Results 1  10
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14
A characterization of Markov equivalence classes for acyclic digraphs
, 1995
"... Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow e ..."
Abstract

Cited by 91 (7 self)
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Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. Whereas the undirected graph associated with a dependence model is uniquely determined, there may, however, be many ADGs that determine the same dependence ( = Markov) model. Thus, the family of all ADGs with a given set of vertices is naturally partitioned into Markovequivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection or model averaging, that fail to take into account these equivalence classes, may incur substantial computational or other inefficiencies. Here it is shown that each Markovequivalence class is uniquely determined by a single chain graph, the essential graph, that is itself simultaneously Markov equivalent to all ADGs in the equivalence class. Essential graphs are characterized, a polynomialtime algorithm for their construction is given, and their applications to model selection and other statistical
AISBN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks
 Journal of Artificial Intelligence Research
, 2000
"... Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, ..."
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Cited by 70 (4 self)
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Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AISBN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in nitedimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from dierent stages of the algorithm. We tested the performance of the AISBN algorithm along with two state of the art general purpose sampling algorithms, lik...
Bayesian Model Averaging And Model Selection For Markov Equivalence Classes Of Acyclic Digraphs
 Communications in Statistics: Theory and Methods
, 1996
"... Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building B ..."
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Cited by 38 (5 self)
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Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. There may, however, be many ADGs that determine the same dependence (= Markov) model. Thus, the family of all ADGs with a given set of vertices is naturally partitioned into Markovequivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection or model averaging, that fail to take into account these equivalence classes, may incur substantial computational or other inefficiencies. Recent results have shown that each Markovequivalence class is uniquely determined by a single chain graph, the essential graph, that is itself Markovequivalent simultaneously to all ADGs in the equivalence clas...
Combining human and machine intelligence in largescale crowdsourcing
 In AAMAS
, 2012
"... We show how machine learning and inference can be harnessed to leverage the complementary strengths of humans and computational agents to solve crowdsourcing tasks. We construct a set of Bayesian predictive models from data and describe how the models operate within an overall crowdsourcing architec ..."
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Cited by 24 (12 self)
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We show how machine learning and inference can be harnessed to leverage the complementary strengths of humans and computational agents to solve crowdsourcing tasks. We construct a set of Bayesian predictive models from data and describe how the models operate within an overall crowdsourcing architecture that combines the efforts of people and machine vision on the task of classifying celestial bodies defined within a citizens ’ science project named Galaxy Zoo. We show how learned probabilistic models can be used to fuse human and machine contributions and to predict the behaviors of workers. We employ multiple inferences in concert to guide decisions on hiring and routing workers to tasks so as to maximize the efficiency of largescale crowdsourcing processes based on expected utility.
A Bayesian Analysis of Simulation Algorithms for Inference in Belief Networks,
 Networks
, 1993
"... A belief network is a graphical representation of the underlying probabilistic relationships in a complex system. Belief networks have been employed as a representation of uncertain relationships in computerbased diagnostic systems. These diagnostic systems provide assistance by assigning likeli ..."
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Cited by 17 (3 self)
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A belief network is a graphical representation of the underlying probabilistic relationships in a complex system. Belief networks have been employed as a representation of uncertain relationships in computerbased diagnostic systems. These diagnostic systems provide assistance by assigning likelihoods to alternative explanatory hypotheses in response to a set of findings or observations. Approximation algorithms have been used to compute likelihoods of hypotheses in large networks. We analyze the performance of leading Monte Carlo approximation algorithms for computing posterior probabilities in belief networks. The analysis differs from earlier attempts to characterize the behavior of simulation algorithms in our explicit use of Bayesian statistics: We update a probability distribution over target probabilities of interest with information from randomized trials. For real ffl; ffi ! 1 and for a probabilistic inference Pr[xje], the output of an inference approximation algorithm is an (ffl; ffi)estimate of Pr[xje] if with probability at least 1 \Gamma ffi the output is within relative error ffl of Pr[xje]. We construct a stopping rule for the number of simulations required by logic sampling, randomized approximation schemes, and likelihood weighting to provide (ffl; ffi)estimates of Pr[xje]. With probability 1 \Gamma ffi, the stopping rule is optimal in the sense that the algorithm performs the minimum number of required simulations. We prove that our stopping rules are insensitive to the prior probability distribution on Pr[xje].
Sensitivity Analysis And Expected Value Of Perfect Information
 Medical Decision Making
, 1997
"... We examine measures of decision sensitivity that have been applied to medical decision problems. Traditional threshold proximity methods have recently been supplemented by probabilistic sensitivity analysis, and by entropybased measures of sensitivity. We propose a fourth measure based upon the exp ..."
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Cited by 9 (1 self)
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We examine measures of decision sensitivity that have been applied to medical decision problems. Traditional threshold proximity methods have recently been supplemented by probabilistic sensitivity analysis, and by entropybased measures of sensitivity. We propose a fourth measure based upon the expected value of perfect information (EVPI), which we believe superior both methodologically and pragmatically. Both the traditional and the newly suggested sensitivity measures focus entirely on the likelihood of decision change without attention to corresponding changes in payoff, which are often small. Consequently, these measures can dramatically overstate problem sensitivity. EVPI, on the other hand, incorporates both the probability of a decision change and the marginal benefit of such a change into a single measure, and therefore provides a superior picture of problem sensitivity. To lend support to this contention, we revisit three problems from the literature and compare the results o...
An evaluation of the diagnostic accuracy
 of Pathfinder. Computers and Biomedical Research
, 1992
"... This work is an adaptation of Heckerman (1991). All figures and tables are printed with permission from MIT Press. We present an evaluation of the diagnostic accuracy of Pathfinder, an expert system that assists pathologists with the diagnosis of lymphnode diseases. We evaluate two versions of the ..."
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Cited by 8 (5 self)
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This work is an adaptation of Heckerman (1991). All figures and tables are printed with permission from MIT Press. We present an evaluation of the diagnostic accuracy of Pathfinder, an expert system that assists pathologists with the diagnosis of lymphnode diseases. We evaluate two versions of the system using both informal and decisiontheoretic metrics of performance. In one version of Pathfinder, we assume incorrectly that all observations are conditionally independent. In the other version, we use a belief network to represent accurately the probabilistic dependencies among the observations. In both versions, we make the assumption—reasonable for this domain—that diseases are mutually exclusive and exhaustive. The results of the study show that (1) it is cost effective to represent probabilistic dependencies among observations in the lymphnode domain, and (2) the diagnostic accuracy of the more complex version of Pathfinder is at least as good as that of the Pathfinder expert. In addition, the study illustrates how informal and decisiontheoretic metrics for performance complement one another. 2 1
A Parallel Learning Algorithm for Bayesian Inference Networks
 IEEE Transactions on Knowledge and Data Engineering
"... We present a new parallel algorithm for learning Bayesian inference networks from data. Our learning algorithm exploits both properties of the MDLbased score metric, and a distributed, asynchronous, adaptive search technique called nagging. Nagging is intrinsically fault tolerant, has dynamic load ..."
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Cited by 4 (0 self)
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We present a new parallel algorithm for learning Bayesian inference networks from data. Our learning algorithm exploits both properties of the MDLbased score metric, and a distributed, asynchronous, adaptive search technique called nagging. Nagging is intrinsically fault tolerant, has dynamic load balancing features, and scales well. We demonstrate the viability, effectiveness, and scalability of our approach empirically with several experiments using on the order of 20 machines. More specifically, we show that our distributed algorithm can provide optimal solutions for larger problems as well as good solutions for Bayesian networks of up to 150 variables. Keywords: Machine Learning, Bayesian Networks, Minimum Description Length Principle, Distributed Systems Support for this research was provided by the Office of Naval Research through grant N00149411178, and by the Advanced Research Project Agency through Rome Laboratory Contract Number F3060293C0018 via Odyssey Research As...
Similarity networks for the construction of multiplefault belief networks
 Uncertainty in Artificial Intelligence
, 1991
"... A similarity network is a tool for constructing belief networks for the diagnosis of a single fault. In this paper, we examine modifications to the similaritynetwork representation that facilitate the construction of belief networks for the diagnosis of multiple coexisting faults. 1 ..."
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Cited by 3 (0 self)
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A similarity network is a tool for constructing belief networks for the diagnosis of a single fault. In this paper, we examine modifications to the similaritynetwork representation that facilitate the construction of belief networks for the diagnosis of multiple coexisting faults. 1