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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...
Learning Bayesian Networks from Data: An InformationTheory Based Approach
, 2001
"... This paper provides algorithms that use an informationtheoretic analysis to learn Bayesian network structures from data. Based on our threephase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional indepe ..."
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Cited by 126 (4 self)
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This paper provides algorithms that use an informationtheoretic analysis to learn Bayesian network structures from data. Based on our threephase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional independence (CI) tests in typical cases. We provide precise conditions that specify when these algorithms are guaranteed to be correct as well as empirical evidence (from real world applications and simulation tests) that demonstrates that these systems work efficiently and reliably in practice.
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 ..."
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Cited by 123 (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
Construction of Bayesian Network Structures From Data: A Brief Survey and an Efficient Algorithm
, 1995
"... Previous algorithms for the recovery of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required on ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches: CI tests ..."
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Cited by 83 (8 self)
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Previous algorithms for the recovery of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required on ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches: CI tests are used to generate an ordering on the nodes from the database, which is then used to recover the underlying Bayesian network structure using a nonCltestbased method. Results of the evaluation of the algorithm on a number of databases (e.g., ALARM, LED, and SOYBEAN) are presented. We also discuss some algorithm performance issues and open problems.
Graphical models and automatic speech recognition
 Mathematical Foundations of Speech and Language Processing
, 2003
"... Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recog ..."
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Cited by 77 (13 self)
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Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recognition techniques commonly used as part of a speech recognition system can be described by a graph – this includes Gaussian distributions, mixture models, decision trees, factor analysis, principle component analysis, linear discriminant analysis, and hidden Markov models. Moreover, this paper shows that many advanced models for speech recognition and language processing can also be simply described by a graph, including many at the acoustic, pronunciation, and languagemodeling levels. A number of speech recognition techniques born directly out of the graphicalmodels paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov modelbased speech recognition by improving structural discriminability. It also includes an example where a graph can be used to represent language model smoothing constraints. As will be seen, the space of models describable by a graph is quite large. A thorough exploration of this space should yield techniques that ultimately will supersede the hidden Markov model.
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 74 (5 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...
Learning Bayesian Networks from Data: An Efficient Approach Based on Information Theory
, 1997
"... This paper addresses the problem of learning Bayesian network structures from data by using an information theoretic dependency analysis approach. Based on our threephase construction mechanism, two efficient algorithms have been developed. One of our algorithms deals with a special case where the ..."
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Cited by 49 (0 self)
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This paper addresses the problem of learning Bayesian network structures from data by using an information theoretic dependency analysis approach. Based on our threephase construction mechanism, two efficient algorithms have been developed. One of our algorithms deals with a special case where the node ordering is given, the algorithm only require ) ( 2 N O CI tests and is correct given that the underlying model is DAGFaithful [Spirtes et. al., 1996]. The other algorithm deals with the general case and requires ) ( 4 N O conditional independence (CI) tests. It is correct given that the underlying model is monotone DAGFaithful (see Section 4.4). A system based on these algorithms has been developed and distributed through the Internet. The empirical results show that our approach is efficient and reliable. 1 Introduction The Bayesian network is a powerful knowledge representation and reasoning tool under conditions of uncertainty. A Bayesian network is a directed acyclic graph ...
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 45 (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...
When Can Association Graphs Admit A Causal Interpretation?
, 1993
"... This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal proce ..."
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Cited by 26 (5 self)
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This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal processes could be responsible for the observed independencies, and our procedures could then be used to elucidate the graphical structure common to these processes, so as to evaluate their compatibility against substantive knowledge of the domain. If we find that the observed pattern of independencies does not agree with any stepwise recursive process, then there are a number of different possibilities. For instance,  some weak dependencies could have been mistaken for independencies and led to the wrong omission of edges from the covariance or concentration graphs.  some of the observed linear dependencies reflect accidental cancellations or hide actual nonlinear relations, or  the process responsible for the data is nonrecursive, involving aggregated variables, simultenous reciprocal interactions, or mixtures of several causal processes. In order to recognize accidental independencies it would be helpful to conduct several longitudinal studies under slightly varying conditions. In such studies the covariances for the same set of variables is estimated under different conditions and the variations in the conditions would typically affect the numerical values of the parameters. But, if the data were generated by a causal process represented by some directed acyclic graph, then the basic structural properties reflected in the missing edges of that graph should remain unchanged. Under such assumptions, the pattern of independencies that is "implied" by the dag (see Definitio...