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Automated Discovery of Linear Feedback Models 1 Thomas Richardson and Peter Spirtes

Summary: 1
Automated Discovery of Linear Feedback Models 1
Thomas Richardson and Peter Spirtes
1. Introduction
The introduction of statistical models represented by directed acyclic graphs (DAGs) has
proved fruitful in the construction of expert systems, in allowing efficient updating
algorithms that take advantage of conditional independence relations (Pearl, 1988,
Lauritzen et al. 1993), and in inferring causal structure from conditional independence
relations (Spirtes and Glymour, 1991, Spirtes, Glymour and Scheines, 1993, Pearl and
Verma, 1991, Cooper, 1992). As a framework for representing the combination of causal
and statistical hypotheses, DAG models have shed light on a number of issues in statistics
ranging from Simpson's Paradox to experimental design (Spirtes, Glymour and Scheines,
1993). The relations of DAGs with statistical constraints, and the equivalence and
distinguishability properties of DAG models, are now well understood, and their
characterization and computation involves three properties connecting graphical structure
and probability distributions: (i) a local directed Markov property, (ii) a global directed
Markov property, (iii) and factorizations of joint densities according to the structure of a
graph (Lauritizen, et al., 1990).
Recursive structural equation models are one kind of DAG model. However, non­


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Richardson, Thomas - Department of Statistics, University of Washington at Seattle


Collections: Mathematics