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20
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 277 (13 self)
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This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feedforward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...
A Guide to the Literature on Learning Probabilistic Networks From Data
, 1996
"... This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the ..."
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Cited by 203 (0 self)
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This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...
Inference in hybrid Bayesian networks with mixtures of truncated exponentials
 Proceedings of the 6th workshop on uncertainty processing (WUPES2003
"... An important class of hybrid Bayesian networks are those that have conditionally deterministic variables (a variable that is a deterministic function of its parents). In this case, if some of the parents are continuous, then the joint density function does not exist. Conditional linear Gaussian (CL ..."
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Cited by 31 (4 self)
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An important class of hybrid Bayesian networks are those that have conditionally deterministic variables (a variable that is a deterministic function of its parents). In this case, if some of the parents are continuous, then the joint density function does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when the deterministic function is linear and continuous variables are normally distributed. In this paper, we develop operations required for performing inference with conditionally deterministic variables using relationships derived from joint cumulative distribution functions (CDF’s). These methods allow inference in networks with deterministic variables where continuous variables are nonGaussian. 1
Graphical Models for Discovering Knowledge
, 1995
"... There are many different ways of representing knowledge, and for each of these ways there are many different discovery algorithms. How can we compare different representations? How can we mix, match and merge representations and algorithms on new problems with their own unique requirements? This cha ..."
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Cited by 30 (2 self)
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There are many different ways of representing knowledge, and for each of these ways there are many different discovery algorithms. How can we compare different representations? How can we mix, match and merge representations and algorithms on new problems with their own unique requirements? This chapter introduces probabilistic modeling as a philosophy for addressing these questions and presents graphical models for representing probabilistic models. Probabilistic graphical models are a unified qualitative and quantitative framework for representing and reasoning with probabilities and independencies. 4.1 Introduction Perhaps one common element of the discovery systems described in this and previous books on knowledge discovery is that they are all different. Since the class of discovery problems is a challenging one, we cannot write a single program to address all of knowledge discovery. The KEFIR discovery system applied to health care by Matheus, PiatetskyShapiro, and McNeill (199...
Mixtures of Gaussians and Minimum Relative Entropy Techniques
 In Uncertainty in Artificial Intelligence: Proceedings of the Ninth Conference: 183–190
, 1993
"... Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is to fit analytically tractable continuous probability distribu ..."
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Cited by 29 (2 self)
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Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is to fit analytically tractable continuous probability distributions. This approach has potential simplicity and accuracy advantages, especially if variables can be transformed first. This paper shows how a minimum relative entropy criterion can drive both transformation and fitting, illustrating with a power and logarithm family of transformations and mixtures of Gaussian (normal) distributions, which allow use of efficient influence diagram methods. The fitting procedure in this case is the wellknown EM algorithm. The selection of the number of components in a fitted mixture distribution is automated with an objective that trades off accuracy and computational cost. 1
A Forward Monte Carlo Method for Solving Influence Diagrams Using Local Computation
, 2000
"... The main goal of this paper is to describe a new Monte Carlo method for solving influence diagrams using local computation. We propose a forward Monte Carlo sampling technique that draws independent and identically distributed observations. Methods that have been proposed in this spirit sample from ..."
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Cited by 10 (2 self)
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The main goal of this paper is to describe a new Monte Carlo method for solving influence diagrams using local computation. We propose a forward Monte Carlo sampling technique that draws independent and identically distributed observations. Methods that have been proposed in this spirit sample from the entire distribution. However, when the number of variables is large, the state space of all variables is exponentially large, and the sample size required for good estimates may be too large to be practical. In this paper, we develop a forward Monte Carlo method, which generates observations from only a small set of chance variables for each decision node in the influence diagram. We use methods developed for exact solution of influence diagrams to limit the number of chance variables sampled at any time. Because influence diagrams model each chance variable with a conditional probability distribution, the forward Monte Carlo solution method lends itself very well to influencediagram representations.
Extended ShenoyShafer Architecture for Inference in Hybrid Bayesian Networks with Deterministic Conditionals
, 2009
"... James C. West ..."
Three approaches to probability model selection
 In de Mantaras and Poole [160
, 1994
"... relative entropy, EM algorithm. This paper compares three approaches to the problem of selecting among probability models to fit data: (1) use of statistical criteria such as Akaike’s information criterion and Schwarz’s “Bayesian information criterion, ” (2) maximization of the posterior probability ..."
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Cited by 4 (0 self)
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relative entropy, EM algorithm. This paper compares three approaches to the problem of selecting among probability models to fit data: (1) use of statistical criteria such as Akaike’s information criterion and Schwarz’s “Bayesian information criterion, ” (2) maximization of the posterior probability of the model, and (3) maximization of an “effectiveness ratio ” trading off accuracy and computational cost. The unifying characteristic of the approaches is that all can be viewed as maximizing a penalized likelihood function. The second approach with suitable prior distributions has been shown to reduce to the first. This paper shows that the third approach reduces to the second for a particular form of the effectiveness ratio, and illustrates all three approaches with the problem of selecting the number of components in a mixture of Gaussian distributions. Unlike the first two approaches, the third can be used even when the candidate models are chosen for computational efficiency, without regard to physical interpretation, so that the likelihoods and the prior distribution over models cannot be interpreted literally. As the most general and computationally oriented of the approaches, it is especially useful for artificial intelligence applications. 1
A review of representation issues and modeling challenges with influence diagrams
 OmegaInternational Journal of Management Science
"... Since their introduction in the mid 1970s, influence diagrams have become a de facto standard for representing Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology designed to increase the ability to represent complex problems. ..."
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Cited by 4 (1 self)
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Since their introduction in the mid 1970s, influence diagrams have become a de facto standard for representing Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology designed to increase the ability to represent complex problems. In this paper, we review the representation issues and modeling challenges associated with influence diagrams. In particular, we look at the representation of asymmetric decision problems including conditional distribution trees, sequential decision diagrams, and sequential valuation networks. We also examine the issue of representing the sequence of decision and chance variables, and how it is done in unconstrained influence diagrams, sequential valuation networks, and sequential influence diagrams. We also discuss the use of continuous chance and decision variables, including continuous conditionally deterministic variables. Finally, we discuss some of the modeling challenges faced in representing decision problems in practice and some software that is currently available. Key words: Decisionmaking under uncertainty, influence diagrams, probabilistic graphical models, sequential decision diagrams, unconstrained influence diagrams, sequential valuation networks, sequential influence diagrams, partial influence diagrams, limited memory influence diagrams, Gaussian influence diagrams, mixture of Gaussians influence diagrams, mixture of truncated exponentials influence diagrams, mixture of polynomials influence diagrams 1
Efficiency of Influence Diagram Models with Continuous Decision Variables. Working Paper, Virginia Military Institute
 Internat. J. Approx. Reason
, 2008
"... A measure of efficiency for influence diagram models with continuous decision variables is presented in order to evaluate whether the additional computational complexity required by a more accurate model is justified. The efficiency measure is a multiobjective utility function that considers both t ..."
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Cited by 3 (3 self)
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A measure of efficiency for influence diagram models with continuous decision variables is presented in order to evaluate whether the additional computational complexity required by a more accurate model is justified. The efficiency measure is a multiobjective utility function that considers both the accuracy and complexity of the ID model. Accuracy is determined as the mean squared error between influence diagram decision rules and an analytical solution. Complexity is assessed by tracking the run time required to obtain the solution. The resulting efficiency score considers the preferences of an individual decision maker for accuracy and complexity. Three influence diagram models are compared using the efficiency measurement, and an iterative solution procedure is introduced to improve model performance. Key words: accuracy, complexity, continuous variable, decision analysis, decision variable, efficiency, graphical model, influence diagram, mixtures of truncated exponentials, probability 1.