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On Ridge Splines Neural Networks And Variational Problems In Radon Domain Bv Spaces
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Book Synopsis On Ridge Splines, Neural Networks, and Variational Problems in Radon-domain BV Spaces by : Rahul Parhi (Ph.D.)
Download or read book On Ridge Splines, Neural Networks, and Variational Problems in Radon-domain BV Spaces written by Rahul Parhi (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep neural networks are not well understood mathematically and their success in many science and engineering applications is usually only backed by empirical evidence. In this dissertation, we study neural networks from first principles, beginning with the simplest architecture of shallow feedforward neural networks. We use tools from variational spline theory to mathematically understand neural networks. In particular, we view neural networks as a type of spline. We propose and study a new family of Banach spaces, which are bounded variation (BV) spaces defined via the Radon transform. These are the "native spaces" for neural networks. We show that finite-width neural networks are solutions to data-fitting variational problems over these spaces. Moreover, these variational problems can be recast as finite-dimensional neural network training problems with regularization schemes related to weight decay and path-norm regularization, giving theoretical insight into these common regularization schemes as well as providing several new, principled forms of regularization for (deep) neural networks. The Radon-domain BV spaces are also interesting from the perspective of functional analysis and statistical estimation. The best approximation and estimation error rates of these spaces are (essentially) independent of the input dimension, while the best linear approximation and estimation error rates suffer the curse of dimensionality. The Radon-domain BV spaces contain functions that are very smooth in all directions except (perhaps) a few directions. The anisotropic nature of these spaces distinguishes them from classical function spaces. This dissertation provides a first step towards a mathematical theory of neural networks through the lens of spline theory and functional analysis.
Book Synopsis A Neural Network Approach to Variational Problems by : Monica C. Jackson
Download or read book A Neural Network Approach to Variational Problems written by Monica C. Jackson and published by . This book was released on 1994 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semi-Supervised Learning by : Olivier Chapelle
Download or read book Semi-Supervised Learning written by Olivier Chapelle and published by MIT Press. This book was released on 2010-01-22 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of an area of machine learning that deals with the use of unlabeled data in classification problems: state-of-the-art algorithms, a taxonomy of the field, applications, benchmark experiments, and directions for future research. In the field of machine learning, semi-supervised learning (SSL) occupies the middle ground, between supervised learning (in which all training examples are labeled) and unsupervised learning (in which no label data are given). Interest in SSL has increased in recent years, particularly because of application domains in which unlabeled data are plentiful, such as images, text, and bioinformatics. This first comprehensive overview of SSL presents state-of-the-art algorithms, a taxonomy of the field, selected applications, benchmark experiments, and perspectives on ongoing and future research.Semi-Supervised Learning first presents the key assumptions and ideas underlying the field: smoothness, cluster or low-density separation, manifold structure, and transduction. The core of the book is the presentation of SSL methods, organized according to algorithmic strategies. After an examination of generative models, the book describes algorithms that implement the low-density separation assumption, graph-based methods, and algorithms that perform two-step learning. The book then discusses SSL applications and offers guidelines for SSL practitioners by analyzing the results of extensive benchmark experiments. Finally, the book looks at interesting directions for SSL research. The book closes with a discussion of the relationship between semi-supervised learning and transduction.
Book Synopsis Sparse and Redundant Representations by : Michael Elad
Download or read book Sparse and Redundant Representations written by Michael Elad and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.
Book Synopsis Equilibrium Problems and Variational Models by : P. Daniele
Download or read book Equilibrium Problems and Variational Models written by P. Daniele and published by Springer Science & Business Media. This book was released on 2003-06-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.
Book Synopsis Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems by : I. Cioranescu
Download or read book Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems written by I. Cioranescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Digital and Image Geometry by : Gilles Bertrand
Download or read book Digital and Image Geometry written by Gilles Bertrand and published by Springer. This book was released on 2003-07-31 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing. This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification.
Book Synopsis Wavelets and Their Applications by : J.S. Byrnes
Download or read book Wavelets and Their Applications written by J.S. Byrnes and published by Springer Science & Business Media. This book was released on 1994-08-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet. Hence, if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments may follow. Werner Heisenberg This volume contains papers presented at the August 1992 NATO Advanced Study Institute on Wavelets and Their Applications. The conference was held at the beautiful Il Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy. Once again we gathered at this idyllic spot to explore and extend the reciprocity between mathematics and engineering. The dynamic interaction between world-renowned scientists from the usu ally disparate communities of pure mathematicians and applied scientists, which occurred at our 1989 and 1991 ASI's, continued at this meeting. Wavelet theory and technology is in an important growth stage at which theoretical and practical results are being compared with existing methods. There have been spectacular wavelet successes and sobering comparisons with traditional ideas-but still there is a wide expanse of scientific problems to explore. Since these problems lie at the forefront of both pure mathematics and applied science, our NATO ASI was especially pertinent at this time.
Book Synopsis Smart Computing Paradigms: New Progresses and Challenges by : Atilla Elçi
Download or read book Smart Computing Paradigms: New Progresses and Challenges written by Atilla Elçi and published by Springer Nature. This book was released on 2019-11-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book focuses on both theory and applications in the broad areas of communication technology, computer science and information security. It brings together contributions from scientists, professors, scholars and students, and presents essential information on computing, networking, and informatics. It also discusses the practical challenges encountered and the solutions used to overcome them, the goal being to promote the “translation” of basic research into applied research, and of applied research into practice. The works presented here will also demonstrate the importance of basic scientific research in a range of fields.
Book Synopsis Numerical Methods in Finance by : René Carmona
Download or read book Numerical Methods in Finance written by René Carmona and published by Springer Science & Business Media. This book was released on 2012-03-23 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Book Synopsis Parallel Computation by : Peter Zinterhof
Download or read book Parallel Computation written by Peter Zinterhof and published by Springer. This book was released on 2003-05-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Parallel Computation, ACPC'99, held in Salzburg, Austria in February 1999; the conference included special tracks on parallel numerics and on parallel computing in image processing, video processing, and multimedia. The volume presents 50 revised full papers selected from a total of 75 submissions. Also included are four invited papers and 15 posters. The papers are organized in topical sections on linear algebra, differential equations and interpolation, (Quasi-)Monte Carlo methods, numerical software, numerical applications, image segmentation and image understanding, motion estimation and block matching, video processing, wavelet techniques, satellite image processing, data structures, data partitioning, resource allocation and performance analysis, cluster computing, and simulation and applications.
Book Synopsis Large Scale Inverse Problems by : Mike Cullen
Download or read book Large Scale Inverse Problems written by Mike Cullen and published by Walter de Gruyter. This book was released on 2013-08-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.
Book Synopsis An Introduction to Sparse Stochastic Processes by : Michael Unser
Download or read book An Introduction to Sparse Stochastic Processes written by Michael Unser and published by Cambridge University Press. This book was released on 2014-08-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.
Book Synopsis The Craft of Probabilistic Modelling by : J. Gani
Download or read book The Craft of Probabilistic Modelling written by J. Gani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the personal accounts and reflections of nineteen mathematical model-builders, whose specialty is probabilistic modelling. The reader may well wonder why, apart from personal interest, one should commission and edit such a collection of articles. There are, of course, many reasons, but perhaps the three most relevant are: (i) a philosophicaJ interest in conceptual models; this is an interest shared by everyone who has ever puzzled over the relationship between thought and reality; (ii) a conviction, not unsupported by empirical evidence, that probabilistic modelling has an important contribution to make to scientific research; and finally (iii) a curiosity, historical in its nature, about the complex interplay between personal events and the development of a field of mathematical research, namely applied probability. Let me discuss each of these in turn. Philosophical Abstraction, the formation of concepts, and the construction of conceptual models present us with complex philosophical problems which date back to Democritus, Plato and Aristotle. We have all, at one time or another, wondered just how we think; are our thoughts, concepts and models of reality approxim&tions to the truth, or are they simply functional constructs helping us to master our environment? Nowhere are these problems more apparent than in mathematical model ling, where idealized concepts and constructions replace the imperfect realities for which they stand.
Book Synopsis Emerging ICT for Bridging the Future - Proceedings of the 49th Annual Convention of the Computer Society of India (CSI) Volume 1 by : Suresh Chandra Satapathy
Download or read book Emerging ICT for Bridging the Future - Proceedings of the 49th Annual Convention of the Computer Society of India (CSI) Volume 1 written by Suresh Chandra Satapathy and published by Springer. This book was released on 2014-11-30 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 73 papers presented at CSI 2014: Emerging ICT for Bridging the Future: Proceedings of the 49th Annual Convention of Computer Society of India. The convention was held during 12-14, December, 2014 at Hyderabad, Telangana, India. This volume contains papers mainly focused on Fuzzy Systems, Image Processing, Software Engineering, Cyber Security and Digital Forensic, E-Commerce, Big Data, Cloud Computing and ICT applications.
Book Synopsis Recent Technologies for Disaster Management and Risk Reduction by : Praveen Kumar Rai
Download or read book Recent Technologies for Disaster Management and Risk Reduction written by Praveen Kumar Rai and published by Springer Nature. This book was released on 2021-08-21 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains to governments, decision makers and disaster professionals the potential uses of recent technologies for disaster monitoring and risk reduction based on the knowledge and experience of prominent experts/researchers in the relevant fields. It discusses the application of recent technological developments for emerging disaster risks in today's societies and deliberates on the various aspects of disaster risk reduction strategies, especially through sustainable community resilience and responses. This book consists of selected invited papers on disaster management, which focus on community resilience and responses towards disaster risk reduction based on experiences, and closely examines the coordinated research activities involving all stakeholders, especially the communities at risk. Many regions of the world and aspects of disaster risk and its management are covered. It is described how recent technologies will support better understanding and action to reduce the number and impact of disasters in future. The principal audience for this book is researchers, urban planners, policy makers, as well as students.
Book Synopsis A First Course in Bayesian Statistical Methods by : Peter D. Hoff
Download or read book A First Course in Bayesian Statistical Methods written by Peter D. Hoff and published by Springer Science & Business Media. This book was released on 2009-06-02 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.
