Download or read book Constrained Regularization for Ill Posed Linear Operator Equations with Applications in Meteorology and Medicine written by Grace Wahba and published by . This book was released on 1981 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between certain regularization methods for solving ill posed linear operator equations and ridge methods in regression problems is described. The regularization estimates we describe may be viewed as ridge estimates in a (reproducing kernel) Hilbert space H. When the solution is known a priori to be in some closed, convex set in H, for example, the set of nonnegative functions, or the set of monotone functions, then one can propose regularized estimates subject to side conditions such as nonnegativity, monotonicity, etc. Some applications in medicine and meteorology are described. We describe the method of generalized cross validation for choosing the smoothing (or ridge) parameter in the presence of a family of linear inequality constraints. Some successful numerical examples, solving ill posed convolution equations with noisy data, subject to nonnegativity constraints, are presented. The technique appears to be quite successful in adding information, doing nearly the optimal amount of smoothing, and resolving distinct peaks in the solution which have been blurred by the convolution operation. (Author).
Download or read book Inverse and Ill Posed Problems written by Heinz W. Engl and published by Elsevier. This book was released on 2014-05-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-01-01 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Download or read book Function Estimates written by James Stephen Marron and published by American Mathematical Soc.. This book was released on 1986 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects together papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. The papers focus especially on various types of spline estimations and convolution problems. The use of estimation and approximation methods as applied to geophysics, numerical analysis, and nonparametric statistics was a special feature of this conference.
Download or read book Advances in Kernel Methods written by Bernhard Schölkopf and published by MIT Press. This book was released on 1999 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: A young girl hears the story of her great-great-great-great- grandfather and his brother who came to the United States to make a better life for themselves helping to build the transcontinental railroad.
Download or read book The Journal of Integral Equations and Applications written by and published by . This book was released on 1988 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Technical Report written by University of Wisconsin--Madison. Department of Statistics and published by . This book was released on 1972 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Large Margin Classifiers written by Alexander J. Smola and published by MIT Press. This book was released on 2000 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an overview of recent developments in large margin classifiers, examines connections with other methods (e.g., Bayesian inference), and identifies strengths and weaknesses of the method, as well as directions for future research. The concept of large margins is a unifying principle for the analysis of many different approaches to the classification of data from examples, including boosting, mathematical programming, neural networks, and support vector machines. The fact that it is the margin, or confidence level, of a classification--that is, a scale parameter--rather than a raw training error that matters has become a key tool for dealing with classifiers. This book shows how this idea applies to both the theoretical analysis and the design of algorithms. The book provides an overview of recent developments in large margin classifiers, examines connections with other methods (e.g., Bayesian inference), and identifies strengths and weaknesses of the method, as well as directions for future research. Among the contributors are Manfred Opper, Vladimir Vapnik, and Grace Wahba.
Download or read book Statistical Decision Theory and Related Topics III written by Shanti S. Gupta and published by Academic Press. This book was released on 2014-05-10 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Decision Theory and Related Topics III, Volume 2 is a collection of papers presented at the Third Purdue Symposium on Statistical Decision Theory and Related Topics, held at Purdue University in June 1981. The symposium brought together many prominent leaders and a number of younger researchers in statistical decision theory and related areas. This volume contains the research papers presented at the symposium and includes works on general decision theory, multiple decision theory, optimum experimental design, sequential and adaptive inference, Bayesian analysis, robustness, and large sample theory. These research areas have seen rapid developments since the preceding Purdue Symposium in 1976, developments reflected by the variety and depth of the works in this volume. Statisticians and mathematicians will find the book very insightful.
Download or read book Regularization Methods for Ill Posed Optimal Control Problems written by Frank Pörner and published by BoD – Books on Demand. This book was released on 2018-10-04 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.
Download or read book Machine Learning Techniques for Space Weather written by Enrico Camporeale and published by Elsevier. This book was released on 2018-05-31 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning Techniques for Space Weather provides a thorough and accessible presentation of machine learning techniques that can be employed by space weather professionals. Additionally, it presents an overview of real-world applications in space science to the machine learning community, offering a bridge between the fields. As this volume demonstrates, real advances in space weather can be gained using nontraditional approaches that take into account nonlinear and complex dynamics, including information theory, nonlinear auto-regression models, neural networks and clustering algorithms. Offering practical techniques for translating the huge amount of information hidden in data into useful knowledge that allows for better prediction, this book is a unique and important resource for space physicists, space weather professionals and computer scientists in related fields. Collects many representative non-traditional approaches to space weather into a single volume Covers, in an accessible way, the mathematical background that is not often explained in detail for space scientists Includes free software in the form of simple MATLAB® scripts that allow for replication of results in the book, also familiarizing readers with algorithms
Download or read book Methods and Procedures for the Verification and Validation of Artificial Neural Networks written by Brian J. Taylor and published by Springer Science & Business Media. This book was released on 2006-03-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural networks are members of a class of software that have the potential to enable intelligent computational systems capable of simulating characteristics of biological thinking and learning. Currently no standards exist to verify and validate neural network-based systems. NASA Independent Verification and Validation Facility has contracted the Institute for Scientific Research, Inc. to perform research on this topic and develop a comprehensive guide to performing V&V on adaptive systems, with emphasis on neural networks used in safety-critical or mission-critical applications. Methods and Procedures for the Verification and Validation of Artificial Neural Networks is the culmination of the first steps in that research. This volume introduces some of the more promising methods and techniques used for the verification and validation (V&V) of neural networks and adaptive systems. A comprehensive guide to performing V&V on neural network systems, aligned with the IEEE Standard for Software Verification and Validation, will follow this book.
Download or read book Regularization Algorithms for Ill Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems
Download or read book Spatial Statistics and Imaging written by Antonio Possolo and published by IMS. This book was released on 1991 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Time Series Analysis of Irregularly Observed Data written by E. Parzen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the support of the Office of Naval Research Program on Statistics and Probability (Dr. Edward J. Wegman, Director), The Department of Statistics at Texas A&M University hosted a Symposium on Time Series Analysis of Irregularly Observed Data during the period February 10-13, 1983. The symposium aimed to provide a review of the state of the art, define outstanding problems for research by theoreticians, transmit to practitioners recently developed algorithms, and stimulate interaction between statisticians and researchers in subject matter fields. Attendance was limited to actively involved researchers. This volume contains refereed versions of the papers presented at the Symposium. We would like to express our appreciation to the many colleagues and staff members whose cheerful help made the Symposium a successful happening which was enjoyed socially and intellectually by all participants. I would like to especially thank Dr. Donald W. Marquardt whose interest led me to undertake to organize this Symposium. This volume is dedicated to the world wide community of researchers who develop and apply methods of statistical analysis of time series. r:;) \J Picture Caption Participants in Symposium on Time Series Analysis of Irregularly Observed Data at Texas A&M University, College Station, Texas, February 10-13, 1983 First Row: Henry L. Gray, D. W. Marquardt, P. M. Robinson, Emanuel Parzen, Julia Abrahams, E. Masry, H. L. Weinert, R. H. Shumway.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1982 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Nonparametric Estimation and Model Selection Using Constrained Splines in Linear Inversion Problems written by Davide Verotta and published by . This book was released on 1992 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
