Sampling Algorithms
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Sampling Algorithms
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Author : Yves Tillé
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-28
Sampling Algorithms written by Yves Tillé and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-28 with Computers categories.
Over the last few decades, important progresses in the methods of sampling have been achieved. This book draws up an inventory of new methods that can be useful for selecting samples. Forty-six sampling methods are described in the framework of general theory. The algorithms are described rigorously, which allows implementing directly the described methods. This book is aimed at experienced statisticians who are familiar with the theory of survey sampling.Yves Tillé is a professor at the University of Neuchâtel (Switzerland)
Simulating Copulas Stochastic Models Sampling Algorithms And Applications
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Author : Matthias Scherer
language : en
Publisher: World Scientific
Release Date : 2012-06-26
Simulating Copulas Stochastic Models Sampling Algorithms And Applications written by Matthias Scherer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Mathematics categories.
This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.
Sampling Algorithms For Probabilistic Graphical Models With Determinism
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Author : Vibhav Giridhar Gogate
language : en
Publisher:
Release Date : 2009
Sampling Algorithms For Probabilistic Graphical Models With Determinism written by Vibhav Giridhar Gogate and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Mixed constraint and probabilistic graphical models occur quite frequently in many real world applications. Examples include: genetic linkage analysis, functional/software verification, target tracking and activity modeling. Query answering and in particular probabilistic inference on such graphical models is computationally hard often requiring exponential time in the worst case. Therefore in practice sampling algorithms are widely used for providing an approximate answer. In presence of deterministic dependencies or hard constraints, however, sampling has to overcome some principal challenges. In particular, importance sampling type schemes suffer from what is known as the rejection problem in that samples having zero weight may be generated with probability arbitrarily close to one yielding useless results. On the other hand, Markov Chain Monte Carlo techniques do not converge at all often yielding highly inaccurate estimates. In this thesis, we address these problems in a two fold manner. First, we utilize research done in constraint satisfaction and satisfiability communities for processing constraints to reduce or eliminate rejection. Second, mindful of the time overhead in sample generation due to determinism, we both make and utilize advances in statistical estimation theory to make the "most" out of the generated samples. Utilizing constraint satisfaction and satisfiability research, we propose two classes of sampling algorithms - one based on consistency enforcement and the other based on systematic search. The consistency enforcement class of algorithms work by shrinking the domains of random variables, by strengthening constraints, or by creating new ones, so that some or all zeros in the problem space can be removed. This improves convergence because of dimensionality reduction and also reduces rejection because many zero weight samples will not be generated. Our systematic search based techniques called SampleSearch manage the rejection problem by interleaving sampling with backtracking search. In this scheme, when a sample is supposed to be rejected, the algorithm continues instead with systematic backtracking search until a strictly positive-weight sample is generated. The strength of this scheme is that any state-of-the-art constraint satisfaction or propositional satisfiability search algorithm can be used with minor modifications. Through large scale experimental evaluation, we show that SampleSearch outperforms all state-of-the-art schemes when a significant amount of determinism is present in the graphical model. Subsequently, we combine SampleSearch with known statistical techniques such as Sampling Importance Resampling and Metropolis Hastings yielding efficient algorithms for sampling solutions from a uniform distribution over the solutions of a Boolean satisfiability formula. Unlike state-of-the-art algorithms, our SampleSearch-based algorithms guarantee convergence in the limit. As to statistical estimation, we make two distinct contributions. First, we propose several new statistical inequalities extending the one-sample Markov inequality to multiple samples which can be used in conjunction with SampleSearch to probabilistically lower bound likelihood tasks over mixed networks. Second, we present a novel framework called "AND/OR importance sampling" which generalizes the process of computing sample mean by exploiting AND/OR search spaces for graphical models. Specifically we provide a spectrum of AND/OR sample means which are defined on the same set of samples but derive different estimates trading variance with time. At one end is the AND/OR sample tree mean which has smaller variance than the conventional OR sample tree mean and has the same time complexity. At the other end is the AND/OR graph sample mean which has even lower variance but has higher time and space complexity. We demonstrate empirically that AND/OR sample means are far closer to the exact answer than the conventional OR sample mean.
Bayesian Prediction And Adaptive Sampling Algorithms For Mobile Sensor Networks
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Author : Yunfei Xu
language : en
Publisher: Springer
Release Date : 2015-10-27
Bayesian Prediction And Adaptive Sampling Algorithms For Mobile Sensor Networks written by Yunfei Xu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Technology & Engineering categories.
This brief introduces a class of problems and models for the prediction of the scalar field of interest from noisy observations collected by mobile sensor networks. It also introduces the problem of optimal coordination of robotic sensors to maximize the prediction quality subject to communication and mobility constraints either in a centralized or distributed manner. To solve such problems, fully Bayesian approaches are adopted, allowing various sources of uncertainties to be integrated into an inferential framework effectively capturing all aspects of variability involved. The fully Bayesian approach also allows the most appropriate values for additional model parameters to be selected automatically by data, and the optimal inference and prediction for the underlying scalar field to be achieved. In particular, spatio-temporal Gaussian process regression is formulated for robotic sensors to fuse multifactorial effects of observations, measurement noise, and prior distributions for obtaining the predictive distribution of a scalar environmental field of interest. New techniques are introduced to avoid computationally prohibitive Markov chain Monte Carlo methods for resource-constrained mobile sensors. Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks starts with a simple spatio-temporal model and increases the level of model flexibility and uncertainty step by step, simultaneously solving increasingly complicated problems and coping with increasing complexity, until it ends with fully Bayesian approaches that take into account a broad spectrum of uncertainties in observations, model parameters, and constraints in mobile sensor networks. The book is timely, being very useful for many researchers in control, robotics, computer science and statistics trying to tackle a variety of tasks such as environmental monitoring and adaptive sampling, surveillance, exploration, and plume tracking which are of increasing currency. Problems are solved creatively by seamless combination of theories and concepts from Bayesian statistics, mobile sensor networks, optimal experiment design, and distributed computation.
Simulating Copulas Stochastic Models Sampling Algorithms And Applications Second Edition
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Author : Scherer Matthias
language : en
Publisher: #N/A
Release Date : 2017-06-07
Simulating Copulas Stochastic Models Sampling Algorithms And Applications Second Edition written by Scherer Matthias and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with Mathematics categories.
The book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.
Sampling Techniques For Supervised Or Unsupervised Tasks
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Author : Frédéric Ros
language : en
Publisher: Springer Nature
Release Date : 2019-10-26
Sampling Techniques For Supervised Or Unsupervised Tasks written by Frédéric Ros and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-26 with Technology & Engineering categories.
This book describes in detail sampling techniques that can be used for unsupervised and supervised cases, with a focus on sampling techniques for machine learning algorithms. It covers theory and models of sampling methods for managing scalability and the “curse of dimensionality”, their implementations, evaluations, and applications. A large part of the book is dedicated to database comprising standard feature vectors, and a special section is reserved to the handling of more complex objects and dynamic scenarios. The book is ideal for anyone teaching or learning pattern recognition and interesting teaching or learning pattern recognition and is interested in the big data challenge. It provides an accessible introduction to the field and discusses the state of the art concerning sampling techniques for supervised and unsupervised task. Provides a comprehensive description of sampling techniques for unsupervised and supervised tasks; Describe implementation and evaluation of algorithms that simultaneously manage scalable problems and curse of dimensionality; Addresses the role of sampling in dynamic scenarios, sampling when dealing with complex objects, and new challenges arising from big data. "This book represents a timely collection of state-of-the art research of sampling techniques, suitable for anyone who wants to become more familiar with these helpful techniques for tackling the big data challenge." M. Emre Celebi, Ph.D., Professor and Chair, Department of Computer Science, University of Central Arkansas "In science the difficulty is not to have ideas, but it is to make them work" From Carlo Rovelli
Maximum Entropy Sampling
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Author : Marcia Fampa
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Maximum Entropy Sampling written by Marcia Fampa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.
Sampling Algorithms For Evolving Datasets
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Author : Rainer Gemulla
language : en
Publisher:
Release Date : 2008
Sampling Algorithms For Evolving Datasets written by Rainer Gemulla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Sampling Algorithms For Big Graph Analytics
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Author : Guyue Han
language : en
Publisher:
Release Date : 2018
Sampling Algorithms For Big Graph Analytics written by Guyue Han and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Electrical engineering categories.
The analysis of large graphs offers new insights into social and other networks, and thus is of increasing interest to marketeers, sociologists, mathematicians and computer scientists. However, the extremely large size of most graphs of interest renders them difficult to analyze because of at least four challenges: lack of memory, restricted access to the full graph, prohibitive computational cost and real-time changes in the graph. This dissertation presents graph sampling as a powerful and attractive approach to meet the above challenges, whereby properties of the full graph are estimated based on an examination of only a small portion of the graph. In this dissertation, we focus on two graph sampling strategies: edge-based sampling and traversal-based sampling. For edge-based sampling, we propose an edge-based sampling framework for big-graph analytics in dynamic graphs. It enhances the traditional model by enabling the use of additional related information. To demonstrate the advantages of our proposed framework, we present a new sampling algorithm which provides an unbiased estimate of the total number of triangles in a fully dynamic graph where both edge additions and deletions are considered. Our algorithm addresses three of the aforementioned challenges; it has low memory and computational costs, and can be applied to dynamic graphs. In particular, it offers a significantly improved performance in real time estimates compared to current state-of-the-art methods. We also propose several traversal-based graph sampling algorithms for the estimation of a micro-structural property (motif statistics) and the estimation of a macro-structural property (the two largest eigenvalues of the graph). All of these algorithms solve the challenges of prohibitive computational and storage costs, and restricted access. For micro-structural property, we develop a new sampling algorithm which estimates the concentration of mo- tifs of any size via random walk. Unlike previous approaches which enumerate subgraphs around the random walk to find motifs, our algorithm achieves its computational efficiency by using a randomized protocol to sample subgraphs in the neighborhood of the nodes visited by the walk. The experimental results show that our algorithm achieves better accuracy and higher precision than previously known algorithms. For macro-structural property, we propose a series of new sampling algorithms which estimate the top eigenvalues of a graph. Unlike previous methods which try to collect a subgraph with the most influential nodes, our algorithms achieve estimates of the two largest eigenvalues by estimating the number of closed walks of a certain length. The experimental results show that our algorithms are much faster and achieve higher accuracy on most graphs than previously known algorithms seeking to address the same challenges.
Counting Sampling And Integrating Algorithms And Complexity
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Author : Mark Jerrum
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Counting Sampling And Integrating Algorithms And Complexity written by Mark Jerrum and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.