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62
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
Online passiveaggressive algorithms
 JMLR
, 2006
"... We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new alg ..."
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Cited by 293 (22 self)
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We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new algorithms and accompanying loss bounds for hingeloss regression and uniclass. We also get refined loss bounds for previously studied classification algorithms. 1
Ultraconservative Online Algorithms for Multiclass Problems
 Journal of Machine Learning Research
, 2001
"... In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarityscore between each prototype and the input instance and th ..."
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Cited by 249 (23 self)
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In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarityscore between each prototype and the input instance and then sets the predicted label to be the index of the prototype achieving the highest similarity. To design and analyze the learning algorithms in this paper we introduce the notion of ultraconservativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarityscores which are higher than the score of the correct label's prototype. We start by describing a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarityscores. We then discuss a specific online algorithm that seeks a set of prototypes which have a small norm. The resulting algorithm, which we term MIRA (for Margin Infused Relaxed Algorithm) is ultraconservative as well. We derive mistake bounds for all the algorithms and provide further analysis of MIRA using a generalized notion of the margin for multiclass problems.
Fast Kernel Classifiers With Online And Active Learning
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This ..."
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Cited by 102 (17 self)
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Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This contribution proposes an empirical answer. We first present an online SVM algorithm based on this premise. LASVM yields competitive misclassification rates after a single pass over the training examples, outspeeding stateoftheart SVM solvers. Then we show how active example selection can yield faster training, higher accuracies, and simpler models, using only a fraction of the training example labels.
A New Approximate Maximal Margin Classification Algorithm
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2001
"... A new incremental learning algorithm is described which approximates the maximal margin hyperplane w.r.t. norm p 2 for a set of linearly separable data. Our algorithm, called alma p (Approximate Large Margin algorithm w.r.t. norm p), takes O (p 1) 2 2 corrections to separate the data wi ..."
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Cited by 87 (6 self)
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A new incremental learning algorithm is described which approximates the maximal margin hyperplane w.r.t. norm p 2 for a set of linearly separable data. Our algorithm, called alma p (Approximate Large Margin algorithm w.r.t. norm p), takes O (p 1) 2 2 corrections to separate the data with pnorm margin larger than (1 ) , where is the (normalized) pnorm margin of the data. alma p avoids quadratic (or higherorder) programming methods. It is very easy to implement and is as fast as online algorithms, such as Rosenblatt's Perceptron algorithm. We performed extensive experiments on both realworld and artificial datasets. We compared alma 2 (i.e., alma p with p = 2) to standard Support vector Machines (SVM) and to two incremental algorithms: the Perceptron algorithm and Li and Long's ROMMA. The accuracy levels achieved by alma 2 are superior to those achieved by the Perceptron algorithm and ROMMA, but slightly inferior to SVM's. On the other hand, alma 2 is quite faster and easier to implement than standard SVM training algorithms. When learning sparse target vectors, alma p with p > 2 largely outperforms Perceptronlike algorithms, such as alma 2 .
Online Bayes Point Machines
"... We present a new and simple algorithm for learning large margin classi ers that works in a truly online manner. The algorithm generates a linear classi er by averaging the weights associated with several perceptronlike algorithms run in parallel in order to approximate the Bayes point. A rand ..."
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Cited by 69 (3 self)
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We present a new and simple algorithm for learning large margin classi ers that works in a truly online manner. The algorithm generates a linear classi er by averaging the weights associated with several perceptronlike algorithms run in parallel in order to approximate the Bayes point. A random subsample of the incoming data stream is used to ensure diversity in the perceptron solutions. We experimentally study the algorithm's performance on online and batch learning settings.
A secondorder perceptron algorithm
, 2005
"... Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptr ..."
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Cited by 59 (21 self)
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Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptron, and analyze its performance within the mistake bound model of online learning. The bound achieved by our algorithm depends on the sensitivity to secondorder data information and is the best known mistake bound for (efficient) kernelbased linearthreshold classifiers to date. This mistake bound, which strictly generalizes the wellknown Perceptron bound, is expressed in terms of the eigenvalues of the empirical data correlation matrix and depends on a parameter controlling the sensitivity of the algorithm to the distribution of these eigenvalues. Since the optimal setting of this parameter is not known a priori, we also analyze two variants of the secondorder Perceptron algorithm: one that adaptively sets the value of the parameter in terms of the number of mistakes made so far, and one that is parameterless, based on pseudoinverses.
Online classification on a budget
 Advances in Neural Information Processing Systems 16
, 2004
"... Online algorithms for classification often require vast amounts of memory and computation time when employed in conjunction with kernel functions. In this paper we describe and analyze a simple approach for an onthefly reduction of the number of past examples used for prediction. Experiments perfo ..."
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Cited by 44 (6 self)
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Online algorithms for classification often require vast amounts of memory and computation time when employed in conjunction with kernel functions. In this paper we describe and analyze a simple approach for an onthefly reduction of the number of past examples used for prediction. Experiments performed with real datasets show that using the proposed algorithmic approach with a single epoch is competitive with the support vector machine (SVM) although the latter, being a batch algorithm, accesses each training example multiple times. 1
WorstCase Analysis of Selective Sampling for Linear Classification
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... A selective sampling algorithm is a learning algorithm for classification that, based on the past observed data, decides whether to ask the label of each new instance to be classified. In this paper, we introduce a general technique for turning linearthreshold classification algorithms from the ..."
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Cited by 41 (5 self)
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A selective sampling algorithm is a learning algorithm for classification that, based on the past observed data, decides whether to ask the label of each new instance to be classified. In this paper, we introduce a general technique for turning linearthreshold classification algorithms from the general additive family into randomized selective sampling algorithms. For the most popular algorithms in this family we derive mistake bounds that hold for individual sequences of examples. These bounds
The Forgetron: A kernelbased perceptron on a fixed budget
 In Advances in Neural Information Processing Systems 18
, 2005
"... The Perceptron algorithm, despite its simplicity, often performs well on online classification problems. The Perceptron becomes especially effective when it is used in conjunction with kernels. However, a common difficulty encountered when implementing kernelbased online algorithms is the amount of ..."
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Cited by 36 (5 self)
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The Perceptron algorithm, despite its simplicity, often performs well on online classification problems. The Perceptron becomes especially effective when it is used in conjunction with kernels. However, a common difficulty encountered when implementing kernelbased online algorithms is the amount of memory required to store the online hypothesis, which may grow unboundedly. In this paper we describe and analyze a new infrastructure for kernelbased learning with the Perceptron while adhering to a strict limit on the number of examples that can be stored. We first describe a template algorithm, called the Forgetron, for online learning on a fixed budget. We then provide specific algorithms and derive a unified mistake bound for all of them. To our knowledge, this is the first online learning paradigm which, on one hand, maintains a strict limit on the number of examples it can store and, on the other hand, entertains a relative mistake bound. We also present experiments with real datasets which underscore the merits of our approach. 1