optimization 95 springer texts in statistics

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Author : Kenneth Lange
ISBN : 9781461458388
Genre : Mathematics
File Size : 43. 29 MB
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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

Integer Points In Polyhedra Geometry Number Theory Representation Theory Algebra Optimization Statistics

Author : Matthias Beck
ISBN : 9780821841730
Genre : Mathematics
File Size : 88. 91 MB
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The AMS-IMS-SIAM Joint Summer Research Conference ``Integer Points in Polyhedra--Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics'' was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference. The volume is a cross section of recent advances connected to lattice-point questions. Similar to the talks given at the conference, topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.

Genetic Algorithm Essentials

Author : Oliver Kramer
ISBN : 9783319521565
Genre : Computers
File Size : 55. 96 MB
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This book introduces readers to genetic algorithms (GAs) with an emphasis on making the concepts, algorithms, and applications discussed as easy to understand as possible. Further, it avoids a great deal of formalisms and thus opens the subject to a broader audience in comparison to manuscripts overloaded by notations and equations. The book is divided into three parts, the first of which provides an introduction to GAs, starting with basic concepts like evolutionary operators and continuing with an overview of strategies for tuning and controlling parameters. In turn, the second part focuses on solution space variants like multimodal, constrained, and multi-objective solution spaces. Lastly, the third part briefly introduces theoretical tools for GAs, the intersections and hybridizations with machine learning, and highlights selected promising applications.

Foundations Of Optimization

Author : Osman Güler
ISBN : 0387684077
Genre : Business & Economics
File Size : 73. 67 MB
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This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

Statistical Learning With Sparsity

Author : Trevor Hastie
ISBN : 9781498712170
Genre : Business & Economics
File Size : 79. 5 MB
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Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of l1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.


Author : Jim Pitman
ISBN : UOM:39015050191603
Genre : Mathematics
File Size : 20. 3 MB
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Preface to the Instructor This is a text for a one-quarter or one-semester course in probability, aimed at stu dents who have done a year of calculus. The book is organized so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail. It is not possible to go through all these examples in class. Rather, I suggest that you deal quickly with the main points of theory, then spend class time on problems from the exercises, or your own favorite problems. The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theo rems and proofs. So the emphasis is on problem solving rather than theory.

The Elements Of Statistical Learning

Author : Trevor Hastie
ISBN : 9780387216065
Genre : Mathematics
File Size : 63. 8 MB
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During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book’s coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for “wide” data (p bigger than n), including multiple testing and false discovery rates. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.


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ISBN : UOM:39015058745988
Genre : Engineering design
File Size : 85. 35 MB
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Proceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference 2005

Author : Asme Conference Proceedings
ISBN : 079184739X
Genre : Computers
File Size : 81. 61 MB
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Evolutionary Computation For Modeling And Optimization

Author : Daniel Ashlock
ISBN : 0387319093
Genre : Computers
File Size : 76. 24 MB
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Concentrates on developing intuition about evolutionary computation and problem solving skills and tool sets. Lots of applications and test problems, including a biotechnology chapter.

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