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24
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 739 (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.
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 172 (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...
A theory of causal learning in children: Causal maps and Bayes nets
 PSYCHOLOGICAL REVIEW
, 2004
"... The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events ..."
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Cited by 158 (33 self)
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The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4yearold children construct new causal maps and that their learning is consistent with the Bayes net formalism.
Scalable Techniques for Mining Causal Structures
 Data Mining and Knowledge Discovery
, 1998
"... Mining for association rules in market basket data has proved a fruitful area of research. Measures such as conditional probability (confidence) and correlation have been used to infer rules of the form "the existence of item A implies the existence of item B." However, such rules indicate only a st ..."
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Cited by 89 (1 self)
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Mining for association rules in market basket data has proved a fruitful area of research. Measures such as conditional probability (confidence) and correlation have been used to infer rules of the form "the existence of item A implies the existence of item B." However, such rules indicate only a statistical relationship between A and B. They do not specify the nature of the relationship: whether the presence of A causes the presence of B, or the converse, or some other attribute or phenomenon causes both to appear together. In applications, knowing such causal relationships is extremely useful for enhancing understanding and effecting change. While distinguishing causality from correlation is a truly difficult problem, recent work in statistics and Bayesian learning provide some avenues of attack. In these fields, the goal has generally been to learn complete causal models, which are essentially impossible to learn in largescale data mining applications with a large number of variab...
A Bayesian Approach to Causal Discovery
, 1997
"... We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that t ..."
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Cited by 80 (1 self)
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We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that the constraintbased approach uses categorical information about conditionalindependence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraintbased counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of finite size. Two, using the Bayesian approach, finer distinctions among model structuresboth quantitative and qualitativecan be made. Three, information from several models can be combined to make better inferences and to better ...
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 46 (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...
Statistical Themes and Lessons for Data Mining
, 1997
"... Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statist ..."
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Cited by 32 (3 self)
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Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.
Statistical Inference and Data Mining
, 1996
"... es of probability distributions, estimation, hypothesis testing, model scoring, Gibb's sampling, rational decision making, causal inference, prediction, and model averaging. For a rigorous survey of statistics, the mathematically inclined reader should see [7]. Due to space limitations, we ..."
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Cited by 22 (3 self)
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es of probability distributions, estimation, hypothesis testing, model scoring, Gibb's sampling, rational decision making, causal inference, prediction, and model averaging. For a rigorous survey of statistics, the mathematically inclined reader should see [7]. Due to space limitations, we must also ignore a number of interesting topics, including time series analysis and metaanalysis. Probability Distributions The statistical literature contains mathematical characterizations of a wealth of probability distributions, as well as properties of random variablesfunctions defined on the "events" to which a probability measure assigns values. Important relations among probability distributions include marginalization (summing over a subset of values) and conditionalization (forming a conditional probability measure from a probability measure on a sample space and some event of positive probability. Essential relations among random variable
The TETRAD Project: Constraint Based Aids to Causal Model Specification
 MULTIVARIATE BEHAVIORAL RESEARCH
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A Bayesian Method for Causal Modeling and Discovery Under Selection
, 2000
"... This paper describes a Bayesian method for learning causal networks using samples that were selected in a nonrandom manner from a population of interest. Examples of data obtained by nonrandom sampling include convenience samples and casecontrol data in which a fixed number of samples with and wi ..."
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Cited by 10 (2 self)
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This paper describes a Bayesian method for learning causal networks using samples that were selected in a nonrandom manner from a population of interest. Examples of data obtained by nonrandom sampling include convenience samples and casecontrol data in which a fixed number of samples with and without some condition is collected; such data are not uncommon. The paper describes a method for combining data under selection with prior beliefs in order to derive a posterior probability for a model of the causal processes that are generating the data in the population of interest. The priors include beliefs about the nature of the nonrandom sampling procedure. Although exact application of the method would be computationally intractable for most realistic datasets, efficient specialcase and approximation methods are discussed. Finally, the paper describes how to combine learning under selection with previous methods for learning from observational and experimental data that are obtained...