similar to ours, the best method to use for model selection is tenfold stratified cross validation, even if computation power allows using more folds.
A comparison of event models for Naive Bayes text classification
, 1998
"... Recent work in text classification has used two different firstorder probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multivariate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey ..."
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Cited by 1002 (27 self)
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Recent work in text classification has used two different firstorder probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multivariate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey and Croft 1996; Koller and Sahami 1997). Others use a multinomial model, that is, a unigram language model with integer word counts (e.g. Lewis and Gale 1994; Mitchell 1997). This paper aims to clarify the confusion by describing the differences and details of these two models, and by empirically comparing their classification performance on five text corpora. We find that the multivariate Bernoulli performs well with small vocabulary sizes, but that the multinomial performs usually performs even better at larger vocabulary sizesproviding on average a 27% reduction in error over the multivariate Bernoulli model at any vocabulary size.
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 805 (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.
Bayesian Network Classifiers
, 1997
"... 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 stateoftheart classifiers such as C4.5. This fact raises the question of whether a classifier with less restr ..."
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Cited by 788 (23 self)
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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 stateoftheart 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.
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 695 (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.
Supervised and unsupervised discretization of continuous features
 in A. Prieditis & S. Russell, eds, Machine Learning: Proceedings of the Twelfth International Conference
, 1995
"... Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify de ning characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised dis ..."
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Cited by 534 (11 self)
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Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify de ning characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised discretization method, to entropybased and puritybased methods, which are supervised algorithms. We found that the performance of the NaiveBayes algorithm signi cantly improved when features were discretized using an entropybased method. In fact, over the 16 tested datasets, the discretized version of NaiveBayes slightly outperformed C4.5 on average. We also show that in some cases, the performance of the C4.5 induction algorithm signi cantly improved if features were discretized in advance � in our experiments, the performance never signi cantly degraded, an interesting phenomenon considering the fact that C4.5 is capable of locally discretizing features. 1
Estimating Continuous Distributions in Bayesian Classifiers
 In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence
, 1995
"... When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality ..."
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Cited by 489 (2 self)
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When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive Bayesian classifier, we present experimental results on a variety of natural and artificial domains, comparing two methods of density estimation: assuming normality and modeling each conditional distribution with a single Gaussian; and using nonparametric kernel density estimation. We observe large reductions in error on several natural and artificial data sets, which suggests that kernel estimation is a useful tool for learning Bayesian models. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers, San Mateo, 1995 1 Introduction In rec...
Toward optimal feature selection
 In 13th International Conference on Machine Learning
, 1995
"... In this paper, we examine a method for feature subset selection based on Information Theory. Initially, a framework for de ning the theoretically optimal, but computationally intractable, method for feature subset selection is presented. We show that our goal should be to eliminate a feature if it g ..."
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Cited by 472 (9 self)
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In this paper, we examine a method for feature subset selection based on Information Theory. Initially, a framework for de ning the theoretically optimal, but computationally intractable, method for feature subset selection is presented. We show that our goal should be to eliminate a feature if it gives us little or no additional information beyond that subsumed by the remaining features. In particular, this will be the case for both irrelevant and redundant features. We then give an e cient algorithm for feature selection which computes an approximation to the optimal feature selection criterion. The conditions under which the approximate algorithm is successful are examined. Empirical results are given on a number of data sets, showing that the algorithm e ectively handles datasets with a very large number of features.
Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier
"... 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 ..."
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Cited by 353 (8 self)
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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 previouslyassumed region of optimality of the SBC is a secondorder 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.