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.

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, graphical models, and deep learning, as well as an even greater number of exercises. 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.

At the crossroads between statistics and machine learning, probabilistic graphical models (PGMs) provide a powerful formal framework to model complex data. An expanding volume of biological data of various types, the so-called 'omics', is in need of accurate and efficient methods for modelling and PGMs are expected to have a prominent role to play. This book provides an overview of the applications of PGMs to genetics, genomics and postgenomics to meet this increased interest.

This book brings together important topics of current research in probabilistic graphical modeling, learning from data and probabilistic inference. Coverage includes such topics as the characterization of conditional independence, the learning of graphical models with latent variables, and extensions to the influence diagram formalism as well as important application fields, such as the control of vehicles, bioinformatics and medicine.

This book constitutes the refereed proceedings of the 7th International Workshop on Probabilistic Graphical Models, PGM 2014, held in Utrecht, The Netherlands, in September 2014. The 38 revised full papers presented in this book were carefully reviewed and selected from 44 submissions. The papers cover all aspects of graphical models for probabilistic reasoning, decision making, and learning.

Familiarize yourself with probabilistic graphical models through real-world problems and illustrative code examples in R About This Book Predict and use a probabilistic graphical models (PGM) as an expert system Comprehend how your computer can learn Bayesian modeling to solve real-world problems Know how to prepare data and feed the models by using the appropriate algorithms from the appropriate R package Who This Book Is For This book is for anyone who has to deal with lots of data and draw conclusions from it, especially when the data is noisy or uncertain. Data scientists, machine learning enthusiasts, engineers, and those who curious about the latest advances in machine learning will find PGM interesting. What You Will Learn Understand the concepts of PGM and which type of PGM to use for which problem Tune the model's parameters and explore new models automatically Understand the basic principles of Bayesian models, from simple to advanced Transform the old linear regression model into a powerful probabilistic model Use standard industry models but with the power of PGM Understand the advanced models used throughout today's industry See how to compute posterior distribution with exact and approximate inference algorithms In Detail Probabilistic graphical models (PGM, also known as graphical models) are a marriage between probability theory and graph theory. Generally, PGMs use a graph-based representation. Two branches of graphical representations of distributions are commonly used, namely Bayesian networks and Markov networks. R has many packages to implement graphical models. We'll start by showing you how to transform a classical statistical model into a modern PGM and then look at how to do exact inference in graphical models. Proceeding, we'll introduce you to many modern R packages that will help you to perform inference on the models. We will then run a Bayesian linear regression and you'll see the advantage of going probabilistic when you want to do prediction. Next, you'll master using R packages and implementing its techniques. Finally, you'll be presented with machine learning applications that have a direct impact in many fields. Here, we'll cover clustering and the discovery of hidden information in big data, as well as two important methods, PCA and ICA, to reduce the size of big problems. Style and approach This book gives you a detailed and step-by-step explanation of each mathematical concept, which will help you build and analyze your own machine learning models and apply them to real-world problems. The mathematics is kept simple and each formula is explained thoroughly.

Probabilistic Graphical Models for Computer Vision introduces probabilistic graphical models (PGMs) for computer vision problems and teaches how to develop the PGM model from training data. This book discusses PGMs and their significance in the context of solving computer vision problems, giving the basic concepts, definitions and properties. It also provides a comprehensive introduction to well-established theories for different types of PGMs, including both directed and undirected PGMs, such as Bayesian Networks, Markov Networks and their variants. Discusses PGM theories and techniques with computer vision examples Focuses on well-established PGM theories that are accompanied by corresponding pseudocode for computer vision Includes an extensive list of references, online resources and a list of publicly available and commercial software Covers computer vision tasks, including feature extraction and image segmentation, object and facial recognition, human activity recognition, object tracking and 3D reconstruction

Nowadays bioinformaticians and geneticists are faced with myriad high-throughput data usually presenting the characteristics of uncertainty, high dimensionality and large complexity. These data will only allow insights into this wealth of so-called 'omics' data if represented by flexible and scalable models, prior to any further analysis. At the interface between statistics and machine learning, probabilistic graphical models (PGMs) represent a powerful formalism to discover complex networks of relations. These models are also amenable to incorporating a priori biological information. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where PGMs have been successfully applied. However these models have also created renewed interest in genetics in the broad sense, in particular regarding association genetics, causality discovery, prediction of outcomes, detection of copy number variations, and epigenetics. This book provides an overview of the applications of PGMs to genetics, genomics and postgenomics to meet this increased interest. A salient feature of bioinformatics, interdisciplinarity, reaches its limit when an intricate cooperation between domain specialists is requested. Currently, few people are specialists in the design of advanced methods using probabilistic graphical models for postgenomics or genetics. This book deciphers such models so that their perceived difficulty no longer hinders their use and focuses on fifteen illustrations showing the mechanisms behind the models. Probabilistic Graphical Models for Genetics, Genomics and Postgenomics covers six main themes: (1) Gene network inference (2) Causality discovery (3) Association genetics (4) Epigenetics (5) Detection of copy number variations (6) Prediction of outcomes from high-dimensional genomic data. Written by leading international experts, this is a collection of the most advanced work at the crossroads of probabilistic graphical models and genetics, genomics, and postgenomics. The self-contained chapters provide an enlightened account of the pros and cons of applying these powerful techniques.

Master probabilistic graphical models by learning through real-world problems and illustrative code examples in Python About This Book Gain in-depth knowledge of Probabilistic Graphical Models Model time-series problems using Dynamic Bayesian Networks A practical guide to help you apply PGMs to real-world problems Who This Book Is For If you are a researcher or a machine learning enthusiast, or are working in the data science field and have a basic idea of Bayesian Learning or Probabilistic Graphical Models, this book will help you to understand the details of Graphical Models and use it in your data science problems. This book will also help you select the appropriate model as well as the appropriate algorithm for your problem. What You Will Learn Get to know the basics of Probability theory and Graph Theory Work with Markov Networks Implement Bayesian Networks Exact Inference Techniques in Graphical Models such as the Variable Elimination Algorithm Understand approximate Inference Techniques in Graphical Models such as Message Passing Algorithms Sample algorithms in Graphical Models Grasp details of Naive Bayes with real-world examples Deploy PGMs using various libraries in Python Gain working details of Hidden Markov Models with real-world examples In Detail Probabilistic Graphical Models is a technique in machine learning that uses the concepts of graph theory to compactly represent and optimally predict values in our data problems. In real world problems, it's often difficult to select the appropriate graphical model as well as the appropriate inference algorithm, which can make a huge difference in computation time and accuracy. Thus, it is crucial to know the working details of these algorithms. This book starts with the basics of probability theory and graph theory, then goes on to discuss various models and inference algorithms. All the different types of models are discussed along with code examples to create and modify them, and also to run different inference algorithms on them. There is a complete chapter devoted to the most widely used networks Naive Bayes Model and Hidden Markov Models (HMMs). These models have been thoroughly discussed using real-world examples. Style and approach An easy-to-follow guide to help you understand Probabilistic Graphical Models using simple examples and numerous code examples, with an emphasis on more widely used models.

This book presents recent advancements in research, a review of new methods and techniques, and applications in decision support systems (DSS) with Machine Learning and Probabilistic Graphical Models, which are very effective techniques in gaining knowledge from Big Data and in interpreting decisions. It explores Bayesian network learning, Control Chart, Reinforcement Learning for multicriteria DSS, Anomaly Detection in Smart Manufacturing with Federated Learning, DSS in healthcare, DSS for supply chain management, etc. Researchers and practitioners alike will benefit from this book to enhance the understanding of machine learning, Probabilistic Graphical Models, and their uses in DSS in the context of decision making with uncertainty. The real-world case studies in various fields with guidance and recommendations for the practical applications of these studies are introduced in each chapter.

The monographic volume addresses, in a systematic and comprehensive way, the state-of-the-art dependability (reliability, availability, risk and safety, security) of systems, using the Artificial Intelligence framework of Probabilistic Graphical Models (PGM). After a survey about the main concepts and methodologies adopted in dependability analysis, the book discusses the main features of PGM formalisms (like Bayesian and Decision Networks) and the advantages, both in terms of modeling and analysis, with respect to classical formalisms and model languages. Methodologies for deriving PGMs from standard dependability formalisms will be introduced, by pointing out tools able to support such a process. Several case studies will be presented and analyzed to support the suitability of the use of PGMs in the study of dependable systems. Contents:Dependability and ReliabilityProbabilistic Graphical ModelsFrom Fault Trees to Bayesian NetworksFrom Dynamic Fault Tree to Dynamic Bayesian NetworksDecision Theoretic DependabilityThe RADyBaN Tool: Supporting DependabilityCase Study 1: Cascading FailuresCase Study 2: Autonomous Fault Detection, Identification and RecoveryCase Study 3: Security Assessment in Critical InfrastructuresCase Study 4: Dynamic Reliability Keywords:Dependability;Reliability;Probabilistic Graphical Models;Bayesian Networks;Fault Detection Identification and Recovery

The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory ofgraphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are describedbriefly, and appendices give details of the multivarate normal distribution and of the theory of regular exponential families. The author has recently been awarded the RSS Guy Medal in Silver 1996 for his innovative contributions to statistical theory and practice, and especially for his work on graphical models.