Reproducing Kernel Hilbert Spaces In Probability And Statistics
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Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet,Christine Thomas-Agnan Pdf
The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.
Kernel Mean Embedding of Distributions by Krikamol Muandet,Kenji Fukumizu,Bharath Sriperumbudur,Bernhard Schölkopf Pdf
Provides a comprehensive review of kernel mean embeddings of distributions and, in the course of doing so, discusses some challenging issues that could potentially lead to new research directions. The targeted audience includes graduate students and researchers in machine learning and statistics.
Hilbert Space Methods in Probability and Statistical Inference by Christopher G. Small,Don L. McLeish Pdf
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.
Theory of Reproducing Kernels and Applications by Saburou Saitoh,Yoshihiro Sawano Pdf
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
More Progresses in Analysis by Heinrich G. W. Begehr,Francesco Nicolosi Pdf
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O. Besov, V. Burenkov and R.P. Gilbert on the occasion of their anniversaries.
Machine Learning for Future Wireless Communications by Fa-Long Luo Pdf
A comprehensive review to the theory, application and research of machine learning for future wireless communications In one single volume, Machine Learning for Future Wireless Communications provides a comprehensive and highly accessible treatment to the theory, applications and current research developments to the technology aspects related to machine learning for wireless communications and networks. The technology development of machine learning for wireless communications has grown explosively and is one of the biggest trends in related academic, research and industry communities. Deep neural networks-based machine learning technology is a promising tool to attack the big challenge in wireless communications and networks imposed by the increasing demands in terms of capacity, coverage, latency, efficiency flexibility, compatibility, quality of experience and silicon convergence. The author – a noted expert on the topic – covers a wide range of topics including system architecture and optimization, physical-layer and cross-layer processing, air interface and protocol design, beamforming and antenna configuration, network coding and slicing, cell acquisition and handover, scheduling and rate adaption, radio access control, smart proactive caching and adaptive resource allocations. Uniquely organized into three categories: Spectrum Intelligence, Transmission Intelligence and Network Intelligence, this important resource: Offers a comprehensive review of the theory, applications and current developments of machine learning for wireless communications and networks Covers a range of topics from architecture and optimization to adaptive resource allocations Reviews state-of-the-art machine learning based solutions for network coverage Includes an overview of the applications of machine learning algorithms in future wireless networks Explores flexible backhaul and front-haul, cross-layer optimization and coding, full-duplex radio, digital front-end (DFE) and radio-frequency (RF) processing Written for professional engineers, researchers, scientists, manufacturers, network operators, software developers and graduate students, Machine Learning for Future Wireless Communications presents in 21 chapters a comprehensive review of the topic authored by an expert in the field.
Stochastic Analysis for Gaussian Random Processes and Fields by Vidyadhar S. Mandrekar,Leszek Gawarecki Pdf
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS
Artificial Intelligence, Big Data and Data Science in Statistics by Ansgar Steland,Kwok-Leung Tsui Pdf
This book discusses the interplay between statistics, data science, machine learning and artificial intelligence, with a focus on environmental science, the natural sciences, and technology. It covers the state of the art from both a theoretical and a practical viewpoint and describes how to successfully apply machine learning methods, demonstrating the benefits of statistics for modeling and analyzing high-dimensional and big data. The book’s expert contributions include theoretical studies of machine learning methods, expositions of general methodologies for sound statistical analyses of data as well as novel approaches to modeling and analyzing data for specific problems and areas. In terms of applications, the contributions deal with data as arising in industrial quality control, autonomous driving, transportation and traffic, chip manufacturing, photovoltaics, football, transmission of infectious diseases, Covid-19 and public health. The book will appeal to statisticians and data scientists, as well as engineers and computer scientists working in related fields or applications.
Mathematical Methods in Survival Analysis, Reliability and Quality of Life by Catherine Huber,Nikolaos Limnios,Mounir Mesbah,Mikhail S. Nikulin Pdf
Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.
Advanced Linear Modeling by Ronald Christensen Pdf
This book introduces several topics related to linear model theory, including: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. This second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subjects and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure.
