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119
An introduction to variable and feature selection
 Journal of Machine Learning Research
, 2003
"... Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. ..."
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Cited by 688 (14 self)
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Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available.
Statistical Comparisons of Classifiers over Multiple Data Sets
, 2006
"... While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all but igno ..."
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Cited by 243 (0 self)
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While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all but ignored. This article reviews the current practice and then theoretically and empirically examines several suitable tests. Based on that, we recommend a set of simple, yet safe and robust nonparametric tests for statistical comparisons of classifiers: the Wilcoxon signed ranks test for comparison of two classifiers and the Friedman test with the corresponding posthoc tests for comparison of more classifiers over multiple data sets. Results of the latter can also be neatly presented with the newly introduced CD (critical difference) diagrams.
Use of the ZeroNorm With Linear Models and Kernel Methods
, 2002
"... We explore the use of the socalled zeronorm of the parameters of linear models in learning. ..."
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Cited by 115 (4 self)
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We explore the use of the socalled zeronorm of the parameters of linear models in learning.
Kernel matching pursuit
 Machine Learning
, 2002
"... Matching Pursuit algorithms learn a function that is a weighted sum of basis functions, by sequentially appending functions to an initially empty basis, to approximate a target function in the leastsquares sense. We show how matching pursuit can be extended to use nonsquared error loss functions, a ..."
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Cited by 62 (0 self)
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Matching Pursuit algorithms learn a function that is a weighted sum of basis functions, by sequentially appending functions to an initially empty basis, to approximate a target function in the leastsquares sense. We show how matching pursuit can be extended to use nonsquared error loss functions, and how it can be used to build kernelbased solutions to machinelearning problems, while keeping control of the sparsity of the solution. We also derive MDL motivated generalization bounds for this type of algorithm, and compare them to related SVM (Support Vector Machine) bounds. Finally, links to boosting algorithms and RBF training procedures, as well as an extensive experimental comparison with SVMs for classification are given, showing comparable results with typically sparser models. 1
Feature Selection for Support Vector Machines by Means of Genetic Algorithms
, 2002
"... The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance, e.g. in bioinformatics. Genetic Algorithms (GAs) offer a natural way to solve this problem. In this paper we present a special Genetic Algorithm, which especially takes into accoun ..."
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Cited by 51 (1 self)
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The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance, e.g. in bioinformatics. Genetic Algorithms (GAs) offer a natural way to solve this problem. In this paper we present a special Genetic Algorithm, which especially takes into account the existing bounds on the generalization error for Support Vector Machines (SVMs). This new approach is compared to the traditional method of performing crossvalidation and to other existing algorithms for feature selection.
Rotation forest: A new classifier ensemble method
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2006
"... We propose a method for generating classifier ensembles based on feature extraction. To create the training data for a base classifier, the feature set is randomly split into K subsets (K is a parameter of the algorithm) and Principal Component Analysis (PCA) is applied to each subset. All principa ..."
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Cited by 44 (4 self)
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We propose a method for generating classifier ensembles based on feature extraction. To create the training data for a base classifier, the feature set is randomly split into K subsets (K is a parameter of the algorithm) and Principal Component Analysis (PCA) is applied to each subset. All principal components are retained in order to preserve the variability information in the data. Thus, K axis rotations take place to form the new features for a base classifier. The idea of the rotation approach is to encourage simultaneously individual accuracy and diversity within the ensemble. Diversity is promoted through the feature extraction for each base classifier. Decision trees were chosen here because they are sensitive to rotation of the feature axes, hence the name “forest. ” Accuracy is sought by keeping all principal components and also using the whole data set to train each base classifier. Using WEKA, we examined the Rotation Forest ensemble on a random selection of 33 benchmark data sets from the UCI repository and compared it with Bagging, AdaBoost, and Random Forest. The results were favorable to Rotation Forest and prompted an investigation into diversityaccuracy landscape of the ensemble models. Diversityerror diagrams revealed that Rotation Forest ensembles construct individual classifiers which are more accurate than these in AdaBoost and Random Forest, and more diverse than these in Bagging, sometimes more accurate as well.
Choosing between two learning algorithms based on calibrated tests. Working paper
, 2003
"... Designing a hypothesis test to determine the best of two machine learning algorithms with only a small data set available is not a simple task. Many popular tests suffer from low power (5x2 cv [2]), or high Type I error (Weka’s 10x10 cross validation [11]). Furthermore, many tests show a low level o ..."
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Cited by 31 (3 self)
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Designing a hypothesis test to determine the best of two machine learning algorithms with only a small data set available is not a simple task. Many popular tests suffer from low power (5x2 cv [2]), or high Type I error (Weka’s 10x10 cross validation [11]). Furthermore, many tests show a low level of replicability, so that tests performed by different scientists with the same pair of algorithms, the same data sets and the same hypothesis test still may present different results. We show that 5x2 cv, resampling and 10 fold cv suffer from low replicability. The main complication is due to the need to use the data multiple times. As a consequence, independence assumptions for most hypothesis tests are violated. In this paper, we pose the case that reuse of the same data causes the effective degrees of freedom to be much lower than theoretically expected. We show how to calibrate the effective degrees of freedom empirically for various tests. Some tests are not calibratable, indicating another flaw in the design. However the ones that are calibratable all show very similar behavior. Moreover, the Type I error of those tests is on the mark for a wide range of circumstances, while they show a power and replicability that is a considerably higher than currently popular hypothesis tests. 1.
Evaluating the replicability of significance tests for comparing learning algorithms
 In PAKDD
, 2004
"... Abstract. Empirical research in learning algorithms for classification tasks generally requires the use of significance tests. The quality of a test is typically judged on Type I error (how often the test indicates a difference when it should not) and Type II error (how often it indicates no differe ..."
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Cited by 28 (0 self)
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Abstract. Empirical research in learning algorithms for classification tasks generally requires the use of significance tests. The quality of a test is typically judged on Type I error (how often the test indicates a difference when it should not) and Type II error (how often it indicates no difference when it should). In this paper we argue that the replicability of a test is also of importance. We say that a test has low replicability if its outcome strongly depends on the particular random partitioning of the data that is used to perform it. We present empirical measures of replicability and use them to compare the performance of several popular tests in a realistic setting involving standard learning algorithms and benchmark datasets. Based on our results we give recommendations on which test to use. 1
Bayesian Model Assessment and Comparison Using CrossValidation Predictive Densities
 Neural Computation
, 2002
"... In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimat ..."
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Cited by 26 (10 self)
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In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate, as it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected utility than some other model. We propose an approach using crossvalidation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions. We also discuss the probabilistic assumptions made and properties of two practical crossvalidation methods, importance sampling and kfold crossvalidation. As illustrative examples, we use MLP neural networks and Gaussian Processes (GP) with Markov chain Monte Carlo sampling in one toy problem and two challenging realworld problems.
No Unbiased Estimator of the Variance of KFold CrossValidation
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2003
"... Most machine learning researchers perform quantitative experiments to estimate generalization error and compare the performance of different algorithms (in particular, their proposed algorithm). In order to be able to draw statistically convincing conclusions, it is important for them to also est ..."
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Cited by 26 (1 self)
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Most machine learning researchers perform quantitative experiments to estimate generalization error and compare the performance of different algorithms (in particular, their proposed algorithm). In order to be able to draw statistically convincing conclusions, it is important for them to also estimate the uncertainty around the error (or error difference) estimate. This paper studies the very commonly used Kfold crossvalidation estimator of generalization performance. The main theorem shows that there exists no universal (valid under all distributions) unbiased estimator of the variance of Kfold crossvalidation. The analysis that accompanies this result is based on the eigendecomposition of the covariance matrix of errors, which has only three different eigenvalues corresponding to three degrees of freedom of the matrix and three components of the total variance. This analysis helps to better understand the nature of the problem and how it can make naive estimators (that don't take into account the error correlations due to the overlap between training and test sets) grossly underestimate variance. This is confirmed by numerical experiments in which the three components of the variance are compared when the difficulty of the learning problem and the number of folds are varied.