Fusion, propagation, and structuring in belief networks
TL;DR: It is shown that if the network is singly connected (e.g. tree-structured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network.
About: This article is published in Artificial Intelligence.The article was published on 1986-09-01. It has received 2266 citations till now. The article focuses on the topics: Tree structure & Longest path problem.
Citations
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Book•
01 Jan 1988TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Abstract: From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
15,671 citations
Book•
01 Jan 2001TL;DR: The book introduces probabilistic graphical models and decision graphs, including Bayesian networks and influence diagrams, and presents a thorough introduction to state-of-the-art solution and analysis algorithms.
Abstract: Probabilistic graphical models and decision graphs are powerful modeling tools for reasoning and decision making under uncertainty. As modeling languages they allow a natural specification of problem domains with inherent uncertainty, and from a computational perspective they support efficient algorithms for automatic construction and query answering. This includes belief updating, finding the most probable explanation for the observed evidence, detecting conflicts in the evidence entered into the network, determining optimal strategies, analyzing for relevance, and performing sensitivity analysis. The book introduces probabilistic graphical models and decision graphs, including Bayesian networks and influence diagrams. The reader is introduced to the two types of frameworks through examples and exercises, which also instruct the reader on how to build these models. The book is a new edition of Bayesian Networks and Decision Graphs by Finn V. Jensen. The new edition is structured into two parts. The first part focuses on probabilistic graphical models. Compared with the previous book, the new edition also includes a thorough description of recent extensions to the Bayesian network modeling language, advances in exact and approximate belief updating algorithms, and methods for learning both the structure and the parameters of a Bayesian network. The second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision processes and partially ordered decision problems. The authors also provide a well-founded practical introduction to Bayesian networks, object-oriented Bayesian networks, decision trees, influence diagrams (and variants hereof), and Markov decision processes. give practical advice on the construction of Bayesian networks, decision trees, and influence diagrams from domain knowledge. give several examples and exercises exploiting computer systems for dealing with Bayesian networks and decision graphs. present a thorough introduction to state-of-the-art solution and analysis algorithms. The book is intended as a textbook, but it can also be used for self-study and as a reference book.
4,566 citations
Cites methods from "Fusion, propagation, and structurin..."
...In (Pearl, 1986), cutset-conditioning was used to reduce propagation in multiply connected networks to propagation in singly connected networks....
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TL;DR: This paper presents a Bayesian method for constructing probabilistic networks from databases, focusing on constructing Bayesian belief networks, and extends the basic method to handle missing data and hidden variables.
Abstract: This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.
3,971 citations
Cites background or methods from "Fusion, propagation, and structurin..."
...A Bayesian belief-network structure Bs is a directed acyclic graph in which nodes represent domain variables and arcs between nodes represent probabilistic dependencies (Cooper, 1989; Horvitz, Breese, & Henrion, 1988; Lauritzen & Spiegelhalter, 1988; Neapolitan, 1990; Pearl, 1986; Pearl, 1988; Shachter, 1988)....
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...Pearl developed a method for constructing from data a treestructured belief network with hidden variables (Pearl, 1986)....
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...…structure Bs is a directed acyclic graph in which nodes represent domain variables and arcs between nodes represent probabilistic dependencies (Cooper, 1989; Horvitz, Breese, & Henrion, 1988; Lauritzen & Spiegelhalter, 1988; Neapolitan, 1990; Pearl, 1986; Pearl, 1988; Shachter, 1988)....
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Book•
01 Jan 2004TL;DR: This chapter discusses Bayesian Networks, a framework for Bayesian Structure Learning, and some of the algorithms used in this framework.
Abstract: Preface. I. BASICS. 1. Introduction to Bayesian Networks. 2. More DAG/Probability Relationships. II. INFERENCE. 3. Inference: Discrete Variables. 4. More Inference Algorithms. 5. Influence Diagrams. III. LEARNING. 6. Parameter Learning: Binary Variables. 7. More Parameter Learning. 8. Bayesian Structure Learning. 9. Approximate Bayesian Structure Learning. 10. Constraint-Based Learning. 11. More Structure Learning. IV. APPICATIONS. 12. Applications. Bibliography. Index.
2,575 citations
References
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TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.
18,761 citations
Book•
01 Jan 1995
TL;DR: Adaptive Control of Thought (ACT*) as mentioned in this paper is a theory of the basic principles of operation built into the cognitive system and is the main focus of Anderson's theory of cognitive architecture.
Abstract: Now available in paper, The Architecture of Cognition is a classic work that remains relevant to theory and research in cognitive science. The new version of Anderson's theory of cognitive architecture -- Adaptive Control of Thought (ACT*) -- is a theory of the basic principles of operation built into the cognitive system and is the main focus of the book. (http://books.google.fr/books?id=Uip3_g7zlAUC&printsec=frontcover&hl=fr#v=onepage&q&f=false)
6,911 citations
IBM1
TL;DR: It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information when applied to empirical observations from an unknown distribution of tree dependence, and the procedure is the maximum-likelihood estimate of the distribution.
Abstract: A method is presented to approximate optimally an n -dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n - 1 first order dependence relationship among the n variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution.
2,854 citations
"Fusion, propagation, and structurin..." refers methods in this paper
...A related structuring task was treated by Chow and Liu [2], who also used tree-dependent random variables to approximate an arbitrary joint distribution ....
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...A related structuring task was treated by Chow and Liu [2], who also used tree-dependent random variables to approximate an arbitrary joint distribution....
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2,061 citations
TL;DR: The need of problem solvers to choose between alternative systems of beliefs is stressed, and a mechanism by which a problem solver can employ rules guiding choices of what to believe, what to want, and what to do is outlined.
1,909 citations
"Fusion, propagation, and structurin..." refers background in this paper
...Similarly, we find it natural to identify a set of direct justifications for q to sufficiently shield it (q) from all other influences and to describe them as the direct neighbors of q [5]....
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