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13
ANCESTRAL GRAPH MARKOV MODELS
, 2002
"... This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of verti ..."
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Cited by 115 (22 self)
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This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.
Causal Inference from Graphical Models
, 2001
"... Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling ..."
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Cited by 77 (6 self)
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Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,
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 64 (6 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...
Caveats for Causal Reasoning with Equilibrium Models
, 2003
"... Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recur ..."
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Cited by 10 (3 self)
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Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recursive equilibrium models that violate the Manipulation Postulate. We relate this class to the existing phenomenon of reversibility and show that all models in F display reversible behavior, thereby providing an explanation for reversibility and suggesting that it is a special case of a more general and perhaps widespread problem. We also show that all models in F possess a set of variables V ′ whose manipulation will cause an instability such that no equilibrium model will exist for the system. We define the Structural Stability Principle which provides a graphical criterion for stability in causal models. Our theorems suggest that drastically incorrect inferences may be obtained when applying the Manipulation Postulate to equilibrium models, a result which has implications for current work on causal modeling, especially causal discovery from data. 1
Causal Inference and Reasoning in Causally Insufficient Systems
, 2006
"... The big question that motivates this dissertation is the following: under what conditions and to what extent can passive observations inform us of the structure of causal connections among a set of variables and of the potential outcome of an active intervention on some of the variables? The partic ..."
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Cited by 10 (2 self)
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The big question that motivates this dissertation is the following: under what conditions and to what extent can passive observations inform us of the structure of causal connections among a set of variables and of the potential outcome of an active intervention on some of the variables? The particular concern here revolves around the common kind of situations where the variables of interest, though measurable themselves, may suffer from confounding due to unobserved common causes. Relying on a graphical representation of causally insufficient systems called maximal ancestral graphs, and two wellknown principles widely discussed in the literature, the causal Markov and Faithfulness conditions, we show that the FCI algorithm, a sound inference procedure in the literature for inferring features of the unknown causal structure from facts of probabilistic independence and dependence, is, with some extra sound inference rules, also complete in the sense that any feature of the causal structure left undecided by the inference procedure is indeed underdetermined by facts of probabilistic independence and dependence. In addition, we consider the issue of quantitative reasoning about effects of local interventions with the FCIlearnable features of the unknown causal structure. We improve and generalize two important pieces of work in the literature about identifying intervention effects. We also provide some preliminary study of the testability of the
Constructing Variables that Support Causal Inference
, 2013
"... to many individuals. David Danks has been an ideal adviser and dissertation committee cochair. Despite a busy schedule and many advisees, he always found time to read drafts and provide careful feedback. His understanding ear and sage advice (both personal and professional) I value immensely. Thank ..."
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Cited by 2 (2 self)
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to many individuals. David Danks has been an ideal adviser and dissertation committee cochair. Despite a busy schedule and many advisees, he always found time to read drafts and provide careful feedback. His understanding ear and sage advice (both personal and professional) I value immensely. Thank you. Richard Scheines, my other cochair, provided the intellectual inspiration for much of this work. His longstanding interests in applied causal inference and matters of variable construction and definition in the social sciences led him to ask challenging questions, seriously improving this work. My committee members have provided guidance and inspiration in a variety of ways. Daniel Neill, some time ago, stimulated my interest in developing interpretable models for predictive and causal inference that might prove useful for realworld policymakers. Partha Saha and Steven Ritter, in different settings and over the course of several years, have demonstrated that the type of questions we ask in this work are important in real educa
Limitations of Statistical Learning from Gene Expression Data Abstract
"... Current technologies for measuring gene expression levels, such as microarray and SAGE, measure the summed expression levels of the genes from a large aggregate of cells, rather than the expression levels of the genes in an individual cell. This paper discusses, from the statistical point of view, w ..."
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Cited by 1 (1 self)
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Current technologies for measuring gene expression levels, such as microarray and SAGE, measure the summed expression levels of the genes from a large aggregate of cells, rather than the expression levels of the genes in an individual cell. This paper discusses, from the statistical point of view, what we could learn, both in principle and in practice, from the microarray and SAGE gene expression level data. We show that, when the summed gene expression levels are measured from a large number of cells, the conditional independence relations among the summed gene expression levels are essentially determined by the correlation matrix among the gene expression levels, and are very unlikely to be the same as the conditional independence relations among the expression levels of the genes in an individual cell. This suggests that any algorithm for learning the gene regulatory network based on the conditional independence relations among the expression levels of the genes would not work with the data generated by the current technologies. Furthermore, we show that, in practice, we probably could not even get an accurate estimation of the correlation matrix of the gene expression levels, for the number of experiments required to estimate the correlation matrix is too large to be feasible. Therefore, the only piece of information we can learn reliably from the current gene expression level data is the expected gene expression levels. 1
Osaka University
"... When observational data is available from practical studies and a directed cyclic graph for how various variables affect each other is known based on substantive understanding of the process, we consider a problem in which a control plan of a treatment variable is conducted in order to bring a res ..."
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When observational data is available from practical studies and a directed cyclic graph for how various variables affect each other is known based on substantive understanding of the process, we consider a problem in which a control plan of a treatment variable is conducted in order to bring a response variable close to a target value with variation reduction. We formulate an optimal control plan concerning a certain treatment variable through path coefficients in the framework of linear nonrecursive structural equation models. Based on the formulation, we clarify the properties of causal effects when conducting a control plan. The results enable us to evaluate the effect of a control plan on the variance from observational data. 1