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The Weighted Majority Algorithm (1992) [441 citations — 38 self]

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@MISC{Littlestone92theweighted,
    author = {Nick Littlestone and Manfred K. Warmuth},
    title = {The Weighted Majority Algorithm},
    year = {1992}
}

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Abstract:

We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials, with a prediction to be made in each, and the goal of the learner is to make few mistakes. We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well, but the learner does not know which one. A simple and effective method, based on weighted voting, is introduced for constructing a compound algorithm in such a circumstance. We call this method the Weighted Majority Algorithm. We show that this algorithm is robust in the presence of errors in the data. We discuss various versions of the Weighted Majority Algorithm and prove mistake bounds for them that are closely related to the mistake bounds of the best algorithms of the pool. For example, given a sequence of trials, if there is an algorithm in the pool A that makes at most m mistakes then the Weighted Majority Algorithm will make at most c(log jAj + m) mi...

Citations

1422	Probability and Measure – Billingsley - 1995
528	Learnability and the Vapnik -Chervonenkis dimension – Blumer, Ehrenfeucht, et al. - 1989
503	Learning quickly when irrelevant attributes abound: A new linear-threshold algorithms – Littlestone - 1988
92	Mistake bounds and logarithmic linear-threshold learning algorithms – Littlestone - 1989
88	Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension – Haussler, Kearns, et al. - 1994
60	From on-line to batch learning – Littlestone - 1989
45	On the prediction of general recursive functions – Barzdin, Freivald - 1972
45	A statistical approach to learning and generalization in layered neural networks – Levin, Tishby, et al. - 1990
34	Learning nested differences of intersection-closedclasses – Helmbold, Sloan, et al. - 1989
32	Learning Probabilistic Prediction Functions – DeSantis, Markowski, et al. - 1992
14	Calculation of the learning curve of Bayes optimal classification algorithm for learning a perceptron with noise – Opper, Haussler - 1991
9	Trade-off among parameters affecting inductive inference – Freivalds, Smith, et al. - 1989
3	Freivalds. Prognozirovanie i predel'nyi sintez effektivno perechislimykh klassov funktsii (prediction and limit synthesis of effectively enumerable classes of functions – Barzdin, V - 1974