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59
A new algorithm for maximum likelihood estimation in Gaussian graphical models for marginal independence
 In U. Kjærulff and C. Meek (Eds.), Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence
, 2003
"... Graphical models with bidirected edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian ..."
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Cited by 18 (8 self)
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Graphical models with bidirected edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorithm which exploits standard regression techniques and establish its convergence properties. Moreover, we contrast our procedure to existing estimation algorithms. 1
Aspects Of Graphical Models Connected With Causality
, 1993
"... This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphica ..."
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Cited by 18 (9 self)
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This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. We first review the Markovian account of causation and show that directed acyclic graphs (DAGs) offer an economical scheme for representing conditional independence assumptions and for deducing and displaying all the logical consequences of such assumptions. We then introduce the manipulative account of causation and show that any DAG defines a simple transformation which tells us how the probability distribution will change as a result of external interventions in the system. Using this transformation it is possible to quantify, from nonexperimental data...
Convolutional factor graphs as probabilistic models
 In Proc. UAI
, 2004
"... Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred to as multiplicative factor graphs (MFGs). This paper sho ..."
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Cited by 16 (4 self)
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Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred to as multiplicative factor graphs (MFGs). This paper shows that CFGs are natural models for probability functions when summation of independent latent random variables is involved. In particular, CFGs capture a large class of linear models, where the linearity is in the sense that the observed variables are obtained as a linear transformation of the latent variables taking arbitrary distributions. We use Gaussian models and independent factor models as examples to demonstrate the use of CFGs. The requirement of a linear transformation between latent variables (with certain independence restriction) and the observed variables, to an extent, limits the modelling flexibility of CFGs. This structural restriction however provides a powerful analytic tool to the framework of CFGs; that is, upon taking the Fourier transform of the function represented by the CFG, the resulting function is represented by a MFG with identical structure. This Fourier transform duality allows inference problems on a CFG to be solved on the corresponding dual MFG. 1
Graphical Models for Multivariate Time Series from Intensive Care Monitoring
, 2000
"... In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial assoc ..."
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Cited by 15 (3 self)
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In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial associations between the components of multivariate time series. We apply this technique to the hemodynamic system of critically ill patients monitored in intensive care. We appraise the practical value of the procedure by reidentifying known associations between the variables. From separate analyses for different pathophysiological states we conclude that distinct clinical states can be characterised by distinct partial correlation structures.
Statistics and Causal Inference: A Review
, 2003
"... This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assump ..."
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Cited by 15 (6 self)
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This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.
Causal Inference in the Health Sciences: A Conceptual Introduction
 Health Services and Outcomes Research Methodology
, 2001
"... This paper provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivari ..."
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Cited by 14 (0 self)
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This paper provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underlie all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, corrections for noncompliance, and a symbiosis between counterfactual and graphical methods of analysis.
The Foundations of Causal Inference
 SUBMITTED TO SOCIOLOGICAL METHODOLOGY.
, 2010
"... This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of ..."
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Cited by 12 (5 self)
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This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 195060s, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring the effects of potential interventions (also called “causal effects” or “policy evaluation”), as well as direct and indirect effects (also known as “mediation”), in both linear and nonlinear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and
Term Dependence: A Basis for Luhn and Zipf Models
, 2001
"... There are regularities in the statistical information provided by natural language terms about neighboring terms. We find that when phrase rank increases, moving from common to less common phrases, the value of the expected mutual information measure (EMIM) between the terms regularly decreases. ..."
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Cited by 10 (1 self)
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There are regularities in the statistical information provided by natural language terms about neighboring terms. We find that when phrase rank increases, moving from common to less common phrases, the value of the expected mutual information measure (EMIM) between the terms regularly decreases. Luhn's model suggests that midrange terms are the best index terms and relevance discriminators. We suggest reasons for this principle based on the empirical relationships shown here between the rank of terms within phrases and the average mutual information between terms, which we refer to as the Inverse RepresentationEMIM principle. We also suggest an
Markov Properties for Linear Causal Models with Correlated Errors
"... A linear causal model with correlated errors, represented by a DAG with bidirected edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the dseparation criterion, the set of all conditional independence relations holding ..."
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Cited by 8 (1 self)
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A linear causal model with correlated errors, represented by a DAG with bidirected edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the dseparation criterion, the set of all conditional independence relations holding in any model associated with a graph. A local Markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global Markov property. For DAGs with bidirected edges associated with arbitrary probability distributions, a local Markov property is given in Richardson (2003) which may invoke an exponential number of conditional independencies. In this paper, we show that for a class of linear structural equation models with correlated errors the local Markov property will invoke only linear number of conditional independence relations. For general linear models, we provide a local Markov property that often invokes far fewer conditional independencies than that in Richardson (2003). The results have applications in testing linear structural equation models with correlated errors.