Stochastic Approximation and Its Applications
Stochastic Approximation and Its Applications

Author: Han-Fu Chen

Publisher: Springer Science & Business Media

Published: 2005-12-30

Total Pages: 369

ISBN-13: 0306481669

DOWNLOAD EBOOK

Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.

Stochastic Approximation and Recursive Algorithms and Applications
Stochastic Approximation and Recursive Algorithms and Applications

Author: Harold Kushner

Publisher: Springer Science & Business Media

Published: 2006-05-04

Total Pages: 485

ISBN-13: 038721769X

DOWNLOAD EBOOK

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.

Stochastic Approximation Methods for Constrained and Unconstrained Systems
Stochastic Approximation Methods for Constrained and Unconstrained Systems

Author: H.J. Kushner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 273

ISBN-13: 1468493523

DOWNLOAD EBOOK

The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.

Adaptive Algorithms and Stochastic Approximations
Adaptive Algorithms and Stochastic Approximations

Author: Albert Benveniste

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 373

ISBN-13: 3642758940

DOWNLOAD EBOOK

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "intelligence" within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a "general theory of adaptive systems" encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.

Stochastic Optimization Methods
Stochastic Optimization Methods

Author: Kurt Marti

Publisher: Springer

Published: 2015-02-21

Total Pages: 389

ISBN-13: 3662462141

DOWNLOAD EBOOK

This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.

Stochastic Approximation and Recursive Estimation
Stochastic Approximation and Recursive Estimation

Author: M. B. Nevel'son

Publisher: American Mathematical Soc.

Published: 1976-10-01

Total Pages: 252

ISBN-13: 9780821809068

DOWNLOAD EBOOK

This book is devoted to sequential methods of solving a class of problems to which belongs, for example, the problem of finding a maximum point of a function if each measured value of this function contains a random error. Some basic procedures of stochastic approximation are investigated from a single point of view, namely the theory of Markov processes and martingales. Examples are considered of applications of the theorems to some problems of estimation theory, educational theory and control theory, and also to some problems of information transmission in the presence of inverse feedback.

Stochastic Approximation
Stochastic Approximation

Author: M. T. Wasan

Publisher: Cambridge University Press

Published: 2004-06-03

Total Pages: 220

ISBN-13: 9780521604857

DOWNLOAD EBOOK

A rigorous mathematical treatment of the technique for studying the properties of an experimental situation.

Design of Experiments for Chemical, Pharmaceutical, Food, and Industrial Applications
Design of Experiments for Chemical, Pharmaceutical, Food, and Industrial Applications

Author: Carrillo-Cedillo, Eugenia Gabriela

Publisher: IGI Global

Published: 2019-12-13

Total Pages: 429

ISBN-13: 179981520X

DOWNLOAD EBOOK

Statistics is a key characteristic that assists a wide variety of professions including business, government, and factual sciences. Companies need data calculation to make informed decisions that help maintain their relevance. Design of experiments (DOE) is a set of active techniques that provides a more efficient approach for industries to test their processes and form effective conclusions. Experimental design can be implemented into multiple professions, and it is a necessity to promote applicable research on this up-and-coming method. Design of Experiments for Chemical, Pharmaceutical, Food, and Industrial Applications is a pivotal reference source that seeks to increase the use of design of experiments to optimize and improve analytical methods and productive processes in order to use less resources and time. While highlighting topics such as multivariate methods, factorial experiments, and pharmaceutical research, this publication is ideally designed for industrial designers, research scientists, chemical engineers, managers, academicians, and students seeking current research on advanced and multivariate statistics.