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57
Stacked generalization
 Neural Networks
, 1992
"... Abstract: This paper introduces stacked generalization, a scheme for minimizing the generalization error rate of one or more generalizers. Stacked generalization works by deducing the biases of the generalizer(s) with respect to a provided learning set. This deduction proceeds by generalizing in a s ..."
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Cited by 685 (8 self)
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Abstract: This paper introduces stacked generalization, a scheme for minimizing the generalization error rate of one or more generalizers. Stacked generalization works by deducing the biases of the generalizer(s) with respect to a provided learning set. This deduction proceeds by generalizing in a second space whose inputs are (for example) the guesses of the original generalizers when taught with part of the learning set and trying to guess the rest of it, and whose output is (for example) the correct guess. When used with multiple generalizers, stacked generalization can be seen as a more sophisticated version of crossvalidation, exploiting a strategy more sophisticated than crossvalidation’s crude winnertakesall for combining the individual generalizers. When used with a single generalizer, stacked generalization is a scheme for estimating (and then correcting for) the error of a generalizer which has been trained on a particular learning set and then asked a particular question. After introducing stacked generalization and justifying its use, this paper presents two numerical experiments. The first demonstrates how stacked generalization improves upon a set of separate generalizers for the NETtalk task of translating text to phonemes. The second demonstrates how stacked generalization improves the performance of a single surfacefitter. With the other experimental evidence in the literature, the usual arguments supporting crossvalidation, and the abstract justifications presented in this paper, the conclusion is that for almost any realworld generalization problem one should use some version of stacked generalization to minimize the generalization error rate. This paper ends by discussing some of the variations of stacked generalization, and how it touches on other fields like chaos theory. Key Words: generalization and induction, combining generalizers, learning set preprocessing, crossvalidation, error estimation and correction.
An experimental and theoretical comparison of model selection methods. Machine Learning 27
, 1997
"... In the model selection problem, we must balance the complexity of a statistical model with its goodness of fit to the training data. This problem arises repeatedly in statistical estimation, machine learning, and scientific inquiry in general. ..."
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Cited by 116 (5 self)
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In the model selection problem, we must balance the complexity of a statistical model with its goodness of fit to the training data. This problem arises repeatedly in statistical estimation, machine learning, and scientific inquiry in general.
Estimating the Generalization Performance of an SVM Efficiently
, 2000
"... This paper proposes and analyzes an approach to estimating the generalization performance of a support vector machine (SVM) for text classification. Without any computation intensive resampling, the new estimators are computationally much more ecient than crossvalidation or bootstrap, since they ca ..."
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Cited by 116 (1 self)
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This paper proposes and analyzes an approach to estimating the generalization performance of a support vector machine (SVM) for text classification. Without any computation intensive resampling, the new estimators are computationally much more ecient than crossvalidation or bootstrap, since they can be computed immediately from the form of the hypothesis returned by the SVM. Moreover, the estimators delevoped here address the special performance measures needed for text classification. While they can be used to estimate error rate, one can also estimate the recall, the precision, and the F 1 . A theoretical analysis and experiments on three text classification collections show that the new method can effectively estimate the performance of SVM text classifiers in a very efficient way.
Covariate shift adaptation by importance weighted cross validation
, 2000
"... A common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase. However, this assumption is not satisfied, for example, when the outside of the training region is extrapo ..."
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Cited by 116 (53 self)
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A common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase. However, this assumption is not satisfied, for example, when the outside of the training region is extrapolated. The situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift. Under the covariate shift, standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained. In this paper, we propose a new method called importance weighted cross validation (IWCV), for which we prove its unbiasedness even under the covariate shift. The IWCV procedure is the only one that can be applied for unbiased classification under covariate shift, whereas alternatives to IWCV exist for regression. The usefulness of our proposed method is illustrated by simulations, and furthermore demonstrated in the braincomputer interface, where strong nonstationarity effects can be seen between training and test sessions. c2000 Masashi Sugiyama, Matthias Krauledat, and KlausRobert Müller.
Improving Regression Estimation: Averaging Methods for Variance Reduction with Extensions to General Convex Measure Optimization
, 1993
"... ..."
R: Prediction error estimation: a comparison of resampling methods
 Bioinformatics
"... In genomic studies, thousands of features are collected on relatively few samples. One of the goals of these studies is to build classifiers to predict the outcome of future observations. There are three inherent steps to this process: feature selection, model selection, and prediction assessment. W ..."
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Cited by 76 (11 self)
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In genomic studies, thousands of features are collected on relatively few samples. One of the goals of these studies is to build classifiers to predict the outcome of future observations. There are three inherent steps to this process: feature selection, model selection, and prediction assessment. With a focus on prediction assessment, we compare several methods for estimating the ’true ’ prediction error of a prediction model in the presence of feature selection. For small studies where features are selected from thousands of candidates, the resubstitution and simple splitsample estimates are seriously biased. In these small samples, leaveoneout (LOOCV), 10fold crossvalidation (CV), and the.632+ bootstrap have the smallest bias for diagonal discriminant analysis, nearest neighbor, and classification trees. LOOCV and 10fold CV have the smallest bias for linear discriminant analysis. Additionally, LOOCV, 5 and 10fold CV, and the.632+ bootstrap have the lowest mean square error. The.632+ bootstrap is quite biased in small sample sizes with strong signal to noise ratios. The differences in performance among resampling methods are reduced as the number of specimens available increases. Supplementary Information: R code for simulations and analyses is available from the authors. Tables and figures for all analyses are available at
Preventing "Overfitting" of CrossValidation Data
 In Proceedings of the Fourteenth International Conference on Machine Learning
, 1997
"... Suppose that, for a learning task, we have to select one hypothesis out of a set of hypotheses (that may, for example, have been generated by multiple applications of a randomized learning algorithm). A common approach is to evaluate each hypothesis in the set on some previously unseen crossvalidat ..."
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Cited by 45 (1 self)
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Suppose that, for a learning task, we have to select one hypothesis out of a set of hypotheses (that may, for example, have been generated by multiple applications of a randomized learning algorithm). A common approach is to evaluate each hypothesis in the set on some previously unseen crossvalidation data, and then to select the hypothesis that had the lowest crossvalidation error. But when the crossvalidation data is partially corrupted such as by noise, and if the set of hypotheses we are selecting from is large, then "folklore" also warns about "overfitting" the crossvalidation data [Klockars and Sax, 1986, Tukey, 1949, Tukey, 1953]. In this paper, we explain how this "overfitting" really occurs, and show the surprising result that it can be overcome by selecting a hypothesis with a higher crossvalidation error, over others with lower crossvalidation errors. We give reasons for not selecting the hypothesis with the lowest crossvalidation error, and propose a new algorithm, L...
On Overfitting Avoidance As Bias
 SFI TR
, 1993
"... In supervised learning it is commonly believed that penalizing complex functions helps one avoid "overfitting" functions to data, and therefore improves generalization. It is also commonly believed that crossvalidation is an effective way to choose amongst algorithms for fitting functions ..."
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Cited by 34 (7 self)
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In supervised learning it is commonly believed that penalizing complex functions helps one avoid "overfitting" functions to data, and therefore improves generalization. It is also commonly believed that crossvalidation is an effective way to choose amongst algorithms for fitting functions to data. In a recent paper, Schaffer (1993) presents experimental evidence disputing these claims. The current paper consists of a formal analysis of these contentions of Schaffer's. It proves that his contentions are valid, although some of his experiments must be interpreted with caution.