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196
Online Learning with Kernels
, 2003
"... Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little u ..."
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Cited by 2029 (128 self)
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Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little use of these methods in an online setting suitable for realtime applications. In this paper we consider online learning in a Reproducing Kernel Hilbert Space. By considering classical stochastic gradient descent within a feature space, and the use of some straightforward tricks, we develop simple and computationally efficient algorithms for a wide range of problems such as classification, regression, and novelty detection. In addition to allowing the exploitation of the kernel trick in an online setting, we examine the value of large margins for classification in the online setting with a drifting target. We derive worst case loss bounds and moreover we show the convergence of the hypothesis to the minimiser of the regularised risk functional. We present some experimental results that support the theory as well as illustrating the power of the new algorithms for online novelty detection. In addition
In defense of onevsall classification
 Journal of Machine Learning Research
, 2004
"... Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This the ..."
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Cited by 202 (0 self)
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Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification. We support our position by means of a critical review of the existing literature, a substantial collection of carefully controlled experimental work, and theoretical arguments.
Regularized multitask learning
, 2004
"... This paper provides a foundation for multi–task learning using reproducing kernel Hilbert spaces of vector–valued functions. In this setting, the kernel is a matrix–valued function. Some explicit examples will be described which go beyond our earlier results in [7]. In particular, we characterize cl ..."
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Cited by 151 (1 self)
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This paper provides a foundation for multi–task learning using reproducing kernel Hilbert spaces of vector–valued functions. In this setting, the kernel is a matrix–valued function. Some explicit examples will be described which go beyond our earlier results in [7]. In particular, we characterize classes of matrix– valued kernels which are linear and are of the dot product or the translation invariant type. We discuss how these kernels can be used to model relations between the tasks and present linear multi–task learning algorithms. Finally, we present a novel proof of the representer theorem for a minimizer of a regularization functional which is based on the notion of minimal norm interpolation. 1
Recognizing Imprecisely Localized, Partially Occluded and Expression Variant Faces from a Single Sample per Class
, 2002
"... The classical way of attempting to solve the face (or object) recognition problem is by using large and representative datasets. In many applications though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate fo ..."
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Cited by 148 (8 self)
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The classical way of attempting to solve the face (or object) recognition problem is by using large and representative datasets. In many applications though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate for imprecisely localized, partially occluded and expression variant faces even when only one single training sample per class is available to the system. To solve the localization problem, we find the subspace (within the feature space, e.g. eigenspace) that represents this error for each of the training images. To resolve the occlusion problem, each face is divided into k local regions which are analyzed in isolation. In contrast with other approaches, where a simple voting space is used, we present a probabilistic method that analyzes how "good" a local match is. To make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images, we weight the results obtained on each local area on the bases of how much of this local area is affected by the expression displayed on the current test image.
The Entire Regularization Path for the Support Vector Machine
, 2004
"... In this paper we argue that the choice of the SVM cost parameter can be critical. We then derive an algorithm that can fit the entire path of SVM solutions for every value of the cost parameter, with essentially the same computational cost as fitting one SVM model. ..."
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Cited by 148 (9 self)
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In this paper we argue that the choice of the SVM cost parameter can be critical. We then derive an algorithm that can fit the entire path of SVM solutions for every value of the cost parameter, with essentially the same computational cost as fitting one SVM model.
1norm Support Vector Machines
 Neural Information Processing Systems
, 2003
"... The standard 2norm SVM is known for its good performance in twoclass classification. In this paper, we consider the 1norm SVM. We argue that the 1norm SVM may have some advantage over the standard 2norm SVM, especially when there are redundant noise features. We also propose an efficient alg ..."
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Cited by 112 (11 self)
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The standard 2norm SVM is known for its good performance in twoclass classification. In this paper, we consider the 1norm SVM. We argue that the 1norm SVM may have some advantage over the standard 2norm SVM, especially when there are redundant noise features. We also propose an efficient algorithm that computes the whole solution path of the 1norm SVM, hence facilitates adaptive selection of the tuning parameter for the 1norm SVM.
Proximal support vector machine classifiers
 Proceedings KDD2001: Knowledge Discovery and Data Mining
, 2001
"... Abstract—A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Each plane is generated such that it is closest to one of the two data sets and as far as possible from the ..."
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Cited by 109 (14 self)
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Abstract—A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set. Each of the two nonparallel proximal planes is obtained by a single MATLAB command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem. Classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems. The effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets. These examples show the advantages of the proposed approach in both computation time and test set correctness. Index Terms—Support vector machines, proximal classification, generalized eigenvalues. 1
The mathematics of learning: Dealing with data
 Notices of the American Mathematical Society
, 2003
"... Draft for the Notices of the AMS Learning is key to developing systems tailored to a broad range of data analysis and information extraction tasks. We outline the mathematical foundations of learning theory and describe a key algorithm of it. 1 ..."
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Cited by 103 (15 self)
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Draft for the Notices of the AMS Learning is key to developing systems tailored to a broad range of data analysis and information extraction tasks. We outline the mathematical foundations of learning theory and describe a key algorithm of it. 1
Kernel Logistic Regression and the Import Vector Machine
 Journal of Computational and Graphical Statistics
, 2001
"... The support vector machine (SVM) is known for its good performance in binary classification, but its extension to multiclass classification is still an ongoing research issue. In this paper, we propose a new approach for classification, called the import vector machine (IVM), which is built on ker ..."
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Cited by 91 (3 self)
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The support vector machine (SVM) is known for its good performance in binary classification, but its extension to multiclass classification is still an ongoing research issue. In this paper, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in binary classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the "support points" of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a computational advantage over the SVM, especially when the size of the training data set is large. 1
Everything Old Is New Again: A Fresh Look at Historical Approaches
 in Machine Learning. PhD thesis, MIT
, 2002
"... 2 Everything Old Is New Again: A Fresh Look at Historical ..."
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Cited by 88 (6 self)
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2 Everything Old Is New Again: A Fresh Look at Historical