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10
Using Bayesian networks to analyze expression data
 Journal of Computational Biology
, 2000
"... DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biologica ..."
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Cited by 731 (16 self)
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DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graphbased model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cellcycle measurements of Spellman et al. (1998). Key words: gene expression, microarrays, Bayesian methods. 1.
Being Bayesian about network structure
 Machine Learning
, 2000
"... Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model sel ..."
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Cited by 202 (5 self)
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Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have nonnegligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and reallife datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a nonBayesian bootstrap approach.
Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 132 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
Variational inference for Dirichlet process mixtures
 Bayesian Analysis
, 2005
"... Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of MonteCarlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis prob ..."
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Cited by 128 (16 self)
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Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of MonteCarlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to explore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, variational methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a largescale image analysis problem.
Chain Graph Models and their Causal Interpretations
 B
, 2001
"... Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultim ..."
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Cited by 48 (4 self)
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Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...
Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models
, 1998
"... We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of p ..."
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Cited by 28 (7 self)
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We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decisiontheoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...
Sampling in Factored Dynamic Systems
 Sequential Monte Carlo Methods in Practice
, 2000
"... this paper, we have examined this issue in the context of two realistic systems  one discrete and one hybrid. Our results indicate that particle filters are surprisingly robust, even for complex systems. Nevertheless, we feel that the curse of dimensionality that plagues instancebased methods is ..."
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Cited by 24 (0 self)
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this paper, we have examined this issue in the context of two realistic systems  one discrete and one hybrid. Our results indicate that particle filters are surprisingly robust, even for complex systems. Nevertheless, we feel that the curse of dimensionality that plagues instancebased methods is also an issue for particle filtering in highdimensional spaces. Therefore, we are currently exploring approaches that address this concern. Two ideas seem particularly useful in this setting:
Learning Naive Bayes Classifier from Noisy Data
, 2003
"... Classification is one of the major tasks in knowledge discovery and data mining. Naive Bayes classifier, in spite of its simplicity, has proven surprisingly effective in many practical applications. In real datasets, noise is inevitable, because of the imprecision of measurement or privacy preservin ..."
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Cited by 4 (0 self)
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Classification is one of the major tasks in knowledge discovery and data mining. Naive Bayes classifier, in spite of its simplicity, has proven surprisingly effective in many practical applications. In real datasets, noise is inevitable, because of the imprecision of measurement or privacy preserving mechanisms. In this paper, we develop a new approach, LinEarEquationbased noiseaWare bAYes classifier (LEEWAY), for learning the underlying naive Bayes classifier from noisy observations. Using
Comparing Institutional Performance using Markov chain Monte Carlo Methods
, 1999
"... There has been a growing interest over recent years in the use of performance indicators in healthcare, which may measure aspects of the process of care, clinical outcomes or the incidence of disease (NHS Executive, 1995; Scottish Office, 1995; New York State Department of Health, 1996). In respo ..."
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Cited by 2 (0 self)
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There has been a growing interest over recent years in the use of performance indicators in healthcare, which may measure aspects of the process of care, clinical outcomes or the incidence of disease (NHS Executive, 1995; Scottish Office, 1995; New York State Department of Health, 1996). In response a sizeable literature has emerged questioning the very use of such indicators as a measure of 'quality of care', as well as stating more specific criticisms of the statistical methods used to obtain estimates adjusted for patient casemix (DuBois et al., 1987; Jencks et al., 1988; Epstein, 1995; Schneider and Epstein, 1996). We do not attempt to further this general discussion of performance indicators and risk adjustment  see, for example (Goldstein and Spiegelhalter, 1996). Rather, the purpose of this chapter is to highlight how recent developments in computerintensive methods can be used to explore a wide range of plausible statisti
Modelbased Clustering with Noise: Bayesian Inference and Estimation
 Journal of Classification
, 2003
"... Bensmail, Celeux, Raftery and Robert (1997) introduced a new approach to cluster analysis based on geometric modeling based on the withingroup covariance in a mixture of multivariate normal distributions using a fully Bayesian framework. This is a modelbased methodology, where the covariance matri ..."
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Cited by 2 (0 self)
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Bensmail, Celeux, Raftery and Robert (1997) introduced a new approach to cluster analysis based on geometric modeling based on the withingroup covariance in a mixture of multivariate normal distributions using a fully Bayesian framework. This is a modelbased methodology, where the covariance matrix structure is involved. Previously, similar structures were used (using a maximum likelihood approach) by Banfield and Raftery (1993) for clustering data where they restricted some parameters of the covariance matrix structure to be known. In the same framework, Dasgupta and Raftery (1998) used the same reparameterization to detect the features in a spatial point process using maximum likelihood approach. These approaches work well, but they have some limitations. These limitations include the fact that not all covariance structures were considered and some parameters of the covariance structures were fixed. This paper proposes a new way of overcoming the existing limitations. It generalizes the model used in the the previous approaches by introducing a more comprehensive portfolio of covariance matrix structures. Further, this paper proposes a Bayesian solution in the presence of the noise in clustering problems. The performance of the proposed method is first