Zur Theorie der Gesellschaftsspiele

Neumann, John von

doi:10.1007/bf01448847

Cited by 2,029 publications

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“…If one assumes that the base learner always achieves a weighted training error t ≤ 1/2 − γ/2 with γ > 0, then AdaBoost generates a hypothesis with margin larger than γ/2 [167,27]. However, from the Min-Max theorem of linear programming [193] (see Theorem 4 below) one finds that the achievable margin ρ * is at least γ [69,27,72].…”

Section: Boosting and Large Marginsmentioning

confidence: 99%

An Introduction to Boosting and Leveraging

Meir

Rätsch

2003

Advanced Lectures on Machine Learning

275

186

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Abstract. We provide an introduction to theoretical and practical aspects of Boosting and Ensemble learning, providing a useful reference for researchers in the field of Boosting as well as for those seeking to enter this fascinating area of research. We begin with a short background concerning the necessary learning theoretical foundations of weak learners and their linear combinations. We then point out the useful connection between Boosting and the Theory of Optimization, which facilitates the understanding of Boosting and later on enables us to move on to new Boosting algorithms, applicable to a broad spectrum of problems. In order to increase the relevance of the paper to practitioners, we have added remarks, pseudo code, "tricks of the trade", and algorithmic considerations where appropriate. Finally, we illustrate the usefulness of Boosting algorithms by giving an overview of some existing applications. The main ideas are illustrated on the problem of binary classification, although several extensions are discussed.

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Section: Boosting and Large Marginsmentioning

confidence: 99%

An Introduction to Boosting and Leveraging

Meir

Rätsch

2003

Advanced Lectures on Machine Learning

275

186

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“…The following theorem, which includes a theorem of Von Neumann [6], which in turn implies the fundamental theorem of two-person zero sum games was proved by Fan ([2] and [3]) and also Browder [1] PROOF: AS before, let P a : X -> X a be the projection of X onto X a for each a. For each a £ / , let P a (K) = X' a which is a non-empty compact convex set in E a .…”

Section: ) Is Open In X a ; (B) For Each A £ I And Each X A £ X A Tmentioning

confidence: 99%

On two theorems concerning sets with convex sections

Tarafdar

1988

Bull. Austral. Math. Soc.

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In this note two theorems of Ma and Fan concerning sets with convex sections are generalised.In this note we generalise two theorems of Fan concerning sets with convex sections. These generalisations involve a relaxation of the compactness conditions on the family of sets. Fan ([4], Theorem 16) proved Theorem I which includes the theorem of Ma [5]. These results are usually proved by using fixed point theorems or the KnasterKuratowski-Mazurkiewicz theorem.The following notation is used throughout. Let {X a -a £ 1} be a family of nonempty sets, where I is an index set. We denote the cartesian product by X, that is X = II X a and for each a £ I, X a = H Xa. We use this theorem to prove the following extended version in which we remove the compactness condition on each X a and add condition (c) below. Condition (c) has been used by Fan ([4], Theorem 15) in the case of a single finite family.

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“…Neumann and Morgenstern (1944), and ultimately, laid the groundwork for the introduction of an interdisciplinary research field of game theory or the strategic game. More importantly, there are the earlier works of many others, including Neumann (1928) and his Zur Theorie der Gesellschaftsspiele (On the Theory of Parlor Games), which also predate the 1944 work of Neumann and Morgenstern.…”

Section: Resultsmentioning

confidence: 99%

Relation of Game Theory to Economic History and Marginalism

Killion

2009

SSRN Journal

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The Article presents a brief survey of economic history, by emphasizing the earlier history of neo-classical economic theory and the economic theory of marginal utility. The Articles does so for exploring the relation of game theory or the strategic game to developments in the field or science of economics, especially developments in economic thought occurring during the earlier marginal revolution or the economic history of marginalism. By doing so, the Article intends to show, though most attribute the new science of modern game theory to the field of mathematics, that the influence of corresponding or correlating developments in the field, science or discipline of economics was equally influential in the birth of game theory or the strategic game.

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Zur Theorie der Gesellschaftsspiele

Cited by 2,029 publications

References 0 publications

An Introduction to Boosting and Leveraging

An Introduction to Boosting and Leveraging

On two theorems concerning sets with convex sections

Relation of Game Theory to Economic History and Marginalism

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