Posted Content•
Loopy Belief Propagation for Approximate Inference: An Empirical Study
TL;DR: In this article, the authors compare the performance of loopy belief propagation with the exact ones in four real world networks, including two real-world networks: ALARM and QMR, and find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals.
Abstract: Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results.
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Book•
24 Aug 2012
TL;DR: This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach, and is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
Abstract: Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
8,059 citations
01 Jan 2002
TL;DR: This thesis will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in Dbns, and how to learn DBN models from sequential data.
Abstract: Dynamic Bayesian Networks: Representation, Inference and Learning by Kevin Patrick Murphy Doctor of Philosophy in Computer Science University of California, Berkeley Professor Stuart Russell, Chair Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T ) time instead of O(T ), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T ) space instead of O(T ); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
2,757 citations
TL;DR: This work explains how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms, and describes empirical results showing that GBP can significantly outperform BP.
Abstract: Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a "valid" or "maxent-normal" approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the "Bethe method", the "junction graph method", the "cluster variation method", and the "region graph method". Finally, we explain how to tell whether a region-based approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
1,827 citations
Book•
01 Jan 2003TL;DR: It is shown that BP can only converge to a fixed point that is also a stationary point of the Bethe approximation to the free energy, which enables connections to be made with variational approaches to approximate inference.
Abstract: "Inference" problems arise in statistical physics, computer vision, error-correcting coding theory, and AI. We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing local messages. We develop a unified approach, with examples, notation, and graphical models borrowed from the relevant disciplines.We explain the close connection between the BP algorithm and the Bethe approximation of statistical physics. In particular, we show that BP can only converge to a fixed point that is also a stationary point of the Bethe approximation to the free energy. This result helps explaining the successes of the BP algorithm and enables connections to be made with variational approaches to approximate inference.The connection of BP with the Bethe approximation also suggests a way to construct new message-passing algorithms based on improvements to Bethe's approximation introduced Kikuchi and others. The new generalized belief propagation (GBP) algorithms are significantly more accurate than ordinary BP for some problems. We illustrate how to construct GBP algorithms with a detailed example.
1,627 citations
TL;DR: This paper attempts to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain, and provides an extensive account of registration techniques in a systematic manner.
Abstract: Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.
1,434 citations
References
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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
Proceedings Article•
01 Jan 1993
7,742 citations
TL;DR: In this article, it was shown that probabilistic inference using belief networks is NP-hard and that it seems unlikely that an exact algorithm can be developed to perform inference efficiently over all classes of belief networks and that research should be directed toward the design of efficient special-case, average-case and approximation algorithms.
1,877 citations
TL;DR: It is shown that Pearl's algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other error-control systems, including Gallager's low-density parity-check codes, serially concatenated codes, and product codes.
Abstract: We describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. (1993) and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl's (1982) belief propagation algorithm. We see that if Pearl's algorithm is applied to the "belief network" of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the experimental performance of turbo decoding is still lacking. However, we also show that Pearl's algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other error-control systems, including Gallager's (1962) low-density parity-check codes, serially concatenated codes, and product codes. Thus, belief propagation provides a very attractive general methodology for devising low-complexity iterative decoding algorithms for hybrid coded systems.
989 citations
01 Jan 1989
TL;DR: Two algorithms were applied to this belief network: a message-passing algorithm by Pearl for probability updating in multiply connected networks using the method of conditioning and the Lauritzen-Spiegelhalter algorithm for local probability computations on graphical structures.
Abstract: ALARM (A Logical Alarm Reduction Mechanism) is a diagnostic application used to explore probabilistic reasoning techniques in belief networks. ALARM implements an alarm message system for patient monitoring; it calculates probabilities for a differential diagnosis based on available evidence. The medical knowledge is encoded in a graphical structure connecting 8 diagnoses, 16 findings and 13 intermediate variables. Two algorithms were applied to this belief network: (1) a message-passing algorithm by Pearl for probability updating in multiply connected networks using the method of conditioning; and (2) the Lauritzen-Spiegelhalter algorithm for local probability computations on graphical structures. The characteristics of both algorithms are analyzed and their specific applications and time complexities are shown.
835 citations