Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models

Dawid, A. P.; Lauritzen, Steffen

doi:10.1214/aos/1176349260

Cited by 385 publications

(469 citation statements)

References 27 publications

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“…The set of nodes in the flow graph are {c 1 In order to combine the collection of binary flow graphs into a general flow graph, Pawlak makes the flow conservation assumption [6]. This assumption means that the normalized decision tables are pairwise consistent [2,13]. Figure 3 is the DAG in Figure 6 together with the appropriate strength, certainty and coverage coefficients in Figure 5.…”

Section: Rough Set Flow Graphsmentioning

confidence: 99%

The Computational Complexity of Inference Using Rough Set Flow Graphs

Butz

Yan

Yang

2005

Lecture Notes in Computer Science

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Abstract. Pawlak recently introduced rough set flow graphs (RSFGs) as a graphical framework for reasoning from data. Each rule is associated with three coefficients, which have been shown to satisfy Bayes' theorem. Thereby, RSFGs provide a new perspective on Bayesian inference methodology. In this paper, we show that inference in RSFGs takes polynomial time with respect to the largest domain of the variables in the decision tables. Thereby, RSFGs provide an efficient tool for uncertainty management. On the other hand, our analysis also indicates that a RSFG is a special case of conventional Bayesian network and that RSFGs make implicit assumptions regarding the problem domain.

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Section: Rough Set Flow Graphsmentioning

confidence: 99%

The Computational Complexity of Inference Using Rough Set Flow Graphs

Butz

Yan

Yang

2005

Lecture Notes in Computer Science

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“…Lam & Bacchus (1994) applied a minimal description length (MDL) method to learning a BN. Dawid and Lauritzen (1993) studied 'hyper Markov laws' in learning numerical parameters of a DMN with a given decomposable graph. Madigan and Raftery (1994) proposed algorithms for learning a set of acceptable models expressed as BNs or DMNs.…”

Section: Algorithmmentioning

confidence: 99%

Learning decomposable markov networks in pseudo-independent domains with local evaluation

Xiang

Lee

2006

Mach Learn

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We consider learning probabilistic graphical models in a problem domain of unknown dependence structure. Common learning algorithms rely on single-link lookahead search, which assumes the underlying domain is not pseudo-independent. Since the dependence structure of the domain is unknown, such assumption is fallible. We study learning algorithms that make no such assumption and return an approximate dependence structure no matter whether the domain is pseudo-independent or not. The focus of this paper is on learning decomposable Markov networks, which can directly be used for model-based inference or as the intermediate step for further learning of directed graphical models. We identify a small subset of domain variables, termed crux, in the graphical models currently being examined during search. We prove that crux is sufficient for computing the incremental change of both model description length as well as data description length given the model. Based on crux, we propose algorithms that reduce evaluation of alternative graphical models to local computation, improve efficiency significantly, and introduce no error to the selection of alternative models.

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“…On the other hand, the marginal likelihood estimator for UDG models was given by Dawid and Lauritzen (1993), and has the form:…”

Section: Bayesian Graphical Model Scoringmentioning

confidence: 99%

“…For any given clique or separator Q, the computation of H (Q) is as follows (Dawid & Lauritzen, 1993):…”

Section: Bayesian Graphical Model Scoringmentioning

confidence: 99%

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Untitled

2003

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Abstract. The motivation of this paper is the application of MCMC model scoring procedures to data mining problems, involving a large number of competing models and other relevant model choice aspects.To achieve this aim we analyze one of the most popular Markov Chain Monte Carlo methods for structural learning in graphical models, namely, the MC 3 algorithm proposed by D. Madigan and J. York (International Statistical Review, 63, 215-232, 1995). Our aim is to improve their algorithm to make it an effective and reliable tool in the field of data mining. In such context, typically highly dimensional in the number of variables, little can be known a priori and, therefore, a good model search algorithm is crucial.We present and describe in detail our implementation of the MC 3 algorithm, which provides an efficient general framework for computations with both Directed Acyclic Graphical (DAG) models and Undirected Decomposable Models (UDG). We believe that the possibility of commuting easily between the two classes of models constitutes an important asset in data mining, where an a priori knowledge of causal effects is usually difficult to establish.Furthermore, in order to improve the MC 3 method we propose provide several graphical monitors which can help extracting results and assessing the goodness of the Markov chain Monte Carlo approximation to the posterior distribution of interest.We apply our proposed methodology first to the well-known coronary heart disease dataset (D. Edwards & T. Havránek, Biometrika, 72:2, 339-351, 1985). We then introduce a novel data mining application which concerns market basket analysis.

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Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models

Cited by 385 publications

References 27 publications

The Computational Complexity of Inference Using Rough Set Flow Graphs

The Computational Complexity of Inference Using Rough Set Flow Graphs

Learning decomposable markov networks in pseudo-independent domains with local evaluation

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