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Author: Luca Oneto Publisher: Springer ISBN: 3030243591 Category : Technology & Engineering Languages : en Pages : 132
Book Description
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.
Author: Luca Oneto Publisher: Springer ISBN: 3030243591 Category : Technology & Engineering Languages : en Pages : 132
Book Description
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.
Author: David Pollard Publisher: Springer Science & Business Media ISBN: 1461218802 Category : Mathematics Languages : en Pages : 456
Book Description
Contributed in honour of Lucien Le Cam on the occasion of his 70th birthday, the papers reflect the immense influence that his work has had on modern statistics. They include discussions of his seminal ideas, historical perspectives, and contributions to current research - spanning two centuries with a new translation of a paper of Daniel Bernoulli. The volume begins with a paper by Aalen, which describes Le Cams role in the founding of the martingale analysis of point processes, and ends with one by Yu, exploring the position of just one of Le Cams ideas in modern semiparametric theory. The other 27 papers touch on areas such as local asymptotic normality, contiguity, efficiency, admissibility, minimaxity, empirical process theory, and biological medical, and meteorological applications - where Le Cams insights have laid the foundations for new theories.
Author: Rob J Hyndman Publisher: OTexts ISBN: 0987507117 Category : Business & Economics Languages : en Pages : 380
Book Description
Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
Author: H. Linhart Publisher: ISBN: Category : Mathematics Languages : en Pages : 328
Book Description
The first work to deal exclusively with objective criteria for comparing statistical models. Using a simple framework, it outlines a general strategy for selecting a model and applies this strategy to develop methods useful for solving specific selection problems. Topics covered include histograms, univariate distributions, simple and multiple regression, the analysis of variance and covariance, the analysis of proportions and contingency tables, time series analysis, and spatial analysis.
Author: Ulisses M. Braga Neto Publisher: John Wiley & Sons ISBN: 1119079373 Category : Technology & Engineering Languages : en Pages : 336
Book Description
This book is the first of its kind to discuss error estimation with a model-based approach. From the basics of classifiers and error estimators to distributional and Bayesian theory, it covers important topics and essential issues pertaining to the scientific validity of pattern classification. Error Estimation for Pattern Recognition focuses on error estimation, which is a broad and poorly understood topic that reaches all research areas using pattern classification. It includes model-based approaches and discussions of newer error estimators such as bolstered and Bayesian estimators. This book was motivated by the application of pattern recognition to high-throughput data with limited replicates, which is a basic problem now appearing in many areas. The first two chapters cover basic issues in classification error estimation, such as definitions, test-set error estimation, and training-set error estimation. The remaining chapters in this book cover results on the performance and representation of training-set error estimators for various pattern classifiers. Additional features of the book include: • The latest results on the accuracy of error estimation • Performance analysis of re-substitution, cross-validation, and bootstrap error estimators using analytical and simulation approaches • Highly interactive computer-based exercises and end-of-chapter problems This is the first book exclusively about error estimation for pattern recognition. Ulisses M. Braga Neto is an Associate Professor in the Department of Electrical and Computer Engineering at Texas A&M University, USA. He received his PhD in Electrical and Computer Engineering from The Johns Hopkins University. Dr. Braga Neto received an NSF CAREER Award for his work on error estimation for pattern recognition with applications in genomic signal processing. He is an IEEE Senior Member. Edward R. Dougherty is a Distinguished Professor, Robert F. Kennedy ’26 Chair, and Scientific Director at the Center for Bioinformatics and Genomic Systems Engineering at Texas A&M University, USA. He is a fellow of both the IEEE and SPIE, and he has received the SPIE Presidents Award. Dr. Dougherty has authored several books including Epistemology of the Cell: A Systems Perspective on Biological Knowledge and Random Processes for Image and Signal Processing (Wiley-IEEE Press).
Author: Tobias Scheffer Publisher: ISBN: Category : Bayesian statistical decision theory Languages : en Pages : 26
Book Description
Abstract: "Model selection is considered the problem of choosing a 'good' hypothesis language from a given ensemble of models. Here, a 'good' model is one for which the true (or generalization) error of the hypothesis returned by a learner which takes the model as hypothesis language is low. The crucial part of model selection is to somehow assess the true error of the apparently best hypothesis (the empirical minimizer) of a model. In this paper, we discuss a new, very efficient approach to model selection. Our approach is inherently Bayesian, but instead of using priors on target functions or hypotheses, we talk about priors on error values -- which leads us to a new insightful characterization of the expected true error. Consequently, our solution is based on the prior of error values for the given problem which is, of course, unknown. But we show next that this prior can be estimated efficiently for a given learning problem by recording the empirical errors of a constant number of randomly drawn hypotheses. Using this estimated prior, our framework yields an estimate of the true error of the empirical minimizer of a model. We report on several controlled experiments (based on artificial problems and boolean concepts) which provide strong empirical evidence for the usefulness of the approach: In terms of accuracy, our algorithm becomes slightly superior to 10-fold cross-validation as the size of the models grows. In terms of time complexity and scalability, our algorithm is quite superior to cross-validation: Whie cross validation requires n invocations of the learner per model, a fast version of our algorithm is constant in the size of the models."
Author: Allan D. R. McQuarrie Publisher: World Scientific ISBN: 9812385452 Category : Mathematics Languages : en Pages : 479
Book Description
This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models.
Author: Evarist Giné Publisher: Springer Science & Business Media ISBN: 1461213584 Category : Mathematics Languages : en Pages : 491
Book Description
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.
Author: Luca Oneto
Author: Luca Oneto
Author: Peter Bartlett
Author: David Pollard
Author: Tobias Scheffer
Author: Rob J Hyndman
Author: H. Linhart
Author: Ulisses M. Braga Neto
Author: Tobias Scheffer
Author: Allan D. R. McQuarrie
Author: Evarist Giné