The weighted majority algorithm

Littlestone, Nick; Warmuth, Manfred K.

doi:10.1109/sfcs.1989.63487

Cited by 477 publications

(490 citation statements)

References 3 publications

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“…The Multiplicative Weights Update algorithm (MW algorithm) is an adaptation of the Winnow algorithm (Littlestone & Warmuth, 1989) for a generalized experts framework as described in (Freund & Schapire, 1997). This framework was implicitly used by (Plotkin et al, 1991) for solving several fractional packing and covering problems and was formalized and extended to semi-definite programs in (Arora et al, 2005a).…”

Section: Multiplicative Weights Update Algorithmmentioning

confidence: 99%

Rank minimization via online learning

Meka

Jain

Caramanis

et al. 2008

Proceedings of the 25th International Conference on Machine Learning - ICML '08

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Minimum rank problems arise frequently in machine learning applications and are notoriously difficult to solve due to the non-convex nature of the rank objective. In this paper, we present the first online learning approach for the problem of rank minimization of matrices over polyhedral sets. In particular, we present two online learning algorithms for rank minimization -our first algorithm is a multiplicative update method based on a generalized experts framework, while our second algorithm is a novel application of the online convex programming framework (Zinkevich, 2003). In the latter, we flip the role of the decision maker by making the decision maker search over the constraint space instead of feasible points, as is usually the case in online convex programming. A salient feature of our online learning approach is that it allows us to give provable approximation guarantees for the rank minimization problem over polyhedral sets. We demonstrate the effectiveness of our methods on synthetic examples, and on the real-life application of low-rank kernel learning.

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Section: Multiplicative Weights Update Algorithmmentioning

confidence: 99%

Rank minimization via online learning

Meka

Jain

Caramanis

et al. 2008

Proceedings of the 25th International Conference on Machine Learning - ICML '08

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“…They appear in context of range-space searching [7] in computational geometry, PAC learning in computational learning theory, and the study of types in mathematical logic. The basic situation of interest is: Given a collection of subsets C from some universe X, analyze the relationship of A ∈ C to the finite subsets of X. Warmuth and Littlestone [10] noted a structural characteristic of some Fig. 1 Select the leftmost, rightmost, lowest and highest points included in the rectangle set systems C which allows this question to be reduced to questions about subsets of X of some uniformly bounded size.…”

Section: Introductionmentioning

confidence: 99%

Compression Schemes, Stable Definable Families, and o-Minimal Structures

Johnson

Laskowski

2009

Discrete Comput Geom

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We show that any family of sets uniformly definable in an o-minimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula.As a consequence, the combinatorial complexity (or density) of any definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula.Extended compression schemes for uniformly definable families corresponding to stable formulas are also shown to exist.

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“…The machine learning literature has studied a variety of meta methods such as bagging, stacking, or boosting [5,29,19,13], and even combinations of heterogeneous learners (e.g., [30]). There are also methods available for combining different clustering methods [26,12,24].…”

Section: Contributionmentioning

confidence: 99%

Automatic Document Organization in a P2P Environment

Siersdorfer¹,

Sizov²

2006

Lecture Notes in Computer Science

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Abstract. This paper describes an efficient method to construct reliable machine learning applications in peer-to-peer (P2P) networks by building ensemble based meta methods. We consider this problem in the context of distributed Web exploration applications like focused crawling. Typical applications are user-specific classification of retrieved Web contents into personalized topic hierarchies as well as automatic refinements of such taxonomies using unsupervised machine learning methods (e.g. clustering). Our approach is to combine models from multiple peers and to construct the advanced decision model that takes the generalization performance of multiple 'local' peer models into account. In addition, meta algorithms can be applied in a restrictive manner, i.e. by leaving out some 'uncertain' documents. The results of our systematic evaluation show the viability of the proposed approach.

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The weighted majority algorithm

Cited by 477 publications

References 3 publications

Rank minimization via online learning

Rank minimization via online learning

Compression Schemes, Stable Definable Families, and o-Minimal Structures

Automatic Document Organization in a P2P Environment

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