Download or read book Nonparametric Bayesian Methods for Extracting Structure from Data written by Edward Meeds and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Nonparametric Data Analysis written by Peter Müller and published by Springer. This book was released on 2015-06-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.
Download or read book Bayesian Methods for Nonlinear Classification and Regression written by David G. T. Denison and published by John Wiley & Sons. This book was released on 2002-05-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bei der Regressionsanalyse von Datenmaterial erhält man leider selten lineare oder andere einfache Zusammenhänge (parametrische Modelle). Dieses Buch hilft Ihnen, auch komplexere, nichtparametrische Modelle zu verstehen und zu beherrschen. Stärken und Schwächen jedes einzelnen Modells werden durch die Anwendung auf Standarddatensätze demonstriert. Verbreitete nichtparametrische Modelle werden mit Hilfe von Bayes-Verfahren in einen kohärenten wahrscheinlichkeitstheoretischen Zusammenhang gebracht.
Download or read book Bayesian Nonparametric Data Analysis written by Peter Muller and published by Createspace Independent Publishing Platform. This book was released on 2017-07-26 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametric Data AnalysisBy Peter M�ller
Download or read book Bayesian Nonparametrics via Neural Networks written by Herbert K. H. Lee and published by SIAM. This book was released on 2004-01-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics via Neural Networks is the first book to focus on neural networks in the context of nonparametric regression and classification, working within the Bayesian paradigm. Its goal is to demystify neural networks, putting them firmly in a statistical context rather than treating them as a black box. This approach is in contrast to existing books, which tend to treat neural networks as a machine learning algorithm instead of a statistical model. Once this underlying statistical model is recognized, other standard statistical techniques can be applied to improve the model. The Bayesian approach allows better accounting for uncertainty. This book covers uncertainty in model choice and methods to deal with this issue, exploring a number of ideas from statistics and machine learning. A detailed discussion on the choice of prior and new noninformative priors is included, along with a substantial literature review. Written for statisticians using statistical terminology, Bayesian Nonparametrics via Neural Networks will lead statisticians to an increased understanding of the neural network model and its applicability to real-world problems.
Download or read book Nonparametric Bayesian Methods for Supervised and Unsupervised Learning written by Vikash Kumar Mansinghka and published by . This book was released on 2009 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: I introduce two nonparametric Bayesian methods for solving problems of supervised and unsupervised learning. The first method simultaneously learns causal networks and causal theories from data. For example, given synthetic co-occurrence data from a simple causal model for the medical domain, it can learn relationships like "having a flu causes coughing", while also learning that observable quantities can be usefully grouped into categories like diseases and symptoms, and that diseases tend to cause symptoms, not the other way around. The second method is an online algorithm for learning a prototype-based model for categorial concepts, and can be used to solve problems of multiclass classification with missing features. I apply it to problems of categorizing newsgroup posts and recognizing handwritten digits. These approaches were inspired by a striking capacity of human learning, which should also be a desideratum for any intelligent system: the ability to learn certain kinds of "simple" or "natural" structures very quickly, while still being able to learn arbitrary -- and arbitrarily complex - structures given enough data. In each case, I show how nonparametric Bayesian modeling and inference based on stochastic simulation give us some of the tools we need to achieve this goal.
Download or read book Nonparametric Bayesian Models for Machine Learning written by Romain Jean Thibaux and published by . This book was released on 2008 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Nonparametrics written by J.K. Ghosh and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.
Download or read book Bayesian Nonparametric Probabilistic Methods in Machine Learning written by Justin C. Sahs and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many aspects of modern science, business and engineering have become data-centric, relying on tools from Artificial Intelligence and Machine Learning. Practitioners and researchers in these fields need tools that can incorporate observed data into rich models of uncertainty to make discoveries and predictions. One area of study that provides such models is the field of Bayesian Nonparametrics. This dissertation is focused on furthering the development of this field. After reviewing the relevant background and surveying the field, we consider two areas of structured data: - We first consider relational data that takes the form of a 2-dimensional array--such as social network data. We introduce a novel nonparametric model that takes advantage of a representation theorem about arrays whose column and row order is unimportant. We then develop an inference algorithm for this model and evaluate it experimentally. - Second, we consider the classification of streaming data whose distribution evolves over time. We introduce a novel nonparametric model that finds and exploits a dynamic hierarchical structure underlying the data. We present an algorithm for inference in this model and show experimental results. We then extend our streaming model to handle the emergence of novel and recurrent classes, and evaluate the extended model experimentally.
Download or read book Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by . This book was released on 2017 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
Download or read book Bayesian Nonparametrics written by Nils Lid Hjort and published by Cambridge University Press. This book was released on 2010-04-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.
Download or read book Nonparametric Bayesian Methods for Visual Data Association written by 孙星 and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Prior Processes and Their Applications written by Eswar G. Phadia and published by Springer. This book was released on 2016-08-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the past four decades for dealing with Bayesian approach to solving selected nonparametric inference problems. This revised edition has been substantially expanded to reflect the current interest in this area. After an overview of different prior processes, it examines the now pre-eminent Dirichlet process and its variants including hierarchical processes, then addresses new processes such as dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which exploit the countable mixture representation of the Dirichlet process. It subsequently discusses various neutral to right type processes, including gamma and extended gamma, beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet and infinite gamma-Poisson processes, which prove to be very useful in areas such as machine learning, information retrieval and featural modeling. Tailfree and Polya tree and their extensions form a separate chapter, while the last two chapters present the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data as well as right censored data. Because of the conjugacy property of some of these processes, most solutions are presented in closed form. However, the current interest in modeling and treating large-scale and complex data also poses a problem – the posterior distribution, which is essential to Bayesian analysis, is invariably not in a closed form, making it necessary to resort to simulation. Accordingly, the book also introduces several computational procedures, such as the Gibbs sampler, Blocked Gibbs sampler and slice sampling, highlighting essential steps of algorithms while discussing specific models. In addition, it features crucial steps of proofs and derivations, explains the relationships between different processes and provides further clarifications to promote a deeper understanding. Lastly, it includes a comprehensive list of references, equipping readers to explore further on their own.
Download or read book Robust Statistical Modeling Through Nonparametric Bayesian Methods written by Ju Hee Lee and published by . This book was released on 2010 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Nonparametric Bayesian models are commonly used to obtain robust statistical inference, and the most popular nonparametric Bayesian model is, arguably, the mixture of Dirichlet processes (MDP) model. In this study, we examine the question of how to obtain more robustness than under a conventional MDP model. In answer to this question, we develop two models from a nonparametric Bayesian viewpoint, and we investigate their properties: (i) the limiting Dirichlet process (limdir) model, and (ii) the local-mass preserving mixture of Dirichlet process (LMDP) model. The limdir model addresses the question of how to perform a ``noninformative" nonparametric Bayesian analysis. Rather than being noninformative, the model requires a slight amount of input, and so provides us with a minimally informative prior distribution with which to conduct a nonparametric Bayesian analysis. The limdir prior distribution can be viewed as the limit of a sequence of mixture of Dirichlet process models. This model requires only modest input, and yet provides posterior behavior which has a number of important qualitative features, including robustness. Second, the LMDP prior distribution focuses on local mass (defined in the paper). To specify such a prior distribution, we carefully consider the behavior of parameters of interest in some small region, and we then select a prior distribution which preserves mass in the region. Local mass preservation ties the mass of the base measure to its dispersion, resulting in robust inference. These two strategies for constructing a prior distribution can be applied to any model based on the Dirichlet process. Calibration of the prior distribution is considered. We use the limdir for the compound decision problem and the one-way analysis of variance problem, and compare its performance to that of mixture of Dirichlet processes models and to parametric Bayesian models on actual data sets. We apply the LMDP model for the one-way analysis of variance problem, and compare its performance to that of a mixture of Dirichlet processes model with a conventional prior structure. In addition to developing the robust nonparametric Bayesian models, the latter part of the study describes a general form of consistency which does not necessarily rely on correct specification of the likelihood. We carefully investigate issues of consistency and inconsistency for a variety of functions of interest, such as equality of subsets of treatment means, without the assumption that the model is correct. We prove that Bayes estimators achieve (asymptotic) consistency under some suitable regularity conditions on the assumed likelihood. More importantly, we find a need to distinguish between the notions of two parameters being "equal to one another" and "close to one another", and we illustrate differences in asymptotic inference for these two statements. This distinction carries with it implications for Bayesian tests of a point null hypothesis.
Download or read book Some Contributions to Nonparametric Bayesian Methods written by Junjing Lin and published by . This book was released on 2015 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis makes contributions to the area of nonparametric Bayesian methods and applications in two distinct subject areas. One is about classification problems in machine learning. The other is on network meta-analysis in the field of clinical trials. We start by introducing some basic facts about Dirichlet distributions and Dirichlet processes. Nonparametric Bayesian methods and models and their construction follows. We then provide a survey of the existing Markov chain Monte Carlo inference algorithms for Dirichlet Process Mixture models (DPMM), which is followed by a detailed description of these methods to the application problems.
Download or read book Bayesian Nonparametric Methods with Applications in Longitudinal Heterogeneous and Spatiotemporal Data written by Li Duan and published by . This book was released on 2015 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric methods provide flexible accommodation to the different structures in the data without imposing strong assumptions. Bayesian consideration of nonparametric models, such as Gaussian process, Dirichlet process and decision tree enables straightforward computation and automatic regularization. In this dissertation, we developed three novel nonparametric methods for handling different types of data. For the longitudinal and time-to-event data, we utilized the multiple subject composition and repeated measurement, and designed a hierarchical Gaussian process that enables extrapolation for personalized forecast. For the regression of heterogeneous data, we combined the clustering properties of the Dirichlet process and the nonlinear incorporation of predictors in decision tree, and developed an efficient method for handling heterogeneity and ensemble estimation. For the spatiotemporal data, we first designed a performant algorithm for stationary Gaussian process, and then extended it to allow non-stationarity and non-Gaussianness of the complex data. We demonstrate the advantages of the Bayesian modeling in latent variable sampling, missing data handling, algorithm acceleration, accurate prediction and probabilistic interpretation.
Download or read book Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by Cambridge University Press. This book was released on 2017-06-26 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
