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Hidden Markov Models and Dynamical Systems

Author: Andrew M. Fraser

Publisher: SIAM

ISBN: 0898717744

Category: Computer algorithms

Page: 132

This text provides an introduction to hidden Markov models (HMMs) for the dynamical systems community. It is a valuable text for third or fourth year undergraduates studying engineering, mathematics, or science that includes work in probability, linear algebra and differential equations. The book presents algorithms for using HMMs, and it explains the derivation of those algorithms. It presents Kalman filtering as the extension to a continuous state space of a basic HMM algorithm. The book concludes with an application to biomedical signals. This text is distinctive for providing essential introductory material as well as presenting enough of the theory behind the basic algorithms so that the reader can use it as a guide to developing their own variants.

Inference in Hidden Markov Models

Author: Olivier Cappé,Eric Moulines,Tobias Ryden

Publisher: Springer Science & Business Media

ISBN: 0387289828

Category: Mathematics

Page: 653

This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.

Hidden Markov Models

Estimation and Control

Author: Robert J Elliott,Lakhdar Aggoun,John B. Moore

Publisher: Springer Science & Business Media

ISBN: 0387848541

Category: Science

Page: 382

As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.

Hidden Semi-Markov Models

Theory, Algorithms and Applications

Author: Shun-Zheng Yu

Publisher: Morgan Kaufmann

ISBN: 0128027711

Category: Computers

Page: 208

Hidden semi-Markov models (HSMMs) are among the most important models in the area of artificial intelligence / machine learning. Since the first HSMM was introduced in 1980 for machine recognition of speech, three other HSMMs have been proposed, with various definitions of duration and observation distributions. Those models have different expressions, algorithms, computational complexities, and applicable areas, without explicitly interchangeable forms. Hidden Semi-Markov Models: Theory, Algorithms and Applications provides a unified and foundational approach to HSMMs, including various HSMMs (such as the explicit duration, variable transition, and residential time of HSMMs), inference and estimation algorithms, implementation methods and application instances. Learn new developments and state-of-the-art emerging topics as they relate to HSMMs, presented with examples drawn from medicine, engineering and computer science. Discusses the latest developments and emerging topics in the field of HSMMs Includes a description of applications in various areas including, Human Activity Recognition, Handwriting Recognition, Network Traffic Characterization and Anomaly Detection, and Functional MRI Brain Mapping. Shows how to master the basic techniques needed for using HSMMs and how to apply them.

Hidden Markov Models

Applications in Computer Vision

Author: Horst Bunke,Terry Caelli

Publisher: World Scientific

ISBN: 9814491470

Category: Computers

Page: 244

Hidden Markov models (HMMs) originally emerged in the domain of speech recognition. In recent years, they have attracted growing interest in the area of computer vision as well. This book is a collection of articles on new developments in the theory of HMMs and their application in computer vision. It addresses topics such as handwriting recognition, shape recognition, face and gesture recognition, tracking, and image database retrieval. This book is also published as a special issue of the International Journal of Pattern Recognition and Artificial Intelligence (February 2001). Contents: Introduction: A Simple Complex in Artificial Intelligence and Machine Learning (B H Juang)An Introduction to Hidden Markov Models and Bayesian Networks (Z Chahramani)Multi-Lingual Machine Printed OCR (P Natarajan et al.)Using a Statistical Language Model to Improve the Performance of an HMM-Based Cursive Handwriting Recognition System (U-V Marti & H Bunke)A 2-D HMM Method for Offline Handwritten Character Recognition (H-S Park et al.)Data-Driven Design of HMM Topology for Online Handwriting Recognition (J J Lee et al.)Hidden Markov Models for Modeling and Recognizing Gesture Under Variation (A D Wilson & A F Bobick)Sentence Lipreading Using Hidden Markov Model with Integrated Grammar (K Yu et al.)Tracking and Surveillance in Wide-Area Spatial Environments Using the Abstract Hidden Markov Model (H H Bui et al.)Shape Tracking and Production Using Hidden Markov Models (T Caelli et al.)An Integrated Approach to Shape and Color-Based Image Retrieval of Rotated Objects Using Hidden Markov Models (S Müller et al.) Readership: Graduate students of computer science, electrical engineering and related fields, as well as researchers at academic and industrial institutions. Keywords:Hidden Markov Models;Gesture Recognitoin;Bayesian Networks;Optical Character Recognition;Handwriting Character Recognition;Cartography;Shape Extraction;Image Feature Extraction.

Hidden Markov Models for Time Series

An Introduction Using R, Second Edition

Author: Walter Zucchini,Iain L. MacDonald,Roland Langrock

Publisher: CRC Press

ISBN: 1482253844

Category: Mathematics

Page: 370

Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture–recapture data

Markov Models for Pattern Recognition

From Theory to Applications

Author: Gernot A. Fink

Publisher: Springer Science & Business Media

ISBN: 1447163087

Category: Computers

Page: 276

This thoroughly revised and expanded new edition now includes a more detailed treatment of the EM algorithm, a description of an efficient approximate Viterbi-training procedure, a theoretical derivation of the perplexity measure and coverage of multi-pass decoding based on n-best search. Supporting the discussion of the theoretical foundations of Markov modeling, special emphasis is also placed on practical algorithmic solutions. Features: introduces the formal framework for Markov models; covers the robust handling of probability quantities; presents methods for the configuration of hidden Markov models for specific application areas; describes important methods for efficient processing of Markov models, and the adaptation of the models to different tasks; examines algorithms for searching within the complex solution spaces that result from the joint application of Markov chain and hidden Markov models; reviews key applications of Markov models.

The Application of Hidden Markov Models in Speech Recognition

Author: Mark Gales,Steve Young

Publisher: Now Publishers Inc

ISBN: 1601981201

Category: Mathematics

Page: 113

The Application of Hidden Markov Models in Speech Recognition presents the core architecture of a HMM-based LVCSR system and proceeds to describe the various refinements which are needed to achieve state-of-the-art performance.

Graphical Models

Foundations of Neural Computation

Author: Michael Irwin Jordan,Terrence Joseph Sejnowski,Tomaso A. Poggio

Publisher: MIT Press

ISBN: 9780262600422

Category: Computers

Page: 421

This book exemplifies the interplay between the general formal framework of graphical models and the exploration of new algorithm and architectures. The selections range from foundational papers of historical importance to results at the cutting edge of research. Graphical models use graphs to represent and manipulate joint probability distributions. They have their roots in artificial intelligence, statistics, and neural networks. The clean mathematical formalism of the graphical models framework makes it possible to understand a wide variety of network-based approaches to computation, and in particular to understand many neural network algorithms and architectures as instances of a broader probabilistic methodology. It also makes it possible to identify novel features of neural network algorithms and architectures and to extend them to more general graphical models.This book exemplifies the interplay between the general formal framework of graphical models and the exploration of new algorithms and architectures. The selections range from foundational papers of historical importance to results at the cutting edge of research. Contributors H. Attias, C. M. Bishop, B. J. Frey, Z. Ghahramani, D. Heckerman, G. E. Hinton, R. Hofmann, R. A. Jacobs, Michael I. Jordan, H. J. Kappen, A. Krogh, R. Neal, S. K. Riis, F. B. Rodríguez, L. K. Saul, Terrence J. Sejnowski, P. Smyth, M. E. Tipping, V. Tresp, Y. Weiss

Entropy of Hidden Markov Processes and Connections to Dynamical Systems

Papers from the Banff International Research Station Workshop

Author: Brian Marcus,Karl Petersen,Tsachy Weissman

Publisher: Cambridge University Press

ISBN: 9780521111133

Category: Mathematics

Page: 278

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterizing the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

Approximation of Large-Scale Dynamical Systems

Author: Athanasios C. Antoulas

Publisher: SIAM

ISBN: 0898716586

Category: Mathematics

Page: 510

Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.

Entropy of Hidden Markov Processes and Connections to Dynamical Systems

Papers from the Banff International Research Station Workshop

Author: Brian Marcus,Karl Petersen,Tsachy Weissman

Publisher: Cambridge University Press

ISBN: 1139495747

Category: Mathematics

Page: N.A

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

Biological Sequence Analysis

Probabilistic Models of Proteins and Nucleic Acids

Author: Richard Durbin,Sean R. Eddy,Anders Krogh,Graeme Mitchison

Publisher: Cambridge University Press

ISBN: 113945739X

Category: Science

Page: N.A

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.

Hidden Markov Models

Estimation and Control

Author: Robert J Elliott,Lakhdar Aggoun,John B. Moore

Publisher: Springer Science & Business Media

ISBN: 0387848541

Category: Science

Page: 382

Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems

Author: Wai-Yuan Tan

Publisher: World Scientific

ISBN: 981448931X

Category: Mathematics

Page: 460

This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems. One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems. As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems. Contents:Discrete Time Markov Chain Models in Genetics and Biomedical SystemsStationary Distributions and MCMC in Discrete Time Markov ChainsContinuous-Time Markov Chain Models in Genetics, Cancers and AIDSAbsorption Probabilities and Stationary Distributions in Continuous-Time Markov Chain ModelsDiffusion Models in Genetics, Cancer and AIDSAsymptotic Distributions, Stationary Distributions and Absorption Probabilities in Diffusion ModelsState Space Models and Some Examples from Cancer and AIDSSome General Theories of State Space Models and Applications Readership: Graduate students and researchers in probability & statistics and the life sciences. Keywords:Stochastic;Genetics;Cancers;AIDS;Biomedical SystemsReviews:“Its strengths include the large number of models described, many of which have previously been published only in research journals; its clear presentation of many detailed analyses; and good accounts of the biology behind the models.”Mathematical Reviews

Differential Dynamical Systems, Revised Edition

Author: James D. Meiss

Publisher: SIAM

ISBN: 161197464X

Category: Mathematics

Page: 392

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.÷ Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Markov Models

Master the Unsupervised Machine Learning in Python and Data Science with Hidden Markov Models and Real World Applications

Author: Robert Wilson

Publisher: Createspace Independent Publishing Platform

ISBN: 9781548002206

Category: Machine learning

Page: 150

Do you want to become a data science Savvy? If reading about Markov models, stochastic processes, and probabilities leaves you scratching your head, then you have definitely come to the right place. If you are looking for the most no-nonsense guide that will keep you on the right course during the turbulent ride filled with scientific enigmas, machine learning, and predicting probabilities of hidden, unobservable states, then you have found your perfect companion. This book will Cover: What is Markov models How to make predictions with Markov Models How to learn without supervision How do Markov Models use prediction? Hidden Markov Models and how to use them The secrets of Markov Chains Tips and tricks on how to use Markov Models and machine learning Markov Models with Python Markov Models Examples and predictions How to build and implement HMM algorithms How to use Markov Models to master machine learning The secrets of Supervised and unsupervised machine learning The three components of Hidden Markov Models And much, much more! By the end of this book, I guarantee that you will dive easily into the data science world. Save yourself the hard work and frustration by downloading this book today. Download your free copy today (Kindle Unlimited only)

Performance Analysis and Modeling of Digital Transmission Systems

Author: William Turin

Publisher: Springer Science & Business Media

ISBN: 1441990704

Category: Mathematics

Page: 441

This book is an expanded third edition of the book Performance Analysis of Digital Transmission Systems, originally published in 1990. Second edition of the book titled Digital Transmission Systems: Performance Analysis and Modeling was published in 1998. The book is intended for those who design communication systems and networks. A computer network designer is interested in selecting communication channels, error protection schemes, and link control protocols. To do this efficiently, one needs a mathematical model that accurately predicts system behavior. Two basic problems arise in mathematical modeling: the problem of identifying a system and the problem of applying a model to the system analysis. System identification consists of selecting a class of mathematical objects to describe fundamental properties of the system behavior. We use a specific class of hidden Markov models (HMMs) to model communication systems. This model was introduced by C. E. Shannon more than 50 years ago as a Noisy Discrete Channel with a finite number of states. The model is described by a finite number of matrices whose elements are estimated on the basis of experimental data. We develop several methods of model identification and show their relationship to other methods of data analysis, such as spectral methods, autoregressive moving average CARMA) approximations, and rational transfer function approximations.

Simulating, Analyzing, and Animating Dynamical Systems

A Guide to XPPAUT for Researchers and Students

Author: Bard Ermentrout

Publisher: SIAM

ISBN: 0898715067

Category: Mathematics

Page: 290

Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations. Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities.

Efficient Learning Machines

Theories, Concepts, and Applications for Engineers and System Designers

Author: Mariette Awad,Rahul Khanna

Publisher: Apress

ISBN: 1430259906

Category: Computers

Page: 268

Machine learning techniques provide cost-effective alternatives to traditional methods for extracting underlying relationships between information and data and for predicting future events by processing existing information to train models. Efficient Learning Machines explores the major topics of machine learning, including knowledge discovery, classifications, genetic algorithms, neural networking, kernel methods, and biologically-inspired techniques. Mariette Awad and Rahul Khanna’s synthetic approach weaves together the theoretical exposition, design principles, and practical applications of efficient machine learning. Their experiential emphasis, expressed in their close analysis of sample algorithms throughout the book, aims to equip engineers, students of engineering, and system designers to design and create new and more efficient machine learning systems. Readers of Efficient Learning Machines will learn how to recognize and analyze the problems that machine learning technology can solve for them, how to implement and deploy standard solutions to sample problems, and how to design new systems and solutions. Advances in computing performance, storage, memory, unstructured information retrieval, and cloud computing have coevolved with a new generation of machine learning paradigms and big data analytics, which the authors present in the conceptual context of their traditional precursors. Awad and Khanna explore current developments in the deep learning techniques of deep neural networks, hierarchical temporal memory, and cortical algorithms. Nature suggests sophisticated learning techniques that deploy simple rules to generate highly intelligent and organized behaviors with adaptive, evolutionary, and distributed properties. The authors examine the most popular biologically-inspired algorithms, together with a sample application to distributed datacenter management. They also discuss machine learning techniques for addressing problems of multi-objective optimization in which solutions in real-world systems are constrained and evaluated based on how well they perform with respect to multiple objectives in aggregate. Two chapters on support vector machines and their extensions focus on recent improvements to the classification and regression techniques at the core of machine learning.