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Author : Florian Wenzel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (115 download)
Download or read book Scalable Inference in Latent Gaussian Process Models written by Florian Wenzel and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yunus Saatçi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (89 download)
Download or read book Scalable Inference for Structured Gaussian Process Models written by Yunus Saatçi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Trung Van Nguyen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (144 download)
Download or read book Scalable and Automated Inference for Gaussian Process Models written by Trung Van Nguyen and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian processes (GPs) are widely used in the Bayesian approach to supervised learning. Their ability to provide rich priors over functions is highly desirable for modeling real-world problems. Unfortunately, there exist two big challenges when doing Bayesian inference (i.e., learning the posteriors over functions) for GP models. The first is analytical intractability: The posteriors cannot be computed in closed- form when non-Gaussian likelihoods are employed. The second is scalability: The inference procedures often cannot be applied to large datasets due to their prohibitive computational costs. In this thesis, I develop practical variational inference methods to address the first challenge. Moreover, I introduce three GP models to deal with the second challenge. First, I focus on the analytical intractability challenge starting with the Gaussian process regression networks (GPRN), an expressive multi-output model with adaptive, input-dependent correlations. I derive a variational inference method with two different variational distributions to approximate the true posterior of GPRN. While one distribution is a standard Gaussian, the other is a Gaussian mixture which can capture more complex, multimodal posteriors. Both distributions are shown to be statistically efficient, requiring only a linear number of parameters to represent their inherent covariance matrices. Experimental results demonstrate clear benefits of having a multimodal variational approximation in GPRN. Next, I use the same two variational distributions to address the analytical in- tractability challenge for a large class of GP models. I show that the aforementioned statistical efficiency also stands for members of this class. I further prove that the gradients required for variational learning can either be approximated efficiently or computed analytically, regardless of the likelihood functions of the models. Based on these insights, I develop an automated variational inference method for GP models with general likelihoods. The method allows easy investigation of existing or new models without having to derive model-specific inference algorithms. I then turn to the scalability challenge, focusing on single-output and multi- output regression. The underpinning technique here is sparse GP - a GP augmented with so-called inducing points/variables that lead to lower computational demands. For single-output regression, I introduce a mixture-of-experts model (FGP) where the experts are independent sparse GPs each having their own inducing variables. Their inducing inputs further define a partitioning structure of the input space, allowing an efficient inference scheme in which computation is carried out locally by the experts. FGP can thus be K2 time faster and use K2 less memory than previous GP models, where K is the number of experts. For multi-output regression, I introduce the collaborative multi-output Gaussian process model (COGP) where the outputs are linear combinations of independent sparse GPs. Their inducing points are represented as global variables which correlate the outputs for joint learning. The variables are then exploited to derive a stochastic variational inference method that can deal with a much larger number of inputs and outputs compared to previous models. Superior empirical performance of FGP and COGP is demonstrated through extensive experiments on various real-world datasets.
Author : David Burt
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book Scalable Approximate Inference and Model Selection in Gaussian Process Regression written by David Burt and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David J. Balding
Publisher : John Wiley & Sons
ISBN 13 : 1119429250
Total Pages : 1828 pages
Book Rating : 4.1/5 (194 download)
Download or read book Handbook of Statistical Genomics written by David J. Balding and published by John Wiley & Sons. This book was released on 2019-07-09 with total page 1828 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely update of a highly popular handbook on statistical genomics This new, two-volume edition of a classic text provides a thorough introduction to statistical genomics, a vital resource for advanced graduate students, early-career researchers and new entrants to the field. It introduces new and updated information on developments that have occurred since the 3rd edition. Widely regarded as the reference work in the field, it features new chapters focusing on statistical aspects of data generated by new sequencing technologies, including sequence-based functional assays. It expands on previous coverage of the many processes between genotype and phenotype, including gene expression and epigenetics, as well as metabolomics. It also examines population genetics and evolutionary models and inference, with new chapters on the multi-species coalescent, admixture and ancient DNA, as well as genetic association studies including causal analyses and variant interpretation. The Handbook of Statistical Genomics focuses on explaining the main ideas, analysis methods and algorithms, citing key recent and historic literature for further details and references. It also includes a glossary of terms, acronyms and abbreviations, and features extensive cross-referencing between chapters, tying the different areas together. With heavy use of up-to-date examples and references to web-based resources, this continues to be a must-have reference in a vital area of research. Provides much-needed, timely coverage of new developments in this expanding area of study Numerous, brand new chapters, for example covering bacterial genomics, microbiome and metagenomics Detailed coverage of application areas, with chapters on plant breeding, conservation and forensic genetics Extensive coverage of human genetic epidemiology, including ethical aspects Edited by one of the leading experts in the field along with rising stars as his co-editors Chapter authors are world-renowned experts in the field, and newly emerging leaders. The Handbook of Statistical Genomics is an excellent introductory text for advanced graduate students and early-career researchers involved in statistical genetics.
Author : Schinichiro Shirota
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Scalable Inference for Space-Time Gaussian Cox Processes written by Schinichiro Shirota and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The log-Gaussian Cox process is a flexible and popular stochastic process for modeling point patterns exhibiting spatial and space-time dependence. Model fitting requires approximation of stochastic integrals which is implemented through discretization over the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally burdensome because of the cost of matrix decompositions and storage, such as the Cholesky, for high dimensional covariance matrices associated with latent Gaussian variables. This article addresses these computational bottlenecks by combining two recent developments: (i) a data augmentation strategy that has been proposed for space-time Gaussian Cox processes that is based on exact Bayesian inference and does not require fine grid approximations for infinite dimensional integrals, and (ii) a recently developed family of sparsity-inducing Gaussian processes, called nearest-neighbor Gaussian processes, to avoid expensive matrix computations. Our inference is delivered within the fully model-based Bayesian paradigm and does not sacrifice the richness of traditional log-Gaussian Cox processes. We apply our method to crime event data in San Francisco and investigate the recovery of the intensity surface.
Author : Alexander Graeme de Garis Matthews
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Scalable Gaussian Process Inference Using Variational Methods written by Alexander Graeme de Garis Matthews and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matthew James Johnson (Ph. D.)
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.:/5 (89 download)
Download or read book Bayesian Time Series Models and Scalable Inference written by Matthew James Johnson (Ph. D.) and published by . This book was released on 2014 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: With large and growing datasets and complex models, there is an increasing need for scalable Bayesian inference. We describe two lines of work to address this need. In the first part, we develop new algorithms for inference in hierarchical Bayesian time series models based on the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and their Bayesian nonparametric extensions. The HMM is ubiquitous in Bayesian time series models, and it and its Bayesian nonparametric extension, the hierarchical Dirichlet process hidden Markov model (HDP-HMM), have been applied in many settings. HSMMs and HDP-HSMMs extend these dynamical models to provide state-specific duration modeling, but at the cost of increased computational complexity for inference, limiting their general applicability. A challenge with all such models is scaling inference to large datasets. We address these challenges in several ways. First, we develop classes of duration models for which HSMM message passing complexity scales only linearly in the observation sequence length. Second, we apply the stochastic variational inference (SVI) framework to develop scalable inference for the HMM, HSMM, and their nonparametric extensions. Third, we build on these ideas to define a new Bayesian nonparametric model that can capture dynamics at multiple timescales while still allowing efficient and scalable inference. In the second part of this thesis, we develop a theoretical framework to analyze a special case of a highly parallelizable sampling strategy we refer to as Hogwild Gibbs sampling. Thorough empirical work has shown that Hogwild Gibbs sampling works very well for inference in large latent Dirichlet allocation models (LDA), but there is little theory to understand when it may be effective in general. By studying Hogwild Gibbs applied to sampling from Gaussian distributions we develop analytical results as well as a deeper understanding of its behavior, including its convergence and correctness in some regimes.
Author : Owen Matthew Truscott Thomas
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Scalable Inference and Private Co-training for Gaussian Processes written by Owen Matthew Truscott Thomas and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carl Edward Rasmussen
Publisher : MIT Press
ISBN 13 : 026218253X
Total Pages : 266 pages
Book Rating : 4.2/5 (621 download)
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Author : Geoff Pleiss
Publisher :
ISBN 13 :
Total Pages : 213 pages
Book Rating : 4.:/5 (124 download)
Download or read book A Scalable and Flexible Framework for Gaussian Processes Via Matrix-vector Multiplication written by Geoff Pleiss and published by . This book was released on 2020 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian processes (GPs) exhibit a classic tension of many machine learning methods: they possess desirable modelling capabilities yet suffer from important practical limitations. In many instances, GPs are able to offer well-calibrated uncertainty estimates, interpretable predictions, and the ability to encode prior knowledge. These properties have made them an indispensable tool for black-box optimization, time series forecasting, and high-risk applications like health care. Despite these benefits, GPs are typically not applied to datasets with more than a few thousand data points. This is in part due to an inference procedure that requires matrix inverses, determinants, and other expensive operations. Moreover, specialty models often require significant implementation efforts. This thesis aims to alleviate these practical concerns through a single simple design decision. Taking inspiration from neural network libraries, we construct GP inference algorithms using only matrix-vector multiplications (MVMs) and other linear operations. This MVM-based approach simultaneously address several of these practical concerns: it reduces asymptotic complexity, effectively utilizes GPU hardware, and provides straight-forward implementations for many specialty GP models. The chapters of this thesis each address a different aspect of Gaussian process inference. Chapter 3 introduces a MVM method for training Gaussian process regression models (i.e. optimizing kernel/likelihood hyperparameters). This approach unifies several existing methods into a highly-parallel and stable algorithm. Chapter 4 focuses on making predictions with Gaussian processes. A memory-efficient cache, which can be computed through MVMs, significantly reduces the computation of predictive distributions. Chapter 5 introduces a multi-purpose MVM algorithm that can be used to draw samples from GP posteriors and perform approximate Gaussian process inference. All three of these methods offer speedups ranging from 4x to 40x. Importantly, applying any of these algorithms to specialty models (e.g. multitask GPs and scalable approximations) simply requires a matrix-vector multiplication routine that exploits covariance structure afforded by the model. The MVM methods from this thesis form the building blocks of the GPyTorch library, an open-sourced GP implementation designed for scalability and simple implementations. In the final chapter, we evaluate GPyTorch models on several large-scale regression datasets. Using the proposed MVM methods, we can apply exact Gaussian processes to datasets that are 2 orders of magnitude larger than what has previously been reported - up to 1 million data points.
Author : Per Sidén
Publisher : Linköping University Electronic Press
ISBN 13 : 9179298184
Total Pages : 53 pages
Book Rating : 4.1/5 (792 download)
Download or read book Scalable Bayesian spatial analysis with Gaussian Markov random fields written by Per Sidén and published by Linköping University Electronic Press. This book was released on 2020-08-17 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points. In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty. We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons. Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter. I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet. Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.
Author : Jakob Lindinger
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Variational Inference for Composite Gaussian Process Models written by Jakob Lindinger and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marc Peter Deisenroth
Publisher : KIT Scientific Publishing
ISBN 13 : 3866445695
Total Pages : 226 pages
Book Rating : 4.8/5 (664 download)
Download or read book Efficient Reinforcement Learning Using Gaussian Processes written by Marc Peter Deisenroth and published by KIT Scientific Publishing. This book was released on 2010 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines Gaussian processes in both model-based reinforcement learning (RL) and inference in nonlinear dynamic systems.First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO takes model uncertainties consistently into account during long-term planning to reduce model bias. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems.
Author : Juš Kocijan
Publisher : Springer
ISBN 13 : 3319210211
Total Pages : 281 pages
Book Rating : 4.3/5 (192 download)
Download or read book Modelling and Control of Dynamic Systems Using Gaussian Process Models written by Juš Kocijan and published by Springer. This book was released on 2015-11-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior knowledge then leading into full-blown control. The book is illustrated by extensive use of examples, line drawings, and graphical presentation of computer-simulation results and plant measurements. The research results presented are applied in real-life case studies drawn from successful applications including: a gas–liquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB® toolbox, for identification and simulation of dynamic GP models is provided for download.
Author : Krikamol Muandet
Publisher :
ISBN 13 : 9781680832884
Total Pages : 154 pages
Book Rating : 4.8/5 (328 download)
Download or read book Kernel Mean Embedding of Distributions written by Krikamol Muandet and published by . This book was released on 2017-06-28 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive review of kernel mean embeddings of distributions and, in the course of doing so, discusses some challenging issues that could potentially lead to new research directions. The targeted audience includes graduate students and researchers in machine learning and statistics.
Author : Virgilio Gomez-Rubio
Publisher : CRC Press
ISBN 13 : 1351707205
Total Pages : 330 pages
Book Rating : 4.3/5 (517 download)
Download or read book Bayesian inference with INLA written by Virgilio Gomez-Rubio and published by CRC Press. This book was released on 2020-02-20 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.
