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16
Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables
 Machine Learning
, 1997
"... We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MD ..."
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Cited by 178 (10 self)
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We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naiveBayes models having a hidden root node, we find that (1) the BIC/MDL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate. 1
Learning with mixtures of trees
 Journal of Machine Learning Research
, 2000
"... This paper describes the mixturesoftrees model, a probabilistic model for discrete multidimensional domains. Mixturesoftrees generalize the probabilistic trees of Chow and Liu [6] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learnin ..."
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Cited by 109 (2 self)
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This paper describes the mixturesoftrees model, a probabilistic model for discrete multidimensional domains. Mixturesoftrees generalize the probabilistic trees of Chow and Liu [6] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learning mixturesoftrees models in maximum likelihood and Bayesian frameworks. We also discuss additional efficiencies that can be obtained when data are “sparse, ” and we present data structures and algorithms that exploit such sparseness. Experimental results demonstrate the performance of the model for both density estimation and classification. We also discuss the sense in which treebased classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.
Asymptotic model selection for directed networks with hidden variables
, 1996
"... We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a ..."
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Cited by 49 (15 self)
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We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node. 1
Building probabilistic networks: where do the numbers come from?  a guide to the literature
 IEEE Transactions on Knowledge and Data Engineering
, 2000
"... Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision, ..."
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Cited by 29 (3 self)
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Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision,
Accelerated Quantification of Bayesian Networks with Incomplete Data
 In Proceedings of First International Conference on Knowledge Discovery and Data Mining
, 1995
"... Probabilistic expert systems based on Bayesian networks (BNs) require initial specification of both a qualitative graphical structure and quantitative assessment of conditional probability tables. This paper considers statistical batch learning of the probability tables on the basis of incomple ..."
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Cited by 28 (2 self)
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Probabilistic expert systems based on Bayesian networks (BNs) require initial specification of both a qualitative graphical structure and quantitative assessment of conditional probability tables. This paper considers statistical batch learning of the probability tables on the basis of incomplete data and expert knowledge. The EM algorithm with a generalized conjugate gradient acceleration method has been dedicated to quantification of BNs by maximum posterior likelihood estimation for a superclass of the recursive graphical models. This new class of models allows a great variety of local functional restrictions to be imposed on the statistical model, which hereby extents the control and applicability of the constructed method for quantifying BNs. Introduction The construction of probabilistic expert systems (Pearl 1988, Andreassen et al. 1989) based on Bayesian networks (BNs) is often a challenging process. It is typically divided into two parts: First the constructi...
Inferring User Goals from Personality and Behavior in a Causal Model of User Affect
, 2003
"... We present a probabilistic model, based on Dynamic Decision Networks, to assess user affect from possible causes of emotional arousal. The model relies on the OCC cognitive theory of emotions and is designed to assess student affect during the interaction with an educational game. A key element of a ..."
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Cited by 18 (3 self)
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We present a probabilistic model, based on Dynamic Decision Networks, to assess user affect from possible causes of emotional arousal. The model relies on the OCC cognitive theory of emotions and is designed to assess student affect during the interaction with an educational game. A key element of applying the OCC theory to assess user affect is knowledge of user goals. Thus, in this paper we focus on describing how our model infers these goals from user personality traits and interaction behavior. In particular, we illustrate how we iteratively defined the structure and parameters for this part of the model by using both empirical data collected through Wizard of Oz experiments and relevant psychological findings.
Inference in hybrid Bayesian networks using dynamic discretization
 Statistics and Computing
, 2007
"... We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction trees structures. Our approach offers a significant extension to Bayesian Network theory and pract ..."
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Cited by 13 (7 self)
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We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction trees structures. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modelling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgement as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.
Outlier management in intelligent data analysis
, 2000
"... In spite of many statistical methods for outlier detection and for robust analysis, there is little work on further analysis of outliers themselves to determine their origins. For example, there are “good ” outliers that provide useful information that can lead to the discovery of new knowledge, or ..."
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Cited by 2 (0 self)
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In spite of many statistical methods for outlier detection and for robust analysis, there is little work on further analysis of outliers themselves to determine their origins. For example, there are “good ” outliers that provide useful information that can lead to the discovery of new knowledge, or “bad ” outliers that include noisy data points. Successfully distinguishing between different types of outliers is an important issue in many applications, including fraud detection, medical tests, process analysis and scientific discovery. It requires not only an understanding of the mathematical properties of data but also relevant knowledge in the domain context in which the outliers occur. This thesis presents a novel attempt in automating the use of domain knowledge in helping distinguish between different types of outliers. Two complementary knowledgebased outlier analysis strategies are proposed: one using knowledge regarding how “normal data ” should be distributed in a domain of interest in order to identify “good ” outliers, and the other using the understanding of “bad ” outliers. This kind of knowledgebased outlier analysis is a useful extension to existing work in both statistical and computing communities on outlier detection.