Results 11  20
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134
Local Learning in Probabilistic Networks With Hidden Variables
, 1995
"... Probabilistic networks, which provide compact descriptions of complex stochastic relationships among several random variables, are rapidly becoming the tool of choice for uncertain reasoning in artificial intelligence. We show that networks with fixed structure containing hidden variables can be lea ..."
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Cited by 77 (4 self)
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Probabilistic networks, which provide compact descriptions of complex stochastic relationships among several random variables, are rapidly becoming the tool of choice for uncertain reasoning in artificial intelligence. We show that networks with fixed structure containing hidden variables can be learned automatically from data using a gradientdescent mechanism similar to that used in neural networks. We also extend the method to networks with intensionally represented distributions, including networks with continuous variables and dynamic probabilistic networks. Because probabilistic networks provide explicit representations of causal structure, human experts can easily contribute prior knowledge to the training process, thereby significantly improving the learning rate. Adaptive probabilistic networks (APNs) may soon compete directly with neural networks as models in computational neuroscience as well as in industrial and financial applications. 1 Introduction Intelligent systems, ...
ANCESTRAL GRAPH MARKOV MODELS
, 2002
"... This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of verti ..."
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Cited by 76 (18 self)
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This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.
Nonuniform Dynamic Discretization in Hybrid Networks
 In Proc. UAI
, 1997
"... We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a n ..."
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Cited by 64 (3 self)
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We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the information loss induced by the discretization. We show that a nonuniform partition across all variables as opposed to uniform partition of each variable separately reduces the size of the data structures needed to represent a continuous function. We also provide a simple but efficient procedure for nonuniform partition. To represent a nonuniform discretization in the computer memory, we introduce a new data structure, which we call a Binary Split Partition (BSP) tree. We show that BSP trees can be an exponential factor smaller than the data structures in the standard uniform discretization in multiple dimensions and show how the BSP trees can be used in the standard join tree algorithm. We show that the accuracy of the inference process can be significa...
Stable Local Computation with Conditional Gaussian Distributions
 Statistics and Computing
, 1999
"... : This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and ..."
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Cited by 60 (0 self)
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: This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and variances provided by the previous algorithm, the new propagation scheme yields full local marginal distributions. The new scheme also handles linear deterministic relationships between continuous variables in the network specification. The new propagation scheme is in many ways faster and simpler than previous schemes and the method has been implemented in the most recent version of the HUGIN software. Key words: Artificial intelligence, Bayesian networks, CG distributions, Gaussian mixtures, probabilistic expert systems, propagation of evidence. 1 Introduction Bayesian networks have developed into an important tool for building systems for decision support in environments characterized by...
Stratified exponential families: Graphical models and model selection
 Annals of Statistics
, 2001
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JS ..."
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Cited by 54 (6 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
An Alternative Markov Property for Chain Graphs
 Scand. J. Statist
, 1996
"... Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially conv ..."
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Cited by 49 (4 self)
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Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially convenient for statistical analysis, arise in such fields as genetics and psychometrics and as models for expert systems and Bayesian belief networks. Lauritzen, Wermuth, and Frydenberg (LWF) introduced a Markov property for chain graphs, which are mixed graphs that can be used to represent simultaneously both causal and associative dependencies and which include both UDGs and ADGs as special cases. In this paper an alternative Markov property (AMP) for chain graphs is introduced, which in some ways is a more direct extension of the ADG Markov property than is the LWF property for chain graph. 1 INTRODUCTION Graphical Markov models use graphs, either undirected, directed, or mixed, to represent...
Chain Graph Models and their Causal Interpretations
 B
, 2001
"... Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultim ..."
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Cited by 48 (4 self)
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Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...
A variational approximation for Bayesian networks with discrete and continuous latent variables
 In UAI
, 1999
"... We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust ..."
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Cited by 43 (6 self)
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We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is much faster than sampling, but comparable in accuracy. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributionson observed nodes, as well as achieving a significant speedup in networks with discrete variables of large cardinality. 1
On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs
 Scandinavian Journal of Statistics
, 1994
"... Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or fo ..."
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Cited by 30 (5 self)
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Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg's (1990) elegant graphtheoretic characterization of the Markov equivalence of chain graphs. 1 Introduction The use of graphs to represent dependence relations among random variables, first introduced by Wright (1921), has generated considerable research activity, especially since the early 1980s. Particular attention has been devoted to gra...
Bayesian Network Classification with Continuous Attributes: Getting the Best of Both Discretization and Parametric Fitting
 In Proceedings of the International Conference on Machine Learning (ICML
, 1998
"... In a recent paper, Friedman, Geiger, and Goldszmidt [8] introduced a classifier based on Bayesian networks, called Tree Augmented Naive Bayes (TAN), that outperforms naive Bayes and performs competitively with C4.5 and other stateoftheart methods. This classifier has several advantages including ..."
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Cited by 28 (2 self)
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In a recent paper, Friedman, Geiger, and Goldszmidt [8] introduced a classifier based on Bayesian networks, called Tree Augmented Naive Bayes (TAN), that outperforms naive Bayes and performs competitively with C4.5 and other stateoftheart methods. This classifier has several advantages including robustness and polynomial computational complexity. One limitation of the TAN classifier is that it applies only to discrete attributes, and thus, continuous attributes must be prediscretized. In this paper, we extend TAN to deal with continuous attributes directly via parametric (e.g., Gaussians) and semiparametric (e.g., mixture of Gaussians) conditional probabilities. The result is a classifier that can represent and combine both discrete and continuous attributes. In addition, we propose a new method that takes advantage of the modeling language of Bayesian networks in order to represent attributes both in discrete and continuous form simultaneously, and use both versions in the classifi...