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60
On the algorithmic implementation of multiclass kernelbased vector machines
 Journal of Machine Learning Research
"... In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic ob ..."
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Cited by 363 (13 self)
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In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function. Unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks, our notion of margin yields a direct method for training multiclass predictors. By using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size. We describe an efficient fixedpoint algorithm for solving the reduced optimization problems and prove its convergence. We then discuss technical details that yield significant running time improvements for large datasets. Finally, we describe various experiments with our approach comparing it to previously studied kernelbased methods. Our experiments indicate that for multiclass problems we attain stateoftheart accuracy.
Logistic Regression, AdaBoost and Bregman Distances
, 2000
"... We give a unified account of boosting and logistic regression in which each learning problem is cast in terms of optimization of Bregman distances. The striking similarity of the two problems in this framework allows us to design and analyze algorithms for both simultaneously, and to easily adapt al ..."
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Cited by 203 (43 self)
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We give a unified account of boosting and logistic regression in which each learning problem is cast in terms of optimization of Bregman distances. The striking similarity of the two problems in this framework allows us to design and analyze algorithms for both simultaneously, and to easily adapt algorithms designed for one problem to the other. For both problems, we give new algorithms and explain their potential advantages over existing methods. These algorithms can be divided into two types based on whether the parameters are iteratively updated sequentially (one at a time) or in parallel (all at once). We also describe a parameterized family of algorithms which interpolates smoothly between these two extremes. For all of the algorithms, we give convergence proofs using a general formalization of the auxiliaryfunction proof technique. As one of our sequentialupdate algorithms is equivalent to AdaBoost, this provides the first general proof of convergence for AdaBoost. We show that all of our algorithms generalize easily to the multiclass case, and we contrast the new algorithms with iterative scaling. We conclude with a few experimental results with synthetic data that highlight the behavior of the old and newly proposed algorithms in different settings.
On the Learnability and Design of Output Codes for Multiclass Problems
 In Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
, 2000
"... . Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problem ..."
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Cited by 161 (5 self)
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. Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problems. For the design problem of discrete codes, which have been used extensively in previous works, we present mostly negative results. We then introduce the notion of continuous codes and cast the design problem of continuous codes as a constrained optimization problem. We describe three optimization problems corresponding to three different norms of the code matrix. Interestingly, for the l 2 norm our formalism results in a quadratic program whose dual does not depend on the length of the code. A special case of our formalism provides a multiclass scheme for building support vector machines which can be solved efficiently. We give a time and space efficient algorithm for solving the quadratic program. We describe preliminary experiments with synthetic data show that our algorithm is often two orders of magnitude faster than standard quadratic programming packages. We conclude with the generalization properties of the algorithm. Keywords: Multiclass categorization,output coding, SVM 1.
Statistical Behavior and Consistency of Classification Methods based on Convex Risk Minimization
, 2001
"... We study how close the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. ..."
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Cited by 112 (6 self)
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We study how close the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. We show that such a classification scheme can be generally regarded as a (non maximumlikelihood) conditional inclass probability estimate, and we use this analysis to compare various convex loss functions that have appeared in the literature. Furthermore, the theoretical insight allows us to design good loss functions with desirable properties. Another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization.
Fast and Robust Classification using Asymmetric AdaBoost and a Detector Cascade
 Advances in Neural Information Processing System 14
, 2001
"... This paper develops a new approach for extremely fast detection in domains where the distribution of positive and negative examples is highly skewed (e.g. face detection or database retrieval). In such domains a cascade of simple classifiers each trained to achieve high detection rates and modes ..."
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Cited by 93 (0 self)
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This paper develops a new approach for extremely fast detection in domains where the distribution of positive and negative examples is highly skewed (e.g. face detection or database retrieval). In such domains a cascade of simple classifiers each trained to achieve high detection rates and modest false positive rates can yield a final detector with many desirable features: including high detection rates, very low false positive rates, and fast performance. Achieving extremely high detection rates, rather than low error, is not a task typically addressed by machine learning algorithms.
The 2001 Trading Agent Competition
 IEEE Internet Computing
, 2000
"... The 2001 Trading Agent Competition was the second in a series of events aiming to shed light on research issues in automating trading strategies. Based on a challenging market scenario in the domain of travel shopping, the competition presents agents with difficult issues in bidding strategy, market ..."
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Cited by 90 (10 self)
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The 2001 Trading Agent Competition was the second in a series of events aiming to shed light on research issues in automating trading strategies. Based on a challenging market scenario in the domain of travel shopping, the competition presents agents with difficult issues in bidding strategy, market prediction, and resource allocation. Entrants in 2001 demonstrated substantial progress over the prior year, with the overall level of competence exhibited suggesting that trading in online markets is a viable domain for highly autonomous agents.
Incorporating Prior Knowledge into Boosting
, 2002
"... We describe a modification to the AdaBoost algorithm that permits the incorporation of prior human knowledge as a means of compensating for a shortage of training data. We give a convergence result for the algorithm. ..."
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Cited by 55 (0 self)
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We describe a modification to the AdaBoost algorithm that permits the incorporation of prior human knowledge as a means of compensating for a shortage of training data. We give a convergence result for the algorithm.
Classifier Chains for Multilabel Classification
"... Abstract. The widely known binary relevance method for multilabel classification, which considers each label as an independent binary problem, has been sidelined in the literature due to the perceived inadequacy of its labelindependence assumption. Instead, most current methods invest considerable ..."
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Cited by 42 (2 self)
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Abstract. The widely known binary relevance method for multilabel classification, which considers each label as an independent binary problem, has been sidelined in the literature due to the perceived inadequacy of its labelindependence assumption. Instead, most current methods invest considerable complexity to model interdependencies between labels. This paper shows that binary relevancebased methods have much to offer, especially in terms of scalability to large datasets. We exemplify this with a novel chaining method that can model label correlations while maintaining acceptable computational complexity. Empirical evaluation over a broad range of multilabel datasets with a variety of evaluation metrics demonstrates the competitiveness of our chaining method against related and stateoftheart methods, both in terms of predictive performance and time complexity. 1
A Geometric Approach to Leveraging Weak Learners
 Computational Learning Theory: 4th European Conference (EuroCOLT '99
, 1998
"... . AdaBoost is a popular and effective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over t ..."
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Cited by 23 (5 self)
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. AdaBoost is a popular and effective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over the sample given to the weak learner is the direction of steepest descent. We introduce a new leveraging algorithm based on a natural potential function. For this potential function, the direction of steepest descent can have negative components. Therefore we provide two transformations for obtaining suitable distributions from these directions of steepest descent. The resulting algorithms have bounds that are incomparable to AdaBoost's, and their empirical performance is similar to AdaBoost's. 1 Introduction Algorithms like AdaBoost [7] that are able to improve the hypotheses generated by weak learning methods have great potential and practical benefits. We call any such algorithm a leverag...
Boosting for document routing
 In Proceedings of CIKM00, 9th ACM Int. Conf. on Information and Knowledge Management
, 2000
"... RankBoost is a recently proposed algorithm for learning ranking functions. It is simple to implement and has strong justifications from computational learning theory. We describe the algorithm and present experimental results on applying it to the document routing problem. The first set of results a ..."
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Cited by 23 (0 self)
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RankBoost is a recently proposed algorithm for learning ranking functions. It is simple to implement and has strong justifications from computational learning theory. We describe the algorithm and present experimental results on applying it to the document routing problem. The first set of results applies RankBoost to a text representation produced using modern term weighting methods. Performance of RankBoost is somewhat inferior to that of a stateoftheart routing algorithm which is, however, more complex and less theoretically justified than RankBoost. RankBoost achieves comparable performance to the stateoftheart algorithm when combined with feature or example selection heuristics. Our second set of results examines the behavior of RankBoost when it has to learn not only a ranking function but also all aspects of term weighting from raw data. Performance is usually, though not always, less good here, but the term weighting functions implicit in the resulting ranking functions are intriguing, and the approach could easily be adapted to mixtures of textual and nontextual data.