A Mixture Approach to Universal Model Selection
Author: Olivier Catoni
Publisher:
Published: 1997
Total Pages: 19
ISBN-13:
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Mixture Models and Applications
Author: Nizar Bouguila
Publisher: Springer
Published: 2019-08-13
Total Pages: 355
ISBN-13: 3030238768
DOWNLOAD EBOOKThis book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.
Learning Theory
Author: Hans Ulrich Simon
Publisher: Springer
Published: 2006-09-29
Total Pages: 667
ISBN-13: 3540352961
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, held in Pittsburgh, Pennsylvania, USA, June 2006. The book presents 43 revised full papers together with 2 articles on open problems and 3 invited lectures. The papers cover a wide range of topics including clustering, un- and semi-supervised learning, statistical learning theory, regularized learning and kernel methods, query learning and teaching, inductive inference, and more.
Universal Coding and Order Identification by Model Selection Methods
Author: Élisabeth Gassiat
Publisher: Springer
Published: 2018-07-28
Total Pages: 158
ISBN-13: 3319962620
DOWNLOAD EBOOKThe purpose of these notes is to highlight the far-reaching connections between Information Theory and Statistics. Universal coding and adaptive compression are indeed closely related to statistical inference concerning processes and using maximum likelihood or Bayesian methods. The book is divided into four chapters, the first of which introduces readers to lossless coding, provides an intrinsic lower bound on the codeword length in terms of Shannon’s entropy, and presents some coding methods that can achieve this lower bound, provided the source distribution is known. In turn, Chapter 2 addresses universal coding on finite alphabets, and seeks to find coding procedures that can achieve the optimal compression rate, regardless of the source distribution. It also quantifies the speed of convergence of the compression rate to the source entropy rate. These powerful results do not extend to infinite alphabets. In Chapter 3, it is shown that there are no universal codes over the class of stationary ergodic sources over a countable alphabet. This negative result prompts at least two different approaches: the introduction of smaller sub-classes of sources known as envelope classes, over which adaptive coding may be feasible, and the redefinition of the performance criterion by focusing on compressing the message pattern. Finally, Chapter 4 deals with the question of order identification in statistics. This question belongs to the class of model selection problems and arises in various practical situations in which the goal is to identify an integer characterizing the model: the length of dependency for a Markov chain, number of hidden states for a hidden Markov chain, and number of populations for a population mixture. The coding ideas and techniques developed in previous chapters allow us to obtain new results in this area. This book is accessible to anyone with a graduate level in Mathematics, and will appeal to information theoreticians and mathematical statisticians alike. Except for Chapter 4, all proofs are detailed and all tools needed to understand the text are reviewed.
Foundations of Computational Mathematics
Author: Felipe Cucker
Publisher: World Scientific
Published: 2002
Total Pages: 488
ISBN-13: 9789812778031
DOWNLOAD EBOOKThis invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 ("From Topology to Computation") held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
Foundations Of Computational Mathematics, Proceedings Of Smalefest 2000
Author: Felipe Cucker
Publisher: World Scientific
Published: 2002-02-25
Total Pages: 479
ISBN-13: 9814489425
DOWNLOAD EBOOKThis invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 (”From Topology to Computation”) held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
Introduction to High-Dimensional Statistics
Author: Christophe Giraud
Publisher: CRC Press
Published: 2014-12-17
Total Pages: 270
ISBN-13: 1482237954
DOWNLOAD EBOOKEver-greater computing technologies have given rise to an exponentially growing volume of data. Today massive data sets (with potentially thousands of variables) play an important role in almost every branch of modern human activity, including networks, finance, and genetics. However, analyzing such data has presented a challenge for statisticians
Statistical Learning Theory and Stochastic Optimization
Author: Olivier Catoni
Publisher: Springer
Published: 2004-08-30
Total Pages: 278
ISBN-13: 3540445072
DOWNLOAD EBOOKStatistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools, that will stimulate further studies and results.
Model Selection in Mixture Modeling
Author: Emilie Shireman
Publisher:
Published: 2016
Total Pages: 72
ISBN-13:
DOWNLOAD EBOOKIn the psychological sciences, mixture modeling (also referred to as latent class or latent profile analysis) is very commonly used to find sub-populations within a sample. However, the process by which researchers select a model (i.e., how many sub-populations and how many covariance parameters) is not standardized. Furthermore, many techniques that researchers use to select a model are ad hoc and have varied statistical theoretical support. This dissertation systematically examines three commonly used but not formally tested model selection heuristics for mixture modeling: (1) using several fit indices to collectively select a model, (2) using the difference in fit to differentiate "weak" versus "strong" evidence of one solution over another, and (3) examining the difficulty in convergence to indicate that a model is over-specified.
Academic Press Library in Signal Processing
Author: Paulo S.R. Diniz
Publisher: Academic Press
Published: 2013-09-21
Total Pages: 1559
ISBN-13: 0123972264
DOWNLOAD EBOOKThis first volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in machine learning and advanced signal processing theory. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its application Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved Quick tutorial reviews of important and emerging topics of research in machine learning Presents core principles in signal processing theory and shows their applications Reference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
