Techniques of Variational Analysis下载

weixin_39821620 2019-05-08 10:00:15

Jonathan M. Borwein Qiji J. Zhu
Techniques of
Variational Analysis
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Jonathan M. Borwein Qiji J. Zhu Techniques of Variational Analysis

In the field of image segmentation, most level-setbased active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines.

刚找到的书,第二版的.. 【原书作者】： Geoffrey J. McLachlan, Thriyambakam Krishnan 【ISBN 】： ISBN-10: 0471201707 / ISBN-13: 978-0471201700 【页数】：360 【开本】：【出版社】：Wiley-Interscience 【出版日期】：March 14, 2008 【文件格式】：DJVU(请去网上下载windjview阅读【摘要或目录】： Review "...should be comprehensible to graduates with statistics as their major subject." (Quarterly of Applied Mathematics, Vol. LIX, No. 3, September 2001) --This text refers to the Hardcover edition. Book Description The EM Algorithm and Extensions remains the only single source to offer a complete and unified treatment of the theory, methodology, and applications of the EM algorithm. The highly applied area of statistics here outlined involves applications in regression, medical imaging, finite mixture analysis, robust statistical modeling, survival analysis, and repeated-measures designs, among other areas. The text includes newly added and updated results on convergence, and new discussion of categorical data, numerical differentiation, and variants of the EM algorithm. It also explores the relationship between the EM algorithm and the Gibbs sampler and Markov Chain Monte Carlo methods. About Authors Geoffrey J. McLachlan, PhD, DSc, is Professor of Statistics in the Department of Mathematics at The University of Queensland, Australia. A Fellow of the American Statistical Association and the Australian Mathematical Society, he has published extensively on his research interests, which include cluster and discriminant analyses, image analysis, machine learning, neural networks, and pattern recognition. Dr. McLachlan is the author or coauthor of Analyzing Microarray Gene Expression Data, Finite Mixture Models, and Discriminant Analysis and Statistical Pattern Recognition, all published by Wiley. Thriyambakam Krishnan, PhD, is Chief Statistical Architect, SYSTAT Software at Cranes Software International Limited in Bangalore, India. Dr. Krishnan has over forty-five years of research, teaching, consulting, and software development experience at the Indian Statistical Institute (ISI). His research interests include biostatistics, image analysis, pattern recognition, psychometry, and the EM algorithm. 目录 Preface to the Second Edition. Preface to the First Edition. List of Examples. 1. General Introduction. 1.1 Introduction. 1.2 Maximum Likelihood Estimation. 1.3 Newton-Type Methods. 1.4 Introductory Examples. 1.5 Formulation of the EM Algorithm. 1.6 EM Algorithm for MAP and MPL Estimation. 1.7 Brief Summary of the Properties of EM Algorithm. 1.8 History of the EM Algorithm. 1.9 Overview of the Book. 1.10 Notations. 2. Examples of the EM Algorithm. 2.1 Introduction. 2.2 Multivariate Data with Missing Values. 2.3 Least Square with the Missing Data. 2.4 Example 2.4: Multinomial with Complex Cell Structure. 2.5 Example 2.5: Analysis of PET and SPECT Data. 2.6 Example 2.6: Multivariate t-Distribution (Known D.F.). 2.7 Finite Normal Mixtures. 2.8 Example 2.9: Grouped and Truncated Data. 2.9 Example 2.10: A Hidden Markov AR(1) Model. 3. Basic Theory of the EM Algorithm. 3.1 Introduction. 3.2 Monotonicity of a Generalized EM Algorithm. 3.3 Monotonicity of a Generalized EM Algorithm. 3.4 Convergence of an EM Sequence to a Stationary Value. 3.5 Convergence of an EM Sequence of Iterates. 3.6 Examples of Nontypical Behavior of an EM (GEM) Sequence. 3.7 Score Statistic. 3.8 Missing Information. 3.9 Rate of Convergence of the EM Algorithm. 4. Standard Errors and Speeding up Convergence. 4.1 Introduction. 4.2 Observed Information Matrix. 4.3 Approximations to Observed Information Matrix: i.i.d. Case. 4.4 Observed Information Matrix for Grouped Data. 4.5 Supplemented EM Algorithm. 4.6 Bookstrap Approach to Standard Error Approximation. 4.7 Baker’s, Louis’, and Oakes’ Methods for Standard Error Computation. 4.8 Acceleration of the EM Algorithm via Aitken’s Method. 4.9 An Aitken Acceleration-Based Stopping Criterion. 4.10 conjugate Gradient Acceleration of EM Algorithm. 4.11 Hybrid Methods for Finding the MLE. 4.12 A GEM Algorithm Based on One Newton-Raphson Algorithm. 4.13 EM gradient Algorithm. 4.14 A Quasi-Newton Acceleration of the EM Algorithm. 4.15 Ikeda Acceleration. 5. Extension of the EM Algorithm. 5.1 Introduction. 5.2 ECM Algorithm. 5.3 Multicycle ECM Algorithm. 5.4 Example 5.2: Normal Mixtures with Equal Correlations. 5.5 Example 5.3: Mixture Models for Survival Data. 5.6 Example 5.4: Contingency Tables with Incomplete Data. 5.7 ECME Algorithm. 5.8 Example 5.5: MLE of t-Distribution with the Unknown D.F. 5.9 Example 5.6: Variance Components. 5.10 Linear Mixed Models. 5.11 Example 5.8: Factor Analysis. 5.12 Efficient Data Augmentation. 5.13 Alternating ECM Algorithm. 5.14 Example 5.9: Mixtures of Factor Analyzers. 5.15 Parameter-Expanded EM (PX-EM) Algorithm. 5.16 EMS Algorithm. 5.17 One-Step-Late Algorithm. 5.18 Variance Estimation for Penalized EM and OSL Algorithms. 5.19 Incremental EM. 5.20 Linear Inverse problems. 6. Monte Carlo Versions of the EM Algorithm. 6.1 Introduction. 6.2 Monte Carlo Techniques. 6.3 Monte Carlo EM. 6.4 Data Augmentation. 6.5 Bayesian EM. 6.6 I.I.D. Monte Carlo Algorithm. 6.7 Markov Chain Monte Carlo Algorithms. 6.8 Gibbs Sampling. 6.9 Examples of MCMC Algorithms. 6.10 Relationship of EM to Gibbs Sampling. 6.11 Data Augmentation and Gibbs Sampling. 6.12 Empirical Bayes and EM. 6.13 Multiple Imputation. 6.14 Missing-Data Mechanism, Ignorability, and EM Algorithm. 7. Some Generalization of the EM Algorithm. 7.1 Introduction. 7.2 Estimating Equations and Estimating Functions. 7.3 Quasi-Score and the Projection-Solution Algorithm. 7.4 Expectation-Solution (ES) Algorithm. 7.5 Other Generalization. 7.6 Variational Bayesian EM Algorithm. 7.7 MM Algorithm. 7.8 Lower Bound Maximization. 7.9 Interval EM Algorithm. 7.10 Competing Methods and Some Comparisons with EM. 7.11 The Delta Algorithm. 7.12 Image Space Reconstruction Algorithm. 8. Further Applications of the EM Algorithm. 8.1 Introduction. 8.2 Hidden Markov Models. 8.3 AIDS Epidemiology. 8.4 Neural Networks. 8.5 Data Mining. 8.6 Bioinformatics. References. Author Index. Subject Index

信息论，推断与学习理论英文原版 Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning

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