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  1. Thomas Richardson, Automated Discovery of Linear Feedback Models.
    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 (...)
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  2. Thomas Richardson & Peter Spirtes, Ancestral Graph Markov Models.
    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.
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  3. Peter Spirtes, Christopher Meek & Thomas Richardson, Causal Inference in the Presence of Latent Variables and Selection Bias.
    Whenever the use of non-experimental data for discovering causal relations or predicting the outcomes of experiments or interventions is contemplated, two difficulties are routinely faced. One is the problem of latent variables, or confounders: factors influencing two or more measured variables may not themselves have been measured or recorded. The other is the problem of sample selection bias: values of the variables or features under study may themselves influence whether a unit is included in the data sample.
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  4. Peter Spirtes, Thomas Richardson, Chris Meek & Richard Scheines, Using 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” or “disturbance” terms), and an associated path diagram corresponding to the functional composition of variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram is (...)
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  5. Peter Spirtes, Thomas Richardson, Christopher Meek, Richard Scheines & Clark Glymour, Using D-Separation to Calculate Zero Partial Correlations in Linear Models with Correlated Errors.
    It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how (...)
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  6. Thomas Richardson, Laura Schulz & Alison Gopnik (2007). Data-Mining Probabilists or Experimental Determinists. In Alison Gopnik & Laura Schulz (eds.), Causal Learning: Psychology, Philosophy, and Computation. Oxford University Press. 208--230.
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  7. Thomas Richardson & Peter Spirtes, Parameterizing and Scoring Mixed Ancestral Graphs.
    Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.
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  8. Thomas Richardson & Peter Spirtes, Scoring Ancestral Graph Models.
    Thomas Richardson and Peter Spirtes. Scoring Ancestral Graph Models.
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  9. Gregory F. Cooper, Constantin F. Aliferis, Richard Ambrosino, John Aronis, Bruce G. Buchanon, Richard Caruana, Michael J. Fine, Clark Glymour, Geoffrey Gordon, Barbara H. Hanusa, Janine E. Janosky, Christopher Meek, Tom Mitchell, Thomas Richardson & Peter Spirtes, An Evaluation of Machine-Learning Methods for Predicting Pneumonia Mortality.
    This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist (...)
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