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An introduction to boosting and leveraging
 Advanced Lectures on Machine Learning, LNCS
, 2003
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Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice
, 2001
"... After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems. Yet, large problems arising from several concrete applications routinely defeat the very best linear programming ..."
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Cited by 70 (4 self)
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After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems. Yet, large problems arising from several concrete applications routinely defeat the very best linear programming codes, running on the fastest computing hardware. Moreover, this is a trend that may well continue and intensify, as problem sizes escalate and the need for fast algorithms becomes more stringent. Traditionally, the focus in optimization algorithms, and in particular, in algorithms for linear programming, has been to solve problems "to optimality." In concrete implementations, this has always meant the solution ofproblems to some finite accuracy (for example, eight digits). An alternative approach would be to explicitly, and rigorously, trade o# accuracy for speed. One motivating factor is that in many practical applications, quickly obtaining a partially accurate solution is much preferable to obtaining a very accurate solution very slowly. A secondary (and independent) consideration is that the input data in many practical applications has limited accuracy to begin with. During the last ten years, a new body ofresearch has emerged, which seeks to develop provably good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context ofthe modern theory ofalgorithms. The result ofthis work has been a family ofalgorithms with solid theoretical foundations and with growing experimental success. In this manuscript we will study these algorithms, starting with some ofthe very earliest examples, and through the latest theoretical and computational developments.
Constructing Boosting Algorithms from SVMs: An Application to Oneclass Classification
, 2002
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Sparse Regression Ensembles in Infinite and Finite Hypothesis Spaces
, 2000
"... We examine methods for constructing regression ensembles based on a linear program (LP). The ensemble regression function consists of linear combina tions of base hypotheses generated by some boostingtype base learning algorithm. Unlike the classification case, for regression the set of possible h ..."
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Cited by 18 (9 self)
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We examine methods for constructing regression ensembles based on a linear program (LP). The ensemble regression function consists of linear combina tions of base hypotheses generated by some boostingtype base learning algorithm. Unlike the classification case, for regression the set of possible hypotheses producible by the base learning algorithm may be infinite. We explicitly tackle the issue of how to define and solve ensemble regression when the hypothesis space is infinite. Our approach is based on a semiinfinite linear program that has an infinite number of constraints and a finite number of variables. We show that the regression problem is well posed for infinite hypothesis spaces in both the primal and dual spaces. Most importantly, we prove there exists an optimal solution to the infinite hypothesisspace problem consisting of a finite number of hypothesis. We propose two algorithms for solving the infinite and finite hypothesis problems. One uses a column generation simplextype algorithm and the other adopts an exponential barrier approach. Furthermore, we give sufficient conditions for the base learning algorithm and the hypothesis set to be used for infinite regression ensembles. Computational resultsshow that these methods are extremely promising.
Barrier Boosting
"... Boosting algorithms like AdaBoost and ArcGV are iterative strategies to minimize a constrained objective function, equivalent to Barrier algorithms. ..."
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Cited by 18 (7 self)
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Boosting algorithms like AdaBoost and ArcGV are iterative strategies to minimize a constrained objective function, equivalent to Barrier algorithms.
SVM and Boosting: One Class
"... We show via an equivalence of mathematical programs that a Support Vector (SV) algorithm can be translated into an equivalent boostinglike algorithm and vice versa. We exemplify this translation procedure for a new algorithm oneclass Leveraging starting from the oneclass Support Vector Machine ..."
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Cited by 6 (1 self)
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We show via an equivalence of mathematical programs that a Support Vector (SV) algorithm can be translated into an equivalent boostinglike algorithm and vice versa. We exemplify this translation procedure for a new algorithm oneclass Leveraging starting from the oneclass Support Vector Machines (1SVM) . This is a first step towards unsupervised learning in a Boosting framework.
Analysis Of Nonstationary Time Series By Mixtures Of SelfOrganizing Predictors
 In Proceedings of IEEE Neural Networks for Signal Processing Workshop
, 2000
"... . We present a method for the analysis of time series from drifting or switching dynamics. In extension to existing approaches that identify switches or drifts between stationary dynamical modes, the method allows to analyze even continuously varying dynamics and can identify mixtures of more than t ..."
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Cited by 2 (0 self)
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. We present a method for the analysis of time series from drifting or switching dynamics. In extension to existing approaches that identify switches or drifts between stationary dynamical modes, the method allows to analyze even continuously varying dynamics and can identify mixtures of more than two dynamical modes. The architecture is based on a mixture of selforganizing NadarayaWatson kernel estimators. The mixture model is trained by barrier optimization, a technique for constrained optimization problems. We apply the proposed method to artificially generated data and EEG recordings from the wake/sleep transition. INTRODUCTION Time series from alternating dynamics are ubiquitous in realworld systems like, for example, speech, climatological data, physiological recordings (EEG, MEG), and financial markets. It is therefore important to find methods that can deal with timevarying dynamical systems, which possibly might also be nonlinear. In [9, 14], we introduced the annealed ...