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23
Model selection and accounting for model uncertainty in graphical models using Occam's window
, 1993
"... We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues leading to the selection o ..."
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Cited by 270 (46 self)
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We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues leading to the selection of a single model; inference is then conditional on the selected model. The sampling properties of such a strategy are complex, and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest. In principle, a panacea is provided by the standard Bayesian formalism which averages the posterior distributions of the quantity of interest under each of the models, weighted by their posterior model probabilities. Furthermore, this approach is optimal in the sense of maximising predictive ability. However, this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large (often greater than 1011). We argue that the standard Bayesian formalism is unsatisfactory and we propose an alternative Bayesian approach that, we contend, takes full account of the true model uncertainty byaveraging overamuch smaller set of models. An efficient search algorithm is developed for nding these models. We consider two classes of graphical models that arise in expert systems: the recursive causal models and the decomposable
Sequential Model Selection for Word Sense Disambiguation
, 1997
"... Statistical models of wordsense disam biguation are often based on a small num ber of contextual features or on a model that is assumed to characterize the inter actions among a set of features. Model selection is presented as an alternative to these approaches, where a sequential search ..."
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Cited by 28 (13 self)
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Statistical models of wordsense disam biguation are often based on a small num ber of contextual features or on a model that is assumed to characterize the inter actions among a set of features. Model selection is presented as an alternative to these approaches, where a sequential search of possible models is conducted in order to find the model that best characterizes the interactions among features. This paper expands existing model selection methodology and presents the first comparative study of model selection search strategies and evaluation criteria when applied to the problem of building probabilistic classifiers for wordsense disambiguation.
Significant lexical relationships
 Proceedings of the 13th National Conference on Artificial Intelligence (AAAI96
, 1996
"... Statistical NLP inevitably deals with a large number of rare events. As a consequence, NLP data often violates the assumptions implicit in traditional statistical procedures such as significance testing. We describe a significance test, an exact conditional test, that is appropriate for NLP data and ..."
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Cited by 26 (16 self)
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Statistical NLP inevitably deals with a large number of rare events. As a consequence, NLP data often violates the assumptions implicit in traditional statistical procedures such as significance testing. We describe a significance test, an exact conditional test, that is appropriate for NLP data and can be performed using freely available software. We apply this test to the study of lexical relationships and demonstrate that the results obtained using this test are both theoretically more reliable and different from the results obtained using previously applied tests.
Multiple testing and error control in Gaussian graphical model selection
 Statistical Science
"... Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of cond ..."
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Cited by 12 (2 self)
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Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables ’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion. Key words and phrases: Acyclic directed graph, Bayesian network, bidirected graph, chain graph, concentration graph, covariance graph, DAG, graphical model, multiple testing, undirected graph. 1.
Graphical models for inference under outcomedependent sampling
 STAT SCI 2010;25:368–87
, 2010
"... We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in casecontrol studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a no ..."
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Cited by 3 (0 self)
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We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in casecontrol studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be made explicit. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples.
Simulate and Reject Monte Carlo Exact Conditional Tests for Quasiindependence
 In Proceedings of COMPSTAT
, 1994
"... this paper, we propose improvements to a naive simulate and reject procedure for generating r \Theta c tables under quasiindependence for an arbitrary pattern of fixed cells. Although some of the algorithmic improvements are described for generating under QI for the offdiagonal cells of a square t ..."
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Cited by 3 (1 self)
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this paper, we propose improvements to a naive simulate and reject procedure for generating r \Theta c tables under quasiindependence for an arbitrary pattern of fixed cells. Although some of the algorithmic improvements are described for generating under QI for the offdiagonal cells of a square table, the ideas are applicable to other patterns of fixed cells. Apart from complete enumeration, which is only viable for small tables, the simulate and reject procedure is currently the only method for generating independent tables from the exact null distribution under QI. Our improvements to the naive procedure greatly increase its efficiency. Smith, McDonald and Forster (1994) discuss another method for generating tables under QI using a Gibbs sampling approach, based on theoretical results in Forster, McDonald and Smith (1994). However, the generated tables are not necessarily independent and are only realizations from an approximation to the exact null distribution. When using a single Markov chain, the observed table is the obvious starting value. For multiple chains, obtaining other starting values with the same sufficient statistics for the nuisance parameters as the observed data is problematic. A possible solution is to generate a small number of independent starting values using the simulate and reject algorithms proposed. Acknowledgements
GraphFitI – A computer program for graphical chain models
"... Fitting a graphical chain model to a multivariate data set consists of different steps some of which being rather tedious. The paper outlines the basic features and overall architecture of the computer program GraphFitI which provides the application of a selection strategy for fitting graphical cha ..."
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Cited by 1 (0 self)
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Fitting a graphical chain model to a multivariate data set consists of different steps some of which being rather tedious. The paper outlines the basic features and overall architecture of the computer program GraphFitI which provides the application of a selection strategy for fitting graphical chain models and for visualising the resulting models as a graph. It additionally supports the user at the different steps of the analysis by an integrated help system. Acknowledgements Financial support by the SFB 386, Deutsche Forschungsgemeinschaft is gratefully acknowledged.
Monte Carlo Exact Conditional Tests for Quasiindependence using Gibbs Sampling
, 1994
"... this paper, is the hypothesis of QI for the offdiagonal cells of a r \Theta r square table, where the sufficient statistics for the nuisance parameters are x i+ ; x +j and x ii , for i; j = 1; : : : ; r. ..."
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Cited by 1 (1 self)
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this paper, is the hypothesis of QI for the offdiagonal cells of a r \Theta r square table, where the sufficient statistics for the nuisance parameters are x i+ ; x +j and x ii , for i; j = 1; : : : ; r.