Download or read book Sampling Algorithms for Probabilistic Graphical Models with Determinism written by Vibhav Giridhar Gogate and published by . This book was released on 2009 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed constraint and probabilistic graphical models occur quite frequently in many real world applications. Examples include: genetic linkage analysis, functional/software verification, target tracking and activity modeling. Query answering and in particular probabilistic inference on such graphical models is computationally hard often requiring exponential time in the worst case. Therefore in practice sampling algorithms are widely used for providing an approximate answer. In presence of deterministic dependencies or hard constraints, however, sampling has to overcome some principal challenges. In particular, importance sampling type schemes suffer from what is known as the rejection problem in that samples having zero weight may be generated with probability arbitrarily close to one yielding useless results. On the other hand, Markov Chain Monte Carlo techniques do not converge at all often yielding highly inaccurate estimates. In this thesis, we address these problems in a two fold manner. First, we utilize research done in constraint satisfaction and satisfiability communities for processing constraints to reduce or eliminate rejection. Second, mindful of the time overhead in sample generation due to determinism, we both make and utilize advances in statistical estimation theory to make the "most" out of the generated samples. Utilizing constraint satisfaction and satisfiability research, we propose two classes of sampling algorithms - one based on consistency enforcement and the other based on systematic search. The consistency enforcement class of algorithms work by shrinking the domains of random variables, by strengthening constraints, or by creating new ones, so that some or all zeros in the problem space can be removed. This improves convergence because of dimensionality reduction and also reduces rejection because many zero weight samples will not be generated. Our systematic search based techniques called SampleSearch manage the rejection problem by interleaving sampling with backtracking search. In this scheme, when a sample is supposed to be rejected, the algorithm continues instead with systematic backtracking search until a strictly positive-weight sample is generated. The strength of this scheme is that any state-of-the-art constraint satisfaction or propositional satisfiability search algorithm can be used with minor modifications. Through large scale experimental evaluation, we show that SampleSearch outperforms all state-of-the-art schemes when a significant amount of determinism is present in the graphical model. Subsequently, we combine SampleSearch with known statistical techniques such as Sampling Importance Resampling and Metropolis Hastings yielding efficient algorithms for sampling solutions from a uniform distribution over the solutions of a Boolean satisfiability formula. Unlike state-of-the-art algorithms, our SampleSearch-based algorithms guarantee convergence in the limit. As to statistical estimation, we make two distinct contributions. First, we propose several new statistical inequalities extending the one-sample Markov inequality to multiple samples which can be used in conjunction with SampleSearch to probabilistically lower bound likelihood tasks over mixed networks. Second, we present a novel framework called "AND/OR importance sampling" which generalizes the process of computing sample mean by exploiting AND/OR search spaces for graphical models. Specifically we provide a spectrum of AND/OR sample means which are defined on the same set of samples but derive different estimates trading variance with time. At one end is the AND/OR sample tree mean which has smaller variance than the conventional OR sample tree mean and has the same time complexity. At the other end is the AND/OR graph sample mean which has even lower variance but has higher time and space complexity. We demonstrate empirically that AND/OR sample means are far closer to the exact answer than the conventional OR sample mean.

Download or read book Reasoning with Probabilistic and Deterministic Graphical Models written by Rina Kraus and published by Springer Nature. This book was released on 2013-12-27 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. In this book we provide comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. We believe the principles outlined here would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

Download or read book Reasoning with Probabilistic and Deterministic Graphical Models written by Rina Sreedharan and published by Springer Nature. This book was released on 2022-06-01 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. This book provides comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. The new edition includes the notion of influence diagrams, which focus on sequential decision making under uncertainty. We believe the principles outlined in the book would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

Download or read book Exact Algorithms for Probabilistic and Deterministic Graphical Models written by Rina Dechter and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. In this book we provide comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. We believe the principles outlined here would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

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.

Download or read book Reasoning With Probabilistic and Deterministic Graphical Models written by Rina Dechter and published by Synthesis Lectures on Artifici. This book was released on 2019-02-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. This book provides comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. The new edition includes the notion of influence diagrams, which focus on sequential decision making under uncertainty. We believe the principles outlined in the book would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

Download or read book Efficient Inference Algorithms for Near deterministic Systems written by Shaunak Chatterjee and published by . This book was released on 2013 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses the problem of performing probabilistic inference in stochastic systems where the probability mass is far from uniformly distributed among all possible outcomes. Such near-deterministic systems arise in several real-world applications. For example, in human physiology, the widely varying evolution rates of physiological variables make certain trajectories much more likely than others; in natural language, a very small fraction of all possible word sequences accounts for a disproportionately high amount of probability under a language model. In such settings, it is often possible to obtain significant computational savings by focusing on the outcomes where the probability mass is concentrated. This contrasts with existing algorithms in probabilistic inference--such as junction tree, sum product, and belief propagation algorithms--which are well-tuned to exploit conditional independence relations. The first topic addressed in this thesis is the structure of discrete-time temporal graphical models of near-deterministic stochastic processes. We show how the structure depends on the ratios between the size of the time step and the effective rates of change of the variables. We also prove that accurate approximations can often be obtained by sparse structures even for very large time steps. Besides providing an intuitive reason for causal sparsity in discrete temporal models, the sparsity also speeds up inference. The next contribution is an eigenvalue algorithm for a linear factored system (e.g., dynamic Bayesian network), where existing algorithms do not scale since the size of the system is exponential in the number of variables. Using a combination of graphical model inference algorithms and numerical methods for spectral analysis, we propose an approximate spectral algorithm which operates in the factored representation and is exponentially faster than previous algorithms. The third contribution is a temporally abstracted Viterbi (TAV) algorithm. Starting with a spatio-temporally abstracted coarse representation of the original problem, the TAV algorithm iteratively refines the search space for the Viterbi path via spatial and temporal refinements. The algorithm is guaranteed to converge to the optimal solution with the use of admissible heuristic costs in the abstract levels and is much faster than the Viterbi algorithm for near-deterministic systems. The fourth contribution is a hierarchical image/video segmentation algorithm, that shares some of the ideas used in the TAV algorithm. A supervoxel tree provides the abstraction hierarchy for this application. The algorithm starts working with the coarsest level supervoxels, and refines portions of the tree which are likely to have multiple labels. Several existing segmentation algorithms can be used to solve the energy minimization problem in each iteration, and admissible heuristic costs once again guarantee optimality. Since large contiguous patches exist in images and videos, this approach is more computationally efficient than solving the problem at the finest level of supervoxels. The final contribution is a family of Markov Chain Monte Carlo (MCMC) algorithms for near-deterministic systems when there exists an efficient algorithm to sample solutions for the corresponding deterministic problem. In such a case, a generic MCMC algorithm's performance worsens as the problem becomes more deterministic despite the existence of the efficient algorithm in the deterministic limit. MCMC algorithms designed using our methodology can bridge this gap. The computational speedups we obtain through the various new algorithms presented in this thesis show that it is indeed possible to exploit near-determinism in probabilistic systems. Near-determinism, much like conditional independence, is a potential (and promising) source of computational savings for both exact and approximate inference. It is a direction that warrants more understanding and better generalized algorithms.

Download or read book Mathematics of Evolution and Phylogeny written by Olivier Gascuel and published by OUP Oxford. This book was released on 2005-02-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers evolution at different scales: sequences, genes, gene families, organelles, genomes and species. The focus is on the mathematical and computational tools and concepts, which form an essential basis of evolutionary studies, indicate their limitations, and give them orientation. Recent years have witnessed rapid progress in the mathematics of evolution and phylogeny, with models and methods becoming more realistic, powerful, and complex. Aimed at graduates and researchers in phylogenetics, mathematicians, computer scientists and biologists, and including chapters by leading scientists: A. Bergeron, D. Bertrand, D. Bryant, R. Desper, O. Elemento, N. El-Mabrouk, N. Galtier, O. Gascuel, M. Hendy, S. Holmes, K. Huber, A. Meade, J. Mixtacki, B. Moret, E. Mossel, V. Moulton, M. Pagel, M.-A. Poursat, D. Sankoff, M. Steel, J. Stoye, J. Tang, L.-S. Wang, T. Warnow, Z. Yang, this book of contributed chapters explains the basis and covers the recent results in this highly topical area.

Download or read book Constraint Processing written by Rina Dechter and published by Morgan Kaufmann. This book was released on 2003-05-05 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. In Constraint Processing, Rina Dechter synthesizes these contributions, as well as her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms.

Download or read book Probabilistic Inference in Piecewise Graphical Models written by Hadi Mohasel Afshar and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications of probabilistic inference the models contain piecewise densities that are differentiable except at partition boundaries. For instance, (1) some models may intrinsically have finite support, being constrained to some regions; (2) arbitrary density functions may be approximated by mixtures of piecewise functions such as piecewise polynomials or piecewise exponentials; (3) distributions derived from other distributions (via random variable transformations) may be highly piecewise; (4) in applications of Bayesian inference such as Bayesian discrete classification and preference learning, the likelihood functions may be piecewise; (5) context-specific conditional probability density functions (tree-CPDs) are intrinsically piecewise; (6) influence diagrams (generalizations of Bayesian networks in which along with probabilistic inference, decision making problems are modeled) are in many applications piecewise; (7) in probabilistic programming, conditional statements lead to piecewise models. As we will show, exact inference on piecewise models is not often scalable (if applicable) and the performance of the existing approximate inference techniques on such models is usually quite poor. This thesis fills this gap by presenting scalable and accurate algorithms for inference in piecewise probabilistic graphical models. Our first contribution is to present a variation of Gibbs sampling algorithm that achieves an exponential sampling speedup on a large class of models (including Bayesian models with piecewise likelihood functions). As a second contribution, we show that for a large range of models, the time-consuming Gibbs sampling computations that are traditionally carried out per sample, can be computed symbolically, once and prior to the sampling process. Among many potential applications, the resulting symbolic Gibbs sampler can be used for fully automated reasoning in the presence of deterministic constraints among random variables. As a third contribution, we are motivated by the behavior of Hamiltonian dynamics in optics -in particular, the reflection and refraction of light on the refractive surfaces- to present a new Hamiltonian Monte Carlo method that demonstrates a significantly improved performance on piecewise models. Hopefully, the present work represents a step towards scalable and accurate inference in an important class of probabilistic models that has largely been overlooked in the literature.

Download or read book Variational Methods for Machine Learning with Applications to Deep Networks written by Lucas Pinheiro Cinelli and published by Springer Nature. This book was released on 2021-05-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a straightforward look at the concepts, algorithms and advantages of Bayesian Deep Learning and Deep Generative Models. Starting from the model-based approach to Machine Learning, the authors motivate Probabilistic Graphical Models and show how Bayesian inference naturally lends itself to this framework. The authors present detailed explanations of the main modern algorithms on variational approximations for Bayesian inference in neural networks. Each algorithm of this selected set develops a distinct aspect of the theory. The book builds from the ground-up well-known deep generative models, such as Variational Autoencoder and subsequent theoretical developments. By also exposing the main issues of the algorithms together with different methods to mitigate such issues, the book supplies the necessary knowledge on generative models for the reader to handle a wide range of data types: sequential or not, continuous or not, labelled or not. The book is self-contained, promptly covering all necessary theory so that the reader does not have to search for additional information elsewhere. Offers a concise self-contained resource, covering the basic concepts to the algorithms for Bayesian Deep Learning; Presents Statistical Inference concepts, offering a set of elucidative examples, practical aspects, and pseudo-codes; Every chapter includes hands-on examples and exercises and a website features lecture slides, additional examples, and other support material.

Download or read book Probabilistic Graphical Models written by Linda C. van der Gaag and published by Springer. This book was released on 2014-09-11 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Lifted Probabilistic Inference written by Guy Van den Broeck and published by MIT Press. This book was released on 2021-08-17 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in the area of lifted inference, which exploits the structure inherent in relational probabilistic models. Statistical relational AI (StaRAI) studies the integration of reasoning under uncertainty with reasoning about individuals and relations. The representations used are often called relational probabilistic models. Lifted inference is about how to exploit the structure inherent in relational probabilistic models, either in the way they are expressed or by extracting structure from observations. This book covers recent significant advances in the area of lifted inference, providing a unifying introduction to this very active field. After providing necessary background on probabilistic graphical models, relational probabilistic models, and learning inside these models, the book turns to lifted inference, first covering exact inference and then approximate inference. In addition, the book considers the theory of liftability and acting in relational domains, which allows the connection of learning and reasoning in relational domains.

Download or read book Learning Probabilistic Graphical Models in R written by David Bellot and published by Packt Publishing Ltd. This book was released on 2016-04-29 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling And Analysis Of Dependable Systems A Probabilistic Graphical Model Perspective written by Luigi Portinale and published by World Scientific. This book was released on 2015-06-09 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Deterministic Sampling for Nonlinear Dynamic State Estimation written by Gilitschenski, Igor and published by KIT Scientific Publishing. This book was released on 2016-04-19 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this work is improving existing and suggesting novel filtering algorithms for nonlinear dynamic state estimation. Nonlinearity is considered in two ways: First, propagation is improved by proposing novel methods for approximating continuous probability distributions by discrete distributions defined on the same continuous domain. Second, nonlinear underlying domains are considered by proposing novel filters that inherently take the underlying geometry of these domains into account.

Download or read book Modeling and Reasoning with Bayesian Networks written by Adnan Darwiche and published by Cambridge University Press. This book was released on 2009-04-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the formal foundations and practical applications of Bayesian networks. It provides an extensive discussion of techniques for building Bayesian networks that model real-world situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis. It also treats exact and approximate inference algorithms at both theoretical and practical levels. The author assumes very little background on the covered subjects, supplying in-depth discussions for theoretically inclined readers and enough practical details to provide an algorithmic cookbook for the system developer.