Journal ArticleDOI
Adaptive linear procedures under general conditions
TLDR
Under mild conditions on the observation processes the almost sure convergence properties of linear stochastic approximation are summarized for least squares and for some of its applications: adaptive filtering, echo cancellation, detection of binary data in Gaussian noise, identification, and linear classification.Abstract:
Under mild conditions on the observation processes the almost sure convergence properties of linear stochastic approximation are summarized for least squares and for some of its applications: adaptive filtering, echo cancellation, detection of binary data in Gaussian noise, identification, and linear classification.read more
Citations
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Book
A Probabilistic Theory of Pattern Recognition
TL;DR: The Bayes Error and Vapnik-Chervonenkis theory are applied as guide for empirical classifier selection on the basis of explicit specification and explicit enforcement of the maximum likelihood principle.
Journal ArticleDOI
Blind adaptive multiuser detection
TL;DR: This paper introduces an adaptive multiuser detector which converges (for any initialization) to the MMSE detector without requiring training sequences and is made robust to imprecise knowledge of the received signature waveform of the user of interest.
Journal ArticleDOI
Stochastic power control for cellular radio systems
Sennur Ulukus,Roy D. Yates +1 more
TL;DR: This work develops distributed iterative power control algorithms that use readily available measurements and proves that the mean-squared error (MSE) of the power vector from the optimal power vector that is the solution of a feasible deterministic power control problem goes to zero.
Journal ArticleDOI
Nonparametric estimation via empirical risk minimization
Gábor Lugosi,Kenneth Zeger +1 more
TL;DR: In this article, a general notion of universal consistency of nonparametric estimators is introduced that applies to regression estimation, conditional median estimation, curve fitting, pattern recognition, and learning concepts.
Journal ArticleDOI
Strategies for Sequential Prediction of Stationary Time Series
László Györfi,Gábor Lugosi +1 more
TL;DR: If the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor.
References
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Journal ArticleDOI
A Stochastic Approximation Method
Herbert Robbins,Sutton Monro +1 more
TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Journal ArticleDOI
Stochastic Estimation of the Maximum of a Regression Function
J. Kiefer,Jacob Wolfowitz +1 more
TL;DR: In this article, the authors give a scheme whereby, starting from an arbitrary point, one obtains successively $x_2, x_3, \cdots$ such that the regression function converges to the unknown point in probability as n \rightarrow \infty.
Journal ArticleDOI
Analysis of recursive stochastic algorithms
TL;DR: It is shown how a deterministic differential equation can be associated with the algorithm and examples of applications of the results to problems in identification and adaptive control.
Book
Stochastic Approximation Methods for Constrained and Unconstrained Systems
Harold J. Kushner,Dean S. Clark +1 more
TL;DR: In this paper, the authors present an algorithm for inequality constraints in a Dynamical System, based on the Robbins-Monro Process and Kiefer-Wolfowitz procedure. But they do not consider the case where the limit satisfies a Generalized ODE.