Download or read book Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems written by Vladimir Koltchinskii and published by Springer. This book was released on 2011-07-29 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.
Download or read book Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems written by Vladimir Koltchinskii and published by . This book was released on 2011-08-02 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Concentration Inequalities written by Stéphane Boucheron and published by OUP Oxford. This book was released on 2013-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.
Download or read book Estimation and Testing Under Sparsity written by Sara van de Geer and published by Springer. This book was released on 2016-06-28 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.
Download or read book Empirical Inference written by Bernhard Schölkopf and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book honours the outstanding contributions of Vladimir Vapnik, a rare example of a scientist for whom the following statements hold true simultaneously: his work led to the inception of a new field of research, the theory of statistical learning and empirical inference; he has lived to see the field blossom; and he is still as active as ever. He started analyzing learning algorithms in the 1960s and he invented the first version of the generalized portrait algorithm. He later developed one of the most successful methods in machine learning, the support vector machine (SVM) – more than just an algorithm, this was a new approach to learning problems, pioneering the use of functional analysis and convex optimization in machine learning. Part I of this book contains three chapters describing and witnessing some of Vladimir Vapnik's contributions to science. In the first chapter, Léon Bottou discusses the seminal paper published in 1968 by Vapnik and Chervonenkis that lay the foundations of statistical learning theory, and the second chapter is an English-language translation of that original paper. In the third chapter, Alexey Chervonenkis presents a first-hand account of the early history of SVMs and valuable insights into the first steps in the development of the SVM in the framework of the generalised portrait method. The remaining chapters, by leading scientists in domains such as statistics, theoretical computer science, and mathematics, address substantial topics in the theory and practice of statistical learning theory, including SVMs and other kernel-based methods, boosting, PAC-Bayesian theory, online and transductive learning, loss functions, learnable function classes, notions of complexity for function classes, multitask learning, and hypothesis selection. These contributions include historical and context notes, short surveys, and comments on future research directions. This book will be of interest to researchers, engineers, and graduate students engaged with all aspects of statistical learning.
Download or read book Compressed Sensing and Its Applications written by Holger Boche and published by Birkhäuser. This book was released on 2019-08-13 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Technical University in Berlin. In addition to methods in compressed sensing, chapters provide insights into cutting edge applications of deep learning in data science, highlighting the overlapping ideas and methods that connect the fields of compressed sensing and deep learning. Specific topics covered include: Quantized compressed sensing Classification Machine learning Oracle inequalities Non-convex optimization Image reconstruction Statistical learning theory This volume will be a valuable resource for graduate students and researchers in the areas of mathematics, computer science, and engineering, as well as other applied scientists exploring potential applications of compressed sensing.
Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer. This book was released on 2017-04-17 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.
Download or read book High Dimensional Probability VI written by Christian Houdré and published by Springer Science & Business Media. This book was released on 2013-04-19 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.
Download or read book Algorithmic Learning Theory written by Ronald Ortner and published by Springer. This book was released on 2016-10-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 27th International Conference on Algorithmic Learning Theory, ALT 2016, held in Bari, Italy, in October 2016, co-located with the 19th International Conference on Discovery Science, DS 2016. The 24 regular papers presented in this volume were carefully reviewed and selected from 45 submissions. In addition the book contains 5 abstracts of invited talks. The papers are organized in topical sections named: error bounds, sample compression schemes; statistical learning, theory, evolvability; exact and interactive learning; complexity of teaching models; inductive inference; online learning; bandits and reinforcement learning; and clustering.
Download or read book Model Selection and Error Estimation in a Nutshell written by Luca Oneto and published by Springer. This book was released on 2019-07-17 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we select the best performing data-driven model? How can we rigorously estimate its generalization error? Statistical learning theory answers these questions by deriving non-asymptotic bounds on the generalization error of a model or, in other words, by upper bounding the true error of the learned model based just on quantities computed on the available data. However, for a long time, Statistical learning theory has been considered only an abstract theoretical framework, useful for inspiring new learning approaches, but with limited applicability to practical problems. The purpose of this book is to give an intelligible overview of the problems of model selection and error estimation, by focusing on the ideas behind the different statistical learning theory approaches and simplifying most of the technical aspects with the purpose of making them more accessible and usable in practice. The book starts by presenting the seminal works of the 80’s and includes the most recent results. It discusses open problems and outlines future directions for research.
Download or read book Adaptive Mobile Computing written by Mauro Migliardi and published by Academic Press. This book was released on 2017-08-14 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive Mobile Computing: Advances in Processing Mobile Data Sets explores the latest advancements in producing, processing and securing mobile data sets. The book provides the elements needed to deepen understanding of this trend which, over the last decade, has seen exponential growth in the number and capabilities of mobile devices. The pervasiveness, sensing capabilities and computational power of mobile devices have turned them into a fundamental instrument in everyday life for a large part of the human population. This fact makes mobile devices an incredibly rich source of data about the dynamics of human behavior, a pervasive wireless sensors network with substantial computational power and an extremely appealing target for a new generation of threats. Offers a coherent and realistic image of today’s architectures, techniques, protocols, components, orchestration, choreography and development related to mobile computing Explains state-of-the-art technological solutions for the main issues hindering the development of next-generation pervasive systems including: supporting components for collecting data intelligently, handling resource and data management, accounting for fault tolerance, security, monitoring and control, addressing the relation with the Internet of Things and Big Data and depicting applications for pervasive context-aware processing Presents the benefits of mobile computing and the development process of scientific and commercial applications and platforms to support them Familiarizes readers with the concepts and technologies that are successfully used in the implementation of pervasive/ubiquitous systems
Download or read book Algorithmic Learning Theory written by Kamalika Chaudhuri and published by Springer. This book was released on 2015-10-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 26th International Conference on Algorithmic Learning Theory, ALT 2015, held in Banff, AB, Canada, in October 2015, and co-located with the 18th International Conference on Discovery Science, DS 2015. The 23 full papers presented in this volume were carefully reviewed and selected from 44 submissions. In addition the book contains 2 full papers summarizing the invited talks and 2 abstracts of invited talks. The papers are organized in topical sections named: inductive inference; learning from queries, teaching complexity; computational learning theory and algorithms; statistical learning theory and sample complexity; online learning, stochastic optimization; and Kolmogorov complexity, algorithmic information theory.
Download or read book Multivariate Nonparametric Regression and Visualization written by Jussi Sakari Klemelä and published by John Wiley & Sons. This book was released on 2014-05-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern approach to statistical learning and its applications through visualization methods With a unique and innovative presentation, Multivariate Nonparametric Regression and Visualization provides readers with the core statistical concepts to obtain complete and accurate predictions when given a set of data. Focusing on nonparametric methods to adapt to the multiple types of data generating mechanisms, the book begins with an overview of classification and regression. The book then introduces and examines various tested and proven visualization techniques for learning samples and functions. Multivariate Nonparametric Regression and Visualization identifies risk management, portfolio selection, and option pricing as the main areas in which statistical methods may be implemented in quantitative finance. The book provides coverage of key statistical areas including linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods. Exploring the additional applications of nonparametric and semiparametric methods, Multivariate Nonparametric Regression and Visualization features: An extensive appendix with R-package training material to encourage duplication and modification of the presented computations and research Multiple examples to demonstrate the applications in the field of finance Sections with formal definitions of the various applied methods for readers to utilize throughout the book Multivariate Nonparametric Regression and Visualization is an ideal textbook for upper-undergraduate and graduate-level courses on nonparametric function estimation, advanced topics in statistics, and quantitative finance. The book is also an excellent reference for practitioners who apply statistical methods in quantitative finance.
Download or read book Markov Paths Loops and Fields written by Yves Le Jan and published by Springer Science & Business Media. This book was released on 2011-07-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the free field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces.
Download or read book Nonparametric Statistics written by Patrice Bertail and published by Springer. This book was released on 2019-03-08 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the latest advances and trends in nonparametric statistics, and gathers selected and peer-reviewed contributions from the 3rd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Avignon, France on June 11-16, 2016. It covers a broad range of nonparametric statistical methods, from density estimation, survey sampling, resampling methods, kernel methods and extreme values, to statistical learning and classification, both in the standard i.i.d. case and for dependent data, including big data. The International Society for Nonparametric Statistics is uniquely global, and its international conferences are intended to foster the exchange of ideas and the latest advances among researchers from around the world, in cooperation with established statistical societies such as the Institute of Mathematical Statistics, the Bernoulli Society and the International Statistical Institute. The 3rd ISNPS conference in Avignon attracted more than 400 researchers from around the globe, and contributed to the further development and dissemination of nonparametric statistics knowledge.
Download or read book High Dimensional Probability VII written by Christian Houdré and published by Birkhäuser. This book was released on 2016-09-21 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'Études Scientifiques de Cargèse (IESC) in Corsica, France. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, and random graphs. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.
Download or read book Integer Programming and Combinatorial Optimization written by Jon Lee and published by Springer. This book was released on 2014-05-17 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014, held in Bonn, Germany, in June 2014. The 34 full papers presented were carefully reviewed and selected from 143 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
