Non-linear Latent Variable Models for Inference and Learning from Non-Gaussian Data

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)

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Book Synopsis Non-linear Latent Variable Models for Inference and Learning from Non-Gaussian Data by : Hamid Mousavi

Download or read book Non-linear Latent Variable Models for Inference and Learning from Non-Gaussian Data written by Hamid Mousavi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a family of probabilistic generative models that encompasses a variety of probability distributions (including Gaussian, Gamma, Beta, Poisson and many more) from the exponential family. In addition, we investigate a point-wise maximum function and introduce a novel non-linear superposition for coupling the latents and observables using two matrices (if the considered noise distribution has two parameters): One to model the component means and another for component variances. We further exploit the Expectation Maximization (EM) algorithm and show that the presented link function allows for the derivation of a very general and concise set of parameter update equations. Concretely, we derive a set of updates that have the same functional form for all regular distributions of the exponential family. Our results then provide directly applicable learning equations for commonly as well as for unusually distributed data. Finally, to assess the reliability of our theoretical findings, we consider different applications of the proposed generative models and investigate a variety of complex datasets including both synthetic and real data.

Enabling Feature-level Interpretability in Non-linear Latent Variable Models

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis Enabling Feature-level Interpretability in Non-linear Latent Variable Models by : Kaspar Märtens

Download or read book Enabling Feature-level Interpretability in Non-linear Latent Variable Models written by Kaspar Märtens and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-linear Latent Factor Models for Revealing Structure in High-dimensional Data

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Publisher :
ISBN 13 : 9780494590188
Total Pages : 288 pages
Book Rating : 4.5/5 (91 download)

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Book Synopsis Non-linear Latent Factor Models for Revealing Structure in High-dimensional Data by : Roland Memisevic

Download or read book Non-linear Latent Factor Models for Revealing Structure in High-dimensional Data written by Roland Memisevic and published by . This book was released on 2008 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real world data is not random: The variability in the data-sets that arise in computer vision, signal processing and other areas is often highly constrained and governed by a number of degrees of freedom that is much smaller than the superficial dimensionality of the data. Unsupervised learning methods can be used to automatically discover the "true", underlying structure in such data-sets and are therefore a central component in many systems that deal with high-dimensional data.We also show how we can introduce supervision signals into latent variable models using conditioning. Supervision signals make it possible to attach "meaning" to the axes of a latent representation and to untangle the factors that contribute to the variability in the data. We develop a model that uses conditional latent variables to extract rich distributed representations of image transformations, and we describe a new model for learning transformation features in structured supervised learning problems.In this thesis we develop several new approaches to modeling the low-dimensional structure in data. We introduce a new non-parametric framework for latent variable modelling, that in contrast to previous methods generalizes learned embeddings beyond the training data and its latent representatives. We show that the computational complexity for learning and applying the model is much smaller than that of existing methods, and we illustrate its applicability on several problems.

Information Theory, Inference and Learning Algorithms

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Publisher : Cambridge University Press
ISBN 13 : 9780521642989
Total Pages : 694 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Information Theory, Inference and Learning Algorithms by : David J. C. MacKay

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.

Practical Algorithms for Latent Variable Models

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.4/5 (711 download)

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Book Synopsis Practical Algorithms for Latent Variable Models by : Gregory W. Gundersen

Download or read book Practical Algorithms for Latent Variable Models written by Gregory W. Gundersen and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Latent variables allow researchers and engineers to encode assumptions into their statistical models. A latent variable might, for example, represent an unobserved covariate, measurement error, or a missing class label. Inference is challenging because one must account for the conditional dependence structure induced by these variables, and marginalization is often intractable. In this thesis, I present several practical algorithms for inferring latent structure in probabilistic models used in computational biology, neuroscience, and time-series analysis.First, I present a multi-view framework that combines neural networks and probabilistic canonical correlation analysis to estimate shared and view-specific latent structure of paired samples of histological images and gene expression levels. The model is trained end-to-end to estimate all parameters simultaneously, and we show that the latent variables capture interpretable structure, such as tissue-specific and morphological variation. Next, I present a family of nonlinear dimension-reduction models that use random features to support non-Gaussian data likelihoods. By approximating a nonlinear relationship between the latent variables and observations with a function that is linear with respect to random features, we induce closed-form gradients of the posterior distribution with respect to the latent variables. This allows for gradient-based nonlinear dimension-reduction models for a variety of data likelihoods. Finally, I discuss lowering the computational cost of online Bayesian filtering of time series with abrupt changes in structure, called changepoints. We consider settings in which a time series has multiple data sources, each with an associated cost. We trade the cost of a data source against the quality or fidelity of that source and how its fidelity affects the estimation of changepoints. Our framework makes cost-sensitive decisions about which data source to use based on minimizing the information entropy of the posterior distribution over changepoints.

Backward Simulation Methods for Monte Carlo Statistical Inference

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ISBN 13 : 9781601986993
Total Pages : 145 pages
Book Rating : 4.9/5 (869 download)

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Book Synopsis Backward Simulation Methods for Monte Carlo Statistical Inference by : Fredrik Lindsten

Download or read book Backward Simulation Methods for Monte Carlo Statistical Inference written by Fredrik Lindsten and published by . This book was released on 2013 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward Simulation Methods for Monte Carlo Statistical Inference presents and discusses various backward simulation methods for Monte Carlo statistical inference. The focus is on SMC-based backward simulators, which are useful for inference in analytically intractable models, such as nonlinear and/or non-Gaussian SSMs, but also in more general latent variable models.

Inference and Learning from Data: Volume 2

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Publisher : Cambridge University Press
ISBN 13 : 1009218255
Total Pages : 1166 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Inference and Learning from Data: Volume 2 by : Ali H. Sayed

Download or read book Inference and Learning from Data: Volume 2 written by Ali H. Sayed and published by Cambridge University Press. This book was released on 2022-12-22 with total page 1166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This second volume, Inference, builds on the foundational topics established in volume I to introduce students to techniques for inferring unknown variables and quantities, including Bayesian inference, Monte Carlo Markov Chain methods, maximum-likelihood estimation, hidden Markov models, Bayesian networks, and reinforcement learning. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including solutions for instructors), 180 solved examples, almost 200 figures, datasets and downloadable Matlab code. Supported by sister volumes Foundations and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.

Latent Variable Models for Multiple Longitudinal Outcomes with Non-ignorable Missing Data

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ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Latent Variable Models for Multiple Longitudinal Outcomes with Non-ignorable Missing Data by : Xiaohong Yan

Download or read book Latent Variable Models for Multiple Longitudinal Outcomes with Non-ignorable Missing Data written by Xiaohong Yan and published by . This book was released on 2007 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Class of Non-Gaussian State Space Models with Exact Likelihood Inference

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ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis A Class of Non-Gaussian State Space Models with Exact Likelihood Inference by : Drew Creal

Download or read book A Class of Non-Gaussian State Space Models with Exact Likelihood Inference written by Drew Creal and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The likelihood function for general non-linear, non-Gaussian state space models is a high- dimensional integral with no closed-form solution. In this paper, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that includes stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a non-negative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the maximum likelihood estimator, I also show how to perform filtering and smoothing to estimate the latent variables in the model. Finally, it is also possible to take random draws from the joint posterior distribution of the latent states conditional on the data and the model's parameters, which is valuable for inference of more complex models.

Handbook of Graphical Models

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Publisher : CRC Press
ISBN 13 : 0429874235
Total Pages : 612 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Handbook of Graphical Models by : Marloes Maathuis

Download or read book Handbook of Graphical Models written by Marloes Maathuis and published by CRC Press. This book was released on 2018-11-12 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference. While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Independent Component Analysis and Signal Separation

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Publisher : Springer
ISBN 13 : 3540744940
Total Pages : 864 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Independent Component Analysis and Signal Separation by : Mike E. Davies

Download or read book Independent Component Analysis and Signal Separation written by Mike E. Davies and published by Springer. This book was released on 2007-12-20 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Independent Component Analysis and Blind Source Separation, ICA 2007, held in London, UK, in September 2007. It covers algorithms and architectures, applications, medical applications, speech and signal processing, theory, and visual and sensory processing.

Latent Variable Models and Factor Analysis

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Publisher : Wiley
ISBN 13 : 9780340692431
Total Pages : 214 pages
Book Rating : 4.6/5 (924 download)

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Book Synopsis Latent Variable Models and Factor Analysis by : David J. Bartholomew

Download or read book Latent Variable Models and Factor Analysis written by David J. Bartholomew and published by Wiley. This book was released on 1999-08-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hitherto latent variable modelling has hovered on the fringes of the statistical mainstream but if the purpose of statistics is to deal with real problems, there is every reason for it to move closer to centre stage. In the social sciences especially, latent variables are common and if they are to be handled in a truly scientific manner, statistical theory must be developed to include them. This book aims to show how that should be done. This second edition is a complete re-working of the book of the same name which appeared in the Griffin’s Statistical Monographs in 1987. Since then there has been a surge of interest in latent variable methods which has necessitated a radical revision of the material but the prime object of the book remains the same. It provides a unified and coherent treatment of the field from a statistical perspective. This is achieved by setting up a sufficiently general framework to enable the derivation of the commonly used models. The subsequent analysis is then done wholly within the realm of probability calculus and the theory of statistical inference. Numerical examples are provided as well as the software to carry them out ( where this is not otherwise available). Additional data sets are provided in some cases so that the reader can aquire a wider experience of analysis and interpretation.

Gaussian Processes for Machine Learning

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Publisher : MIT Press
ISBN 13 : 026218253X
Total Pages : 266 pages
Book Rating : 4.2/5 (621 download)

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Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen

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.

Handbook of Bayesian, Fiducial, and Frequentist Inference

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Publisher : CRC Press
ISBN 13 : 1003837646
Total Pages : 421 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Handbook of Bayesian, Fiducial, and Frequentist Inference by : James Berger

Download or read book Handbook of Bayesian, Fiducial, and Frequentist Inference written by James Berger and published by CRC Press. This book was released on 2024-02-26 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference. Key Features: Provides a comprehensive introduction to the key developments in the BFF schools of inference Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge Is accessible for readers with different perspectives and backgrounds

Advanced State Space Methods for Neural and Clinical Data

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Publisher : Cambridge University Press
ISBN 13 : 1107079195
Total Pages : 397 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Advanced State Space Methods for Neural and Clinical Data by : Zhe Chen

Download or read book Advanced State Space Methods for Neural and Clinical Data written by Zhe Chen and published by Cambridge University Press. This book was released on 2015-10-15 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative and in-depth treatment of state space methods, with a range of applications in neural and clinical data.

Modelling and Control of Dynamic Systems Using Gaussian Process Models

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Publisher : Springer
ISBN 13 : 3319210211
Total Pages : 281 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Modelling and Control of Dynamic Systems Using Gaussian Process Models by : Juš Kocijan

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.

Non-linear Latent Variable Model

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ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis Non-linear Latent Variable Model by : S. H. C. Du Toit

Download or read book Non-linear Latent Variable Model written by S. H. C. Du Toit and published by . This book was released on 1982 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: