Download or read book Efficient and Scalable Exact Inference Algorithms for Bayesian Networks written by John G. Sandiford and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient and Scalable Exact Inference Algorithms for Bayesian Networks written by John G. Sandiford and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: With the proliferation of data, and the increased use of Bayesian networks as a statistical modelling technique, the expectations and demands on Bayesian networks have increased substantially. In this text we explore novel techniques for performing exact inference with Bayesian networks, in an efficient stable and scalable manner. We consider not only discrete variable Bayesian networks but also those with continuous variables, and Dynamic Bayesian networks for modelling time series/sequential data. We first examine how existing algorithms can be decomposed into a library of techniques which can then be used when constructing novel algorithms or extending existing algorithms. We then go on to develop novel techniques, including an algorithm for the efficient and scalable manipulation of distributions during inference and algorithms for performing numerically stable inference. Additionally we develop a technique for performing fixed memory inference, which can be used to extend existing algorithms, and we also identify an inference mechanism which has similar performance to the polytree algorithm, but can operate on classes of networks that are not trees. Finally, we explore how nodes with multiple variables can lead to both graphical simplicity and performance gains.
Download or read book Efficient Inference for Hybrid Bayesian Networks written by Wei Sun and published by . This book was released on 2007 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Uncertainty is everywhere in real life so we have to use stochastic model for most real-world problems. In general, both the systems mechanism and the observable measurements involve random noise. Therefore, probability theory and statistical estimation play important roles in decision making. First of all, we need a good knowledge representation to integrate information under uncertainty; then we need to conduct efficient reasoning about the state of the world given noisy observations. Bayesian networks (BNs) provide a compact, efficient and easy-to-interpret way to model the joint probability distribution of random variables over a problem domain. A Bayesian network encodes dependency relationship between random variables into a graphical probabilistic model. The structural properties and expressive power of Bayesian network make it an excellent knowledge base for effective probabilistic inference. Over the past several decades, a number of exact and approximate inference algorithms have been proposed and applied for inference in different types of Bayesian networks. However, in general, BN probabilistic inference is NP-hard. In particular, probabilistic reasoning for BNs with nonlinear non-Gaussian hybrid model is known to be one of the most difficult problems. First, no exact method is possible to compute the posterior distributions in such case. Second, relatively little research has been done for general hybrid models. Unfortunately, most real-world problems are naturally modeled with both categorical variables and continuous variables with typically nonlinear relationship. This dissertation focuses on the hybrid Bayesian networks containing both discrete and continuous random variables. The hybrid model may involve nonlinear functions in conditional probability distributions and the distributions could be arbitrary. I first give a thorough introduction to Bayesian networks and review of the state-of-the-art inference algorithms in the literature. Then a suite of efficient algorithms is proposed to compute the posterior distributions of hidden variables for arbitrary continuous and hybrid Bayesian networks. Moreover, in order to evaluate the performance of the algorithms with hybrid Bayesian networks, I present an approximate analytical method to estimate the performance bound. This method can help the decision maker to understand the prediction performance of a BN model without extensive simulation. It can also help the modeler to build and validate a model effectively. Solid theoretical derivations and promising numerical experimental results show that the research in this dissertation is fundamentally sound and can be applied in various decision support systems"--Abstract.
Download or read book Representations and Algorithms for Efficient Inference in Bayesian Networks written by Masami Takikawa and published by . This book was released on 1998 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian networks are used for building intelligent agents that act under uncertainty. They are a compact representation of agents' probabilistic knowledge. A Bayesian network can be viewed as representing a factorization of a full joint probability distribution into the multiplication of a set of conditional probability distributions. Independence of causal influence enables one to further factorize the conditional probability distributions into a combination of even smaller factors. The efficiency of inference in Bayesian networks depends on how these factors are combined. Finding an optimal combination is NP-hard. We propose a new method for efficient inference in large Bayesian networks, which is a combination of new representations and new combination algorithms. We present new, purely multiplicative representations of independence of causal influence models. They are easy to use because any standard inference algorithm can work with them. Also, they allow for exploiting independence of causal influence fully because they do not impose any constraints on combination ordering. We develop combination algorithms that work with heuristics. Heuristics are generated automatically by using machine learning techniques. Empirical studies, based on the CPCS network for medical diagnosis, show that this method is more efficient and allows for inference in larger networks than existing methods.
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 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is 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 treatment of exact algorithms covers the main inference paradigms based on elimination and conditioning and includes advanced methods for compiling Bayesian networks, time-space tradeoffs, and exploiting local structure of massively connected networks. The treatment of approximate algorithms covers the main inference paradigms based on sampling and optimization and includes influential algorithms such as importance sampling, MCMC, and belief propagation. 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.
Download or read book Advances in Bayesian Networks written by José A. Gámez and published by Springer. This book was released on 2013-06-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years probabilistic graphical models, especially Bayesian networks and decision graphs, have experienced significant theoretical development within areas such as artificial intelligence and statistics. This carefully edited monograph is a compendium of the most recent advances in the area of probabilistic graphical models such as decision graphs, learning from data and inference. It presents a survey of the state of the art of specific topics of recent interest of Bayesian Networks, including approximate propagation, abductive inferences, decision graphs, and applications of influence. In addition, Advances in Bayesian Networks presents a careful selection of applications of probabilistic graphical models to various fields such as speech recognition, meteorology or information retrieval.
Download or read book Bayesian Networks written by Marco Scutari and published by CRC Press. This book was released on 2021-07-28 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the material step-by-step starting from meaningful examples Steps detailed with R code in the spirit of reproducible research Real world data analyses from a Science paper reproduced and explained in detail Examples span a variety of fields across social and life sciences Overview of available software in and outside R
Download or read book Hierarchical Bayesian Optimization Algorithm written by Martin Pelikan and published by Springer Science & Business Media. This book was released on 2005-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a framework for the design of competent optimization techniques by combining advanced evolutionary algorithms with state-of-the-art machine learning techniques. The book focuses on two algorithms that replace traditional variation operators of evolutionary algorithms by learning and sampling Bayesian networks: the Bayesian optimization algorithm (BOA) and the hierarchical BOA (hBOA). BOA and hBOA are theoretically and empirically shown to provide robust and scalable solution for broad classes of nearly decomposable and hierarchical problems. A theoretical model is developed that estimates the scalability and adequate parameter settings for BOA and hBOA. The performance of BOA and hBOA is analyzed on a number of artificial problems of bounded difficulty designed to test BOA and hBOA on the boundary of their design envelope. The algorithms are also extensively tested on two interesting classes of real-world problems: MAXSAT and Ising spin glasses with periodic boundary conditions in two and three dimensions. Experimental results validate the theoretical model and confirm that BOA and hBOA provide robust and scalable solution for nearly decomposable and hierarchical problems with only little problem-specific information.
Download or read book Patterns of Scalable Bayesian Inference written by Elaine Angelino and published by . This book was released on 2016-11-17 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Identifies unifying principles, patterns, and intuitions for scaling Bayesian inference. Reviews existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, it characterizes the general principles that have proven successful for designing scalable inference procedures.
Download or read book Gated Bayesian Networks written by Marcus Bendtsen and published by Linköping University Electronic Press. This book was released on 2017-06-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian networks have grown to become a dominant type of model within the domain of probabilistic graphical models. Not only do they empower users with a graphical means for describing the relationships among random variables, but they also allow for (potentially) fewer parameters to estimate, and enable more efficient inference. The random variables and the relationships among them decide the structure of the directed acyclic graph that represents the Bayesian network. It is the stasis over time of these two components that we question in this thesis. By introducing a new type of probabilistic graphical model, which we call gated Bayesian networks, we allow for the variables that we include in our model, and the relationships among them, to change overtime. We introduce algorithms that can learn gated Bayesian networks that use different variables at different times, required due to the process which we are modelling going through distinct phases. We evaluate the efficacy of these algorithms within the domain of algorithmic trading, showing how the learnt gated Bayesian networks can improve upon a passive approach to trading. We also introduce algorithms that detect changes in the relationships among the random variables, allowing us to create a model that consists of several Bayesian networks, thereby revealing changes and the structure by which these changes occur. The resulting models can be used to detect the currently most appropriate Bayesian network, and we show their use in real-world examples from both the domain of sports analytics and finance.
Download or read book Bayesian Programming written by Pierre Bessiere and published by CRC Press. This book was released on 2013-12-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in natur
Download or read book Learning Bayesian Networks written by Richard E. Neapolitan and published by Prentice Hall. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first edition book, methods are discussed for doing inference in Bayesian networks and inference diagrams. Hundreds of examples and problems allow readers to grasp the information. Some of the topics discussed include Pearl's message passing algorithm, Parameter Learning: 2 Alternatives, Parameter Learning r Alternatives, Bayesian Structure Learning, and Constraint-Based Learning. For expert systems developers and decision theorists.
Download or read book Mathematical Foundations of Computer Science 2006 written by Rastislav Královic and published by Springer. This book was released on 2006-08-29 with total page 827 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006. The book presents 62 revised full papers together with the full papers or abstracts of 7 invited talks. All current aspects in theoretical computer science and its mathematical foundations are addressed, from algorithms and data structures, to complexity, automata, semantics, logic, formal specifications, models of computation, concurrency theory, computational geometry and more.
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 Optimizing Inference in Bayesian Networks written by Andre Evaristo dos Santos and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many di erent platforms, techniques, and concepts can be employed while modelling and reasoning with Bayesian networks (BNs). A problem domain is modelled initially as a directed acyclic graph (DAG) and the strengths of relationships are quanti ed by conditional probability tables (CPTs). We consider four perspectives to BN inference. First, a central task in discrete BN inference is to determine those variables relevant to answer a given query. Two linear algorithms for this task explore the possibly relevant and active parts of a BN, respectively. We empirically compare these two methods along with a variation of each. Second, we start with BN inference using message passing in a join tree. We start with BN inference using message passing in a join tree. Here, we propose Simple Propagation (SP) as a new join tree propagation algorithm for exact inference in discrete Bayesian networks. We establish the correctness of SP. The striking feature of SP is that its message construction exploits the factorization of potentials at a sending node but without the overhead of building and examining graphs as done in Lazy Propagation (LP). Experimental results on optimal (or close to optimal) join trees built from numerous benchmark Bayesian networks show that SP is often faster than LP. Sum-Product Networks (SPNs) are a probabilistic graphical model with deep learning applications. A key feature in an SPN is that inference is tractable under certain structural constraints. This is a strong feature when compared to BNs, where inference is NP-hard. SPNs internal nodes can be understood as marginal inference recording of a BN. This is the third perspective. SPNs have shown to excel at many tasks, achieving even state-of-the-art in important tasks such as image completion. Even though SPNs pose a clear advantage against BNs, the later still have a clearer illustration of in uence among the variables they represent. To take advantage of both, we use an SPN to perform inference, but utilize BNs to observe i the bacterial relationships in soil datasets. We rst learn a BN to read independencies in linear time between bacterial community characteristics. These independencies are useful in understanding the semantic relationships between bacteria within communities. Next, we learn an SPN to perform e cient inference. Here, inference can be conducted to answer traditional queries, involving marginals, or most probable expla- nation (MPE) queries, requesting the most likely values of the non-evidence variables given evidence. Our results extend the literature by showing that known relationships between soil bacteria holding in one or a few datasets, in fact, hold across at least 3500 diverse datasets. This study paves the way for future large-scale studies of agricultural, health, and environmental applications, for which data are publicly available. In an SPN, leaf nodes are indicator variables for each value that a random variable can assume and the remaining nodes are either sum or product. As contribution to SPN inference, we derive partial propagation (PP), which performs SPN exact inference without requiring a full propagation over all nodes in the SPN as currently done. Experimental results on SPN datasets demonstrate that PP has several advantages over full propagation in SPNs, including relative time savings, absolute time savings in large SPNs, and scalability. Finally, as the fourth perspective to BN inference, we give conditions under which convolutional neural networks (CNNs) de ne valid SPNs. One subclass, called con- volutional SPNs (CSPNs), can be implemented using tensors but also can su er from being too shallow. Fortunately, tensors can be augmented while maintaining valid SPNs. This yielded a larger subclass of CNNs, which is called deep convolutional SPNs (DCSPNs), where the convolutional and sum-pooling layers form rich directed acyclic graph structures. One salient feature of DCSPNs is that they keep the rigorousness probabilistic model. As such, they can exploit multiple kinds of probabilistic reasoning, including marginal inference and MPE inference. This allowed an alternative method for learning DCSPNs using vectorized di erentiable MPE, which plays a similar role to the generator in generative adversarial networks (GANs). Image sampling is yet another application demonstrating the robustness of DCSPNs. The results on image sampling were encouraging and sampled images exhibited variability, a salient attribute.
Download or read book Probabilistic Networks and Expert Systems written by Robert G. Cowell and published by Springer Science & Business Media. This book was released on 2007-07-16 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic expert systems are graphical networks which support the modeling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms. The book will be of interest to researchers in both artificial intelligence and statistics, who desire an introduction to this fascinating and rapidly developing field. The book, winner of the DeGroot Prize 2002, the only book prize in the field of statistics, is new in paperback.
