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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 naive-Bayes 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

This paper describes the mixtures-of-trees model, a probabilistic model for discrete multidimensional domains. Mixtures-of-trees 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 mixtures-of-trees 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 tree-based classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.

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

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 super-class 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...

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,

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.

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.

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 knowledge-based 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 knowledge-based outlier analysis is a useful extension to existing work in both statistical and computing communities on outlier detection.

Abstract. In this paper we present a novel approach to modelling a manufacturing process that allows one to learn about causal mechanisms of manufacturing defects through a Process Modelling and Executable Bayesian Network (PMEBN). The method combines probabilistic reasoning with time dependent parameters which are of crucial interest to quality control in manufacturing environments. We demonstrate the concept through a case study of a caravan manufacturing line using inspection data. 1