Spatial Applications of Markov Random Fields and Neural Networks for Spatio-temporal Denoising, Causal Inference and Reinforcement Learning

Spatial Applications of Markov Random Fields and Neural Networks for Spatio-temporal Denoising, Causal Inference and Reinforcement Learning

Author: Mauricio Benjamín García Tec

Publisher:

Published: 2022

Total Pages: 0

ISBN-13:

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Discrete spatial structures are ubiquitous in statistical analysis. They can take the form of images, grids, and more generally, graphs. This work develops novel methodology leading to broadly applicable algorithms of graph smoothing and neural newtorks to improve statistical learning in a variety of tasks and spatially-structured domains, including temporal and sequential decision-making processes. Thus, each chapter corresponds to a case study with applications in spatio-temporal denoising, causal inference, and reinforcement learning. Graph smoothing methods are used in all of them and their effectiveness is evaluated. In addition, some chapters develop more specialized methods that further exploit the spatial and statistical structure of the data. One of the objectives sustained throughout the work will be developing scalable algorithms to handle high-resolution spatial data or other computationally demanding scenarios


Control of Spatially Structured Random Processes and Random Fields with Applications

Control of Spatially Structured Random Processes and Random Fields with Applications

Author: Ruslan K. Chornei

Publisher: Springer Science & Business Media

Published: 2006-09-03

Total Pages: 269

ISBN-13: 038731279X

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This book is devoted to the study and optimization of spatiotemporal stochastic processes - processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems. The book presents problems and content not considered in other books on controlled Markov processes, especially regarding controlled Markov fields on graphs.


Statistical Inference and Applications of a Spatial-temporal Markov Random Field

Statistical Inference and Applications of a Spatial-temporal Markov Random Field

Author: Zack Nadrich

Publisher:

Published: 2020

Total Pages: 51

ISBN-13:

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Markov random fields (MRF) form a broad class of stochastic models frequently applied to spatial data. A generalization of Markov chains, the MRF models capture spatial correlation by introducing dependence among data on the surface through a chosen neighborhood structure. We introduce a three-dimensional MRF with such neighborhoods that incorporate spatial patterns as well as the time dimension to create a spatio-temporal model. The proposed clique configuration forces spatial dependencies to evolve through time, reflecting dynamics of an observed process.Our statistical inference approach to the Markov Random field is likelihood based. The complex form of the joint distribution of observed spatially and longitudinally dependent data does not allow a closed form of the likelihood function. We show that the pseudolikelihood of this MRF model, as applied to Bernoulli data, can be conveniently expressed as logistic regression. The theory of maximum pseudolikelihood estimation shows that our resulting parameter estimates are consistent and asymptotically normal. As a case study, we use our Markov random field specification to model the dynamics and spread of wildfires. We show that the model can be used to detect wildfire spread and explain the direction and speed at which a wildfire is moving, as well as changes in their behavior in time and in space. We also apply the Markov random field as a generative model in simulations to develop accurate, timely, and probabilistic wildfire spread forecasts, to complement state-of-the-art physical models.


Hybrid Random Fields

Hybrid Random Fields

Author: Antonino Freno

Publisher: Springer Science & Business Media

Published: 2011-04-11

Total Pages: 217

ISBN-13: 3642203086

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This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it. -- Marco Gori, Università degli Studi di Siena Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.


Gaussian Markov Random Fields

Gaussian Markov Random Fields

Author: Havard Rue

Publisher: CRC Press

Published: 2005-02-18

Total Pages: 280

ISBN-13: 0203492021

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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie


Random Fields on a Network

Random Fields on a Network

Author: Xavier Guyon

Publisher: Springer Science & Business Media

Published: 1995-06-23

Total Pages: 294

ISBN-13: 9780387944289

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The theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which assumes only a basic knowledge of probability and statistics, finite Markov chains, and the spectral theory of second-order processes. A particular strength of this book is its emphasis on examples - both to motivate the theory which is being developed, and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms.


Markov Random Fields and Their Applications

Markov Random Fields and Their Applications

Author: Ross Kindermann

Publisher:

Published: 1980

Total Pages: 160

ISBN-13:

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The study of Markov random fields has brought exciting new problems to probability theory which are being developed in parallel with basic investigation in other disciplines, most notably physics. The mathematical and physical literature is often quite technical. This book aims at a more gentle introduction to these new areas of research.


Markov Random Fields

Markov Random Fields

Author: Rama Chellappa

Publisher:

Published: 1993

Total Pages: 608

ISBN-13:

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Introduces the theory and application of Markov random fields in image processing/computer vision. Modelling images through the local interaction of Markov models produces algorithms for use in texture analysis, image synthesis, restoration, segmentation and surface reconstruction.


Modeling Spatio-Temporal Data

Modeling Spatio-Temporal Data

Author: Marco A. R. Ferreira

Publisher:

Published: 2024-11-29

Total Pages: 0

ISBN-13: 9781032622095

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Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Aims to fill some of this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets.


On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory

On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory

Author: Fabian Guignard

Publisher: Springer Nature

Published: 2022-03-12

Total Pages: 170

ISBN-13: 3030952312

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The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.