Identification And Other Probabilistic Models

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Identification and Other Probabilistic Models

Author : Rudolf Ahlswede
Publisher : Springer Nature
ISBN 13 : 3030650723
Total Pages : 720 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Identification and Other Probabilistic Models by : Rudolf Ahlswede

Download or read book Identification and Other Probabilistic Models written by Rudolf Ahlswede and published by Springer Nature. This book was released on 2021-06-22 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Identification Theory. In contrast to Shannon's classical coding scheme for the transmission of a message over a noisy channel, in the theory of identification the decoder is not really interested in what the received message is, but only in deciding whether a message, which is of special interest to him, has been sent or not. There are also algorithmic problems where it is not necessary to calculate the solution, but only to check whether a certain given answer is correct. Depending on the problem, this answer might be much easier to give than finding the solution. ``Easier'' in this context means using fewer resources like channel usage, computing time or storage space. Ahlswede and Dueck's main result was that, in contrast to transmission problems, where the possible code sizes grow exponentially fast with block length, the size of identification codes will grow doubly exponentially fast. The theory of identification has now developed into a sophisticated mathematical discipline with many branches and facets, forming part of the Post Shannon theory in which Ahlswede was one of the leading experts. New discoveries in this theory are motivated both by concrete engineering problems and by explorations of the inherent properties of the mathematical structures. Rudolf Ahlswede wrote: It seems that the whole body of present day Information Theory will undergo serious revisions and some dramatic expansions. In this book we will open several directions of future research and start the mathematical description of communication models in great generality. For some specific problems we provide solutions or ideas for their solutions. The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs. The book also contains an afterword by Gunter Dueck.

Identification and Other Probabilistic Models

Author : Rudolf Ahlswede
Publisher :
ISBN 13 : 9783030650711
Total Pages : 0 pages
Book Rating : 4.6/5 (57 download)

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Book Synopsis Identification and Other Probabilistic Models by : Rudolf Ahlswede

Download or read book Identification and Other Probabilistic Models written by Rudolf Ahlswede and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Identification Theory. In contrast to Shannon's classical coding scheme for the transmission of a message over a noisy channel, in the theory of identification the decoder is not really interested in what the received message is, but only in deciding whether a message, which is of special interest to him, has been sent or not. There are also algorithmic problems where it is not necessary to calculate the solution, but only to check whether a certain given answer is correct. Depending on the problem, this answer might be much easier to give than finding the solution. ``Easier'' in this context means using fewer resources like channel usage, computing time or storage space. Ahlswede and Dueck's main result was that, in contrast to transmission problems, where the possible code sizes grow exponentially fast with block length, the size of identification codes will grow doubly exponentially fast. The theory of identification has now developed into a sophisticated mathematical discipline with many branches and facets, forming part of the Post Shannon theory in which Ahlswede was one of the leading experts. New discoveries in this theory are motivated both by concrete engineering problems and by explorations of the inherent properties of the mathematical structures. Rudolf Ahlswede wrote: It seems that the whole body of present day Information Theory will undergo serious revisions and some dramatic expansions. In this book we will open several directions of future research and start the mathematical description of communication models in great generality. For some specific problems we provide solutions or ideas for their solutions. The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs. The book also contains an afterword by Gunter Dueck.

Probabilistic Graphical Models

Author : Luis Enrique Sucar
Publisher : Springer Nature
ISBN 13 : 3030619435
Total Pages : 370 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Probabilistic Graphical Models by : Luis Enrique Sucar

Download or read book Probabilistic Graphical Models written by Luis Enrique Sucar and published by Springer Nature. This book was released on 2020-12-23 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fully updated new edition of a uniquely accessible textbook/reference provides a general introduction to probabilistic graphical models (PGMs) from an engineering perspective. It features new material on partially observable Markov decision processes, causal graphical models, causal discovery and deep learning, as well as an even greater number of exercises; it also incorporates a software library for several graphical models in Python. The book covers the fundamentals for each of the main classes of PGMs, including representation, inference and learning principles, and reviews real-world applications for each type of model. These applications are drawn from a broad range of disciplines, highlighting the many uses of Bayesian classifiers, hidden Markov models, Bayesian networks, dynamic and temporal Bayesian networks, Markov random fields, influence diagrams, and Markov decision processes. Topics and features: Presents a unified framework encompassing all of the main classes of PGMs Explores the fundamental aspects of representation, inference and learning for each technique Examines new material on partially observable Markov decision processes, and graphical models Includes a new chapter introducing deep neural networks and their relation with probabilistic graphical models Covers multidimensional Bayesian classifiers, relational graphical models, and causal models Provides substantial chapter-ending exercises, suggestions for further reading, and ideas for research or programming projects Describes classifiers such as Gaussian Naive Bayes, Circular Chain Classifiers, and Hierarchical Classifiers with Bayesian Networks Outlines the practical application of the different techniques Suggests possible course outlines for instructors This classroom-tested work is suitable as a textbook for an advanced undergraduate or a graduate course in probabilistic graphical models for students of computer science, engineering, and physics. Professionals wishing to apply probabilistic graphical models in their own field, or interested in the basis of these techniques, will also find the book to be an invaluable reference. Dr. Luis Enrique Sucar is a Senior Research Scientist at the National Institute for Astrophysics, Optics and Electronics (INAOE), Puebla, Mexico. He received the National Science Prize en 2016.

Probabilistic Graphical Models

Author : Daphne Koller
Publisher : MIT Press
ISBN 13 : 0262258358
Total Pages : 1270 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Probabilistic Graphical Models by : Daphne Koller

Download or read book Probabilistic Graphical Models written by Daphne Koller and published by MIT Press. This book was released on 2009-07-31 with total page 1270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions. Most tasks require a person or an automated system to reason—to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

A Probabilistic Theory of Pattern Recognition

Author : Luc Devroye
Publisher : Springer Science & Business Media
ISBN 13 : 1461207118
Total Pages : 631 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis A Probabilistic Theory of Pattern Recognition by : Luc Devroye

Download or read book A Probabilistic Theory of Pattern Recognition written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Each chapter concludes with problems and exercises to further the readers understanding. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.

Handbook of Probabilistic Models

Author : Pijush Samui
Publisher : Butterworth-Heinemann
ISBN 13 : 0128165464
Total Pages : 590 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Handbook of Probabilistic Models by : Pijush Samui

Download or read book Handbook of Probabilistic Models written by Pijush Samui and published by Butterworth-Heinemann. This book was released on 2019-10-05 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. Explains the application of advanced probabilistic models encompassing multidisciplinary research Applies probabilistic modeling to emerging areas in engineering Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems

Analyzing Risk through Probabilistic Modeling in Operations Research

Author : Jakóbczak, Dariusz Jacek
Publisher : IGI Global
ISBN 13 : 1466694599
Total Pages : 442 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Analyzing Risk through Probabilistic Modeling in Operations Research by : Jakóbczak, Dariusz Jacek

Download or read book Analyzing Risk through Probabilistic Modeling in Operations Research written by Jakóbczak, Dariusz Jacek and published by IGI Global. This book was released on 2015-11-03 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic modeling represents a subject spanning many branches of mathematics, economics, and computer science to connect pure mathematics with applied sciences. Operational research also relies on this connection to enable the improvement of business functions and decision making. Analyzing Risk through Probabilistic Modeling in Operations Research is an authoritative reference publication discussing the various challenges in management and decision science. Featuring exhaustive coverage on a range of topics within operational research including, but not limited to, decision analysis, data mining, process modeling, probabilistic interpolation and extrapolation, and optimization methods, this book is an essential reference source for decision makers, academicians, researchers, advanced-level students, technology developers, and government officials interested in the implementation of probabilistic modeling in various business applications.

Biological Sequence Analysis

Author : Richard Durbin
Publisher : Cambridge University Press
ISBN 13 : 113945739X
Total Pages : 372 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Biological Sequence Analysis by : Richard Durbin

Download or read book Biological Sequence Analysis written by Richard Durbin and published by Cambridge University Press. This book was released on 1998-04-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic models are becoming increasingly important in analysing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analysing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it aims to be accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time present the state-of-the-art in this new and highly important field.

A Probabilistic Model of the Genotype/Phenotype Relationship

Author : Jean-Pierre Hugot
Publisher : CRC Press
ISBN 13 : 0429841671
Total Pages : 164 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis A Probabilistic Model of the Genotype/Phenotype Relationship by : Jean-Pierre Hugot

Download or read book A Probabilistic Model of the Genotype/Phenotype Relationship written by Jean-Pierre Hugot and published by CRC Press. This book was released on 2018-06-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Probabilistic Model of the Genotype/Phenotype Relationship provides a new hypothesis on the relationship between genotype and phenotype. The main idea of the book is that this relationship is probabilistic, in other words, the genotype does not fully explain the phenotype. This idea is developed and discussed using the current knowledge on complex genetic diseases, phenotypic plasticity, canalization and others.

Scalable Optimization via Probabilistic Modeling

Author : Martin Pelikan
Publisher : Springer
ISBN 13 : 3540349545
Total Pages : 363 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Scalable Optimization via Probabilistic Modeling by : Martin Pelikan

Download or read book Scalable Optimization via Probabilistic Modeling written by Martin Pelikan and published by Springer. This book was released on 2007-01-12 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: I’m not usually a fan of edited volumes. Too often they are an incoherent hodgepodge of remnants, renegades, or rejects foisted upon an unsuspecting reading public under a misleading or fraudulent title. The volume Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications is a worthy addition to your library because it succeeds on exactly those dimensions where so many edited volumes fail. For example, take the title, Scalable Optimization via Probabilistic M- eling: From Algorithms to Applications. You need not worry that you’re going to pick up this book and ?nd stray articles about anything else. This book focuseslikealaserbeamononeofthehottesttopicsinevolutionary compu- tion over the last decade or so: estimation of distribution algorithms (EDAs). EDAs borrow evolutionary computation’s population orientation and sel- tionism and throw out the genetics to give us a hybrid of substantial power, elegance, and extensibility. The article sequencing in most edited volumes is hard to understand, but from the get go the editors of this volume have assembled a set of articles sequenced in a logical fashion. The book moves from design to e?ciency enhancement and then concludes with relevant applications. The emphasis on e?ciency enhancement is particularly important, because the data-mining perspectiveimplicitinEDAsopensuptheworldofoptimizationtonewme- ods of data-guided adaptation that can further speed solutions through the construction and utilization of e?ective surrogates, hybrids, and parallel and temporal decompositions.

Probabilistic Nodes Combination (PNC) for Object Modeling and Contour Reconstruction

Author : Jakóbczak, Dariusz Jacek
Publisher : IGI Global
ISBN 13 : 1522525327
Total Pages : 312 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Probabilistic Nodes Combination (PNC) for Object Modeling and Contour Reconstruction by : Jakóbczak, Dariusz Jacek

Download or read book Probabilistic Nodes Combination (PNC) for Object Modeling and Contour Reconstruction written by Jakóbczak, Dariusz Jacek and published by IGI Global. This book was released on 2017-03-24 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape representation and reconstruction is a vital aspect of modern computer science applications. New modeling methods and techniques can significantly optimize these processes. Probabilistic Nodes Combination (PNC) for Object Modeling and Contour Reconstruction is an innovative reference source that examines the latest trends in 2D curve interpolation and modeling methodologies. Focusing on a range of pertinent topics such as 3D surface modeling, high-dimensional data, and numerical methods, this is an ideal publication for programmers, researchers, students, and practitioners interested in emerging methods in object modeling and contour reconstruction.

Analyzing Data Through Probabilistic Modeling in Statistics

Author : Jakóbczak, Dariusz Jacek
Publisher : IGI Global
ISBN 13 : 1799847071
Total Pages : 331 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Analyzing Data Through Probabilistic Modeling in Statistics by : Jakóbczak, Dariusz Jacek

Download or read book Analyzing Data Through Probabilistic Modeling in Statistics written by Jakóbczak, Dariusz Jacek and published by IGI Global. This book was released on 2021-02-19 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic modeling represents a subject arising in many branches of mathematics, economics, and computer science. Such modeling connects pure mathematics with applied sciences. Similarly, data analyzing and statistics are situated on the border between pure mathematics and applied sciences. Therefore, when probabilistic modeling meets statistics, it is a very interesting occasion that has gained much research recently. With the increase of these technologies in life and work, it has become somewhat essential in the workplace to have planning, timetabling, scheduling, decision making, optimization, simulation, data analysis, and risk analysis and process modeling. However, there are still many difficulties and challenges that arrive in these sectors during the process of planning or decision making. There continues to be the need for more research on the impact of such probabilistic modeling with other approaches. Analyzing Data Through Probabilistic Modeling in Statistics is an essential reference source that builds on the available literature in the field of probabilistic modeling, statistics, operational research, planning and scheduling, data extrapolation in decision making, probabilistic interpolation and extrapolation in simulation, stochastic processes, and decision analysis. This text will provide the resources necessary for economics and management sciences and for mathematics and computer sciences. This book is ideal for interested technology developers, decision makers, mathematicians, statisticians and practitioners, stakeholders, researchers, academicians, and students looking to further their research exposure to pertinent topics in operations research and probabilistic modeling.

The Oxford Handbook of Public Choice, Volume 1

Author : Roger D. Congleton
Publisher : Oxford University Press
ISBN 13 : 0190469757
Total Pages : 800 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis The Oxford Handbook of Public Choice, Volume 1 by : Roger D. Congleton

Download or read book The Oxford Handbook of Public Choice, Volume 1 written by Roger D. Congleton and published by Oxford University Press. This book was released on 2018-12-07 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of Public Choice provides a comprehensive overview of the research in economics, political science, law, and sociology that has generated considerable insight into the politics of democratic and authoritarian systems as well as the influence of different institutional frameworks on incentives and outcomes. The result is an improved understanding of public policy, public finance, industrial organization, and macroeconomics as the combination of political and economic analysis shed light on how various interests compete both within a given rules of the games and, at times, to change the rules. These volumes include analytical surveys, syntheses, and general overviews of the many subfields of public choice focusing on interesting, important, and at times contentious issues. Throughout the focus is on enhancing understanding how political and economic systems act and interact, and how they might be improved. Both volumes combine methodological analysis with substantive overviews of key topics. This first volume covers voting and elections; interest group competition and rent seeking, including corruption and various normative approaches to evaluating policies and politics. Throughout both volumes important analytical concepts and tools are discussed, including their application to substantive topics. Readers will gain increased understanding of rational choice and its implications for collective action; various explanations of voting, including economic and expressive; the role of taxation and finance in government dynamics; how trust and persuasion influence political outcomes; and how revolution, coups, and authoritarianism can be explained by the same set of analytical tools as enhance understanding of the various forms of democracy.

Probabilistic Machine Learning

Author : Kevin P. Murphy
Publisher : MIT Press
ISBN 13 : 0262369303
Total Pages : 858 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Probabilistic Machine Learning by : Kevin P. Murphy

Download or read book Probabilistic Machine Learning written by Kevin P. Murphy and published by MIT Press. This book was released on 2022-03-01 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory. This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the new book is accompanied by online Python code, using libraries such as scikit-learn, JAX, PyTorch, and Tensorflow, which can be used to reproduce nearly all the figures; this code can be run inside a web browser using cloud-based notebooks, and provides a practical complement to the theoretical topics discussed in the book. This introductory text will be followed by a sequel that covers more advanced topics, taking the same probabilistic approach.

Probabilistic Models and Inference for Multi-View People Detection in Overlapping Depth Images

Author : Wetzel, Johannes
Publisher : KIT Scientific Publishing
ISBN 13 : 3731511770
Total Pages : 204 pages
Book Rating : 4.7/5 (315 download)

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Book Synopsis Probabilistic Models and Inference for Multi-View People Detection in Overlapping Depth Images by : Wetzel, Johannes

Download or read book Probabilistic Models and Inference for Multi-View People Detection in Overlapping Depth Images written by Wetzel, Johannes and published by KIT Scientific Publishing. This book was released on 2022-07-12 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the task of wide-area indoor people detection in a network of depth sensors is examined. In particular, we investigate how the redundant and complementary multi-view information, including the temporal context, can be jointly leveraged to improve the detection performance. We recast the problem of multi-view people detection in overlapping depth images as an inverse problem and present a generative probabilistic framework to jointly exploit the temporal multi-view image evidence.

Probabilistic Maneuver Recognition in Traffic Scenarios

Author : Firl, Jonas
Publisher : KIT Scientific Publishing
ISBN 13 : 3731502879
Total Pages : 176 pages
Book Rating : 4.7/5 (315 download)

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Book Synopsis Probabilistic Maneuver Recognition in Traffic Scenarios by : Firl, Jonas

Download or read book Probabilistic Maneuver Recognition in Traffic Scenarios written by Firl, Jonas and published by KIT Scientific Publishing. This book was released on 2015-01-07 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work an approach is presented to model and recognize traffic maneuvers in terms of interactions between different traffic participants on extra urban roads. Results of the recognition concept are presented and evaluated using different sensor setups and its benefit is outlined by an integration into a software framework in the field of Car-to-Car (C2C) communications. Furthermore, recognition results are used in this work to robustly predict vehicle's trajectories while driving dynamic.

Pattern Recognition and Machine Learning

Author : Christopher M. Bishop
Publisher : Springer
ISBN 13 : 9781493938438
Total Pages : 0 pages
Book Rating : 4.9/5 (384 download)

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Book Synopsis Pattern Recognition and Machine Learning by : Christopher M. Bishop

Download or read book Pattern Recognition and Machine Learning written by Christopher M. Bishop and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.