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Using Path Diagrams as a Structural Equation Modelling Tool
, 1997
"... this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. There are a number of problems associated with structural equation modeling. These problems include: ..."
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Cited by 36 (8 self)
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this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. There are a number of problems associated with structural equation modeling. These problems include:
Learning linear cyclic causal models with latent variables. Submitted. Available online from the authors’ homepages
, 2012
"... Identifying causeeffect relationships between variables of interest is a central problem in science. Given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables. We provide a detailed description of the model family, full proofs of t ..."
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Identifying causeeffect relationships between variables of interest is a central problem in science. Given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables. We provide a detailed description of the model family, full proofs of the necessary and sufficient conditions for identifiability, a search algorithm that is complete, and a discussion of what can be done when the identifiability conditions are not satisfied. The algorithm is comprehensively tested in simulations, comparing it to competing algorithms in the literature. Furthermore, we adapt the procedure to the problem of cellular network inference, applying it to the biologically realistic data of the DREAM challenges. The paper provides a full theoretical foundation for the causal discovery procedure first presented by Eberhardt et al. (2010) and Hyttinen et al. (2010).
Discovering Cyclic Causal Models with Latent Variables: A General SATBased Procedure
"... We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent varia ..."
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We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns “unknown ” otherwise. Many existing constraintbased causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales. 1
Causal discovery for linear cyclic models with latent variables
"... We consider the problem of identifying the causal relationships among a set of variables in the presence of both feedback loops and unmeasured confounders. This is a challenging task which, for full identification, typically requires the use of randomized experiments. For linear systems, Eberhardt e ..."
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Cited by 5 (3 self)
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We consider the problem of identifying the causal relationships among a set of variables in the presence of both feedback loops and unmeasured confounders. This is a challenging task which, for full identification, typically requires the use of randomized experiments. For linear systems, Eberhardt et al (2010) recently provided a procedure for integrating data from several experiments, and gave a corresponding, but demanding, identifiability condition. In this paper we (i) characterize the underdetermination of the model when the identifiability condition is not fully satisfied, (ii) show that their algorithm is complete with regard to the search space and the assumptions, and (iii) extend the procedure to incorporate the common assumption of faithfulness, and any prior knowledge. The resulting method typically resolves much additional structure and often yields full identification with many fewer experiments. We demonstrate our procedure using simulated data, and apply it to the protein signaling dataset of Sachs et al (2005). 1
Reasoning about Independence in Probabilistic Models of Relational Data
, 2013
"... The rules of dseparation provide a theoretical and algorithmic framework for deriving conditional independence facts from model structure. However, this theory only applies to Bayesian networks. Many realworld systems are characterized by interacting heterogeneous entities and probabilistic depend ..."
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Cited by 4 (2 self)
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The rules of dseparation provide a theoretical and algorithmic framework for deriving conditional independence facts from model structure. However, this theory only applies to Bayesian networks. Many realworld systems are characterized by interacting heterogeneous entities and probabilistic dependencies that cross the boundaries of entities. Consequently, researchers have developed extensions to Bayesian networks that can represent these relational dependencies. We show that the theory of dseparation inaccurately infers conditional independence when applied directly to the structure of probabilistic models of relational data. We introduce relational dseparation, a theory for deriving conditional independence facts from relational models, and we provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering dseparation queries about relational models.
1Using Path Diagrams as a Structural Equation Modelling Tool
"... Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error ” ..."
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Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error ” or “disturbance ” terms), and an associated path
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, 2014
"... Computer Science To my wonderful children, Ella and Max. May you always reach the goals you set. Problems worthy of attack prove their worth by hitting back. —Piet Hein ACKNOWLEDGMENTS This thesis would not exist without the direction of my advisor, David Jensen. I have been incredibly fortunate to ..."
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Computer Science To my wonderful children, Ella and Max. May you always reach the goals you set. Problems worthy of attack prove their worth by hitting back. —Piet Hein ACKNOWLEDGMENTS This thesis would not exist without the direction of my advisor, David Jensen. I have been incredibly fortunate to have had the opportunity to work with David; he has time and again shown me (and many others) the path to being a successful scientist and researcher. David continually inspires me, and he has always provided me with support—both professionally and personally. He is truly the most influential teacher and mentor I’ve ever had. I am also grateful for the feedback I’ve received from my committee—Andrew Barto, Hanna Wallach, and Andrew Papachristos. I look forward to more feedback throughout my career. The students and staff (past and present) of the Knowledge Discovery Labora