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.

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.

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.

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.

Download or read book Powered Prostheses written by Houman Dallali and published by Academic Press. This book was released on 2020-04-17 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Powered Prostheses: Design, Control, and Clinical Applications presents the state-of-the-art in design, control and application of assistive technologies used in rehabilitation, including powered prostheses used in lower and upper extremity amputees and orthosis used in the rehabilitation of various joint disorders. The progress made in this field over the last decade is so vast that any new researcher in this field will have to spend years digesting the main achievements and challenges that remain. This book provides a comprehensive vision of advances, along with the challenges that remain on the path to the development of true bionic technology. - Describes the latest assistive technologies that can help individuals deal with joint pain or limb loss - Presents a tangible and intuitive description of scientific achievements made - Highlights the existing technologies and devices that are available and used by amputees or patients with mobility limitations - Suggests solutions and new results that can further enhance assistive technologies

Download or read book Automated Machine Learning written by Frank Hutter and published by Springer. This book was released on 2019-05-17 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents the first comprehensive overview of general methods in Automated Machine Learning (AutoML), collects descriptions of existing systems based on these methods, and discusses the first series of international challenges of AutoML systems. The recent success of commercial ML applications and the rapid growth of the field has created a high demand for off-the-shelf ML methods that can be used easily and without expert knowledge. However, many of the recent machine learning successes crucially rely on human experts, who manually select appropriate ML architectures (deep learning architectures or more traditional ML workflows) and their hyperparameters. To overcome this problem, the field of AutoML targets a progressive automation of machine learning, based on principles from optimization and machine learning itself. This book serves as a point of entry into this quickly-developing field for researchers and advanced students alike, as well as providing a reference for practitioners aiming to use AutoML in their work.

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.

Download or read book A Tutorial on Thompson Sampling written by Daniel J. Russo and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this tutorial is to explain when, why, and how to apply Thompson sampling.

Download or read book Machine Learning and Knowledge Discovery in Databases written by Michelangelo Ceci and published by Springer. This book was released on 2017-12-29 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume proceedings LNAI 10534 – 10536 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2017, held in Skopje, Macedonia, in September 2017. The total of 101 regular papers presented in part I and part II was carefully reviewed and selected from 364 submissions; there are 47 papers in the applied data science, nectar and demo track. The contributions were organized in topical sections named as follows: Part I: anomaly detection; computer vision; ensembles and meta learning; feature selection and extraction; kernel methods; learning and optimization, matrix and tensor factorization; networks and graphs; neural networks and deep learning. Part II: pattern and sequence mining; privacy and security; probabilistic models and methods; recommendation; regression; reinforcement learning; subgroup discovery; time series and streams; transfer and multi-task learning; unsupervised and semisupervised learning. Part III: applied data science track; nectar track; and demo track.

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.

Download or read book Bayesian Modeling of Spatio Temporal Data with R written by Sujit Sahu and published by CRC Press. This book was released on 2022-02-23 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied sciences, both physical and social, such as atmospheric, biological, climate, demographic, economic, ecological, environmental, oceanic and political, routinely gather large volumes of spatial and spatio-temporal data in order to make wide ranging inference and prediction. Ideally such inferential tasks should be approached through modelling, which aids in estimation of uncertainties in all conclusions drawn from such data. Unified Bayesian modelling, implemented through user friendly software packages, provides a crucial key to unlocking the full power of these methods for solving challenging practical problems. Key features of the book: • Accessible detailed discussion of a majority of all aspects of Bayesian methods and computations with worked examples, numerical illustrations and exercises • A spatial statistics jargon buster chapter that enables the reader to build up a vocabulary without getting clouded in modeling and technicalities • Computation and modeling illustrations are provided with the help of the dedicated R package bmstdr, allowing the reader to use well-known packages and platforms, such as rstan, INLA, spBayes, spTimer, spTDyn, CARBayes, CARBayesST, etc • Included are R code notes detailing the algorithms used to produce all the tables and figures, with data and code available via an online supplement • Two dedicated chapters discuss practical examples of spatio-temporal modeling of point referenced and areal unit data • Throughout, the emphasis has been on validating models by splitting data into test and training sets following on the philosophy of machine learning and data science This book is designed to make spatio-temporal modeling and analysis accessible and understandable to a wide audience of students and researchers, from mathematicians and statisticians to practitioners in the applied sciences. It presents most of the modeling with the help of R commands written in a purposefully developed R package to facilitate spatio-temporal modeling. It does not compromise on rigour, as it presents the underlying theories of Bayesian inference and computation in standalone chapters, which would be appeal those interested in the theoretical details. By avoiding hard core mathematics and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.

Download or read book Partitional Clustering Algorithms written by M. Emre Celebi and published by Springer. This book was released on 2014-11-07 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on partitional clustering algorithms, which are commonly used in engineering and computer scientific applications. The goal of this volume is to summarize the state-of-the-art in partitional clustering. The book includes such topics as center-based clustering, competitive learning clustering and density-based clustering. Each chapter is contributed by a leading expert in the field.

Download or read book Machine Learning and Knowledge Discovery in Databases written by Michelangelo Ceci and published by Springer. This book was released on 2017-12-29 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume proceedings LNAI 10534 – 10536 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2017, held in Skopje, Macedonia, in September 2017. The total of 101 regular papers presented in part I and part II was carefully reviewed and selected from 364 submissions; there are 47 papers in the applied data science, nectar and demo track. The contributions were organized in topical sections named as follows: Part I: anomaly detection; computer vision; ensembles and meta learning; feature selection and extraction; kernel methods; learning and optimization, matrix and tensor factorization; networks and graphs; neural networks and deep learning. Part II: pattern and sequence mining; privacy and security; probabilistic models and methods; recommendation; regression; reinforcement learning; subgroup discovery; time series and streams; transfer and multi-task learning; unsupervised and semisupervised learning. Part III: applied data science track; nectar track; and demo track.

Download or read book Information Theory Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Download or read book Simulation for a Sustainable Future written by Miguel Mujica Mota and published by Springer Nature. This book was released on with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Learning for Neural Networks written by Radford M. Neal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence.

Download or read book Advances in Neural Information Processing Systems 19 written by Bernhard Schölkopf and published by MIT Press. This book was released on 2007 with total page 1668 pages. Available in PDF, EPUB and Kindle. Book excerpt: The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation and machine learning. This volume contains the papers presented at the December 2006 meeting, held in Vancouver.