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  1. Kevin Kelly & Peter Spirtes, The Expected Complexity of Problem Solving.
    Worst case complexity analyses of algorithms are sometimes held to be less informative about the real difficulty of computation than are expected complexity analyses. We show that the two most common representations of problem solving in cognitive science each admit aigorithms that have constant expected complexity, and for one of these representations we obtain constant expected complexity bounds under a variety of probability measures.
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  2. Joseph Ramsey, Peter Spirtes & Clark Glymour, Automated Remote Sensing with Near Infrared Reflectance Spectra: Carbonate Recognition.
    Reflectance spectroscopy is a standard tool for studying the mineral composition of rock and soil samples and for remote sensing of terrestrial and extraterrestrial surfaces. We describe research on automated methods of mineral identification from reflectance spectra and give evidence that a simple algorithm, adapted from a well-known search procedure for Bayes nets, identifies the most frequently occurring classes of carbonates with reliability equal to or greater than that of human experts. We compare the reliability of the procedure to the (...)
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  3. 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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  4. Richard Scheines & Peter Spirtes, Uniform Consistency in Causal Inference.
    S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...)
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  5. Richard Scheines, Peter Spirtes & Clark Glymour, Building Latent Variable Models'.
    Researchers routinely face the problem of inferring causal relationships from large amounts of data, sometimes involving hundreds of variables. Often, it is the causal relationships between "latent" (unmeasured) variables that are of primary interest. The problem is how causal relationships between unmeasured variables can be inferred from measured data. For example, naval manpower researchers have been asked to infer the causal relations among psychological traits such as job satisfaction and job challenge from a data base in which neither trait is (...)
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  6. Peter Spirtes, An Anytime Algorithm for Causal Inference.
    The Fast Casual Inference (FCI) algorithm searches for features common to observationally equivalent sets of causal directed acyclic graphs. It is correct in the large sample limit with probability one even if there is a possibility of hidden variables and selection bias. In the worst case, the number of conditional independence tests performed by the algorithm grows exponentially with the number of variables in the data set. This affects both the speed of the algorithm and the accuracy of the algorithm (...)
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  7. Peter Spirtes, An Algorithm for Fast Recovery of Sparse Causal Graphs.
    Previous asymptotically correct algorithms for recovering causal structure from sample probabilities have been limited even in sparse graphs to a few variables. We describe an asymptotically correct algorithm whose complexity for fixed graph connectivity increases polynomially in the number of vertices, and may in practice recover sparse graphs with several hundred variables. From..
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  8. Peter Spirtes, A Polynomial Time Algorithm for Determining Dag Equivalence in the Presence of Latent Variables and Selection Bias.
    if and only if for every W in V, W is independent of the set of all its non-descendants conditional on the set of its parents. One natural question that arises with respect to DAGs is when two DAGs are “statistically equivalent”. One interesting sense of “statistical equivalence” is “d-separation equivalence” (explained in more detail below.) In the case of DAGs, d-separation equivalence is also corresponds to a variety of other natural senses of statistical equivalence (such as representing the same (...)
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  9. Peter Spirtes, Heuristic Greedy Search Algorithms for Latent Variable Models.
    A Bayesian network consists of two distinct parts: a directed acyclic graph (DAG or belief-network structure) and a set of parameters for the DAG. The DAG in a Bayesian network can be used to represent both causal hypotheses and sets of probability distributions. Under the causal interpretation, a DAG represents the causal relations in a given population with a set of vertices V when there is an edge from A to B if and only if A is a direct cause (...)
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  10. Peter Spirtes, The Limits of Causal Inference From Observational Data.
    The following quotation from Rosenbaum (1995) expresses a commonly held view about the problem of potential confounders, and how they can be dealt with. (We will take a “confounder” of treatment and response to be a variable that is a cause of both treatment and response.).
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  11. Peter Spirtes & Clark Glymour, Automated Remote Sensing with Near Infrared Reflectance Spectra: Carbonate Recognition.
    Reflectance spectroscopy is a standard tool for studying the mineral composition of rock and soil samples and for remote sensing of terrestrial and extraterrestrial surfaces. We describe research on automated methods of mineral identification from reflectance spectra and give evidence that a simple algorithm, adapted from a well-known search procedure for Bayes nets, identifies the most frequently occurring classes of carbonates with reliability equal to or greater than that of human experts. We compare the reliability of the procedure to the (...)
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  12. Peter Spirtes & Clark Glymour, With Unmeasured Variables.
    In recent papers we have described a framework for inferring causal structure from relations of statistical independence among a set of measured variables. Using Pearl's notion of the perfect representation of a set of independence relations by a directed acyclic graph we proved..
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  13. Peter Spirtes, Clark Glymour & Richard Scheines, Causality From Probability.
    Data analysis that merely fits an empirical covariance matrix or that finds the best least squares linear estimator of a variable is not of itself a reliable guide to judgements about policy, which inevitably involve causal conclusions. The policy implications of empirical data can be completely reversed by alternative hypotheses about the causal relations of variables, and the estimates of a particular causal influence can be radically altered by changes in the assumptions made about other dependencies.2 For these reasons, one (...)
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  14. 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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  15. 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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  16. 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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  17. Jiji Zhang & Peter Spirtes, A Transformational Characterization of Markov Equivalence for Directed Maximal Ancestral Graphs.
    The conditional independence relations present in a data set usually admit multiple causal explanations — typically represented by directed graphs — which are Markov equivalent in that they entail the same conditional independence relations among the observed variables. Markov equivalence between directed acyclic graphs (DAGs) has been characterized in various ways, each of which has been found useful for certain purposes. In particular, Chickering’s transformational characterization is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is (...)
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  18. Richard Scheines, Clark Glymour & Peter Spirtes, Learning the Structure of Linear Latent Variable Models.
    We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...)
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  19. 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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  20. Peter Spirtes, Learning the Structure of Linear Latent Variable Models.
    We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...)
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  21. Peter Spirtes, Uniform Consistency in Causal Inference.
    There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results are (...)
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  22. Peter Spirtes, Variable Definition and Causal Inference.
    In the last several decades, a confluence of work in the social sciences, philosophy, statistics, and computer science has developed a theory of causal inference using directed graphs. This theory typically rests either explicitly or implicitly on two major assumptions.
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  23. Peter Spirtes, Clark Glymour & Richard Scheines, Automated Search for Causal Relations - Theory and Practice.
    nature of modern data collection and storage techniques, and the increases in the speed and storage capacities of computers. Statistics books from 30 years ago often presented examples with fewer than 10 variables, in domains where some background knowledge was plausible. In contrast, in new domains, such as climate research where satellite data now provide daily quantities of data unthinkable a few decades ago, fMRI brain imaging, and microarray measurements of gene expression, the number of variables can range into the (...)
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  24. Peter Spirtes (2011). Intervention, Determinism, and the Causal Minimality Condition. Synthese 182 (3):335-347.
    We clarify the status of the so-called causal minimality condition in the theory of causal Bayesian networks, which has received much attention in the recent literature on the epistemology of causation. In doing so, we argue that the condition is well motivated in the interventionist (or manipulability) account of causation, assuming the causal Markov condition which is essential to the semantics of causal Bayesian networks. Our argument has two parts. First, we show that the causal minimality condition, rather than an (...)
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  25. Kenneth Easwaran, Philip Ehrlich, David Ross, Christopher Hitchcock, Peter Spirtes, Roy T. Cook, Jean-Pierre Marquis, Stewart Shapiro & Royt Cook (2010). The Palmer House Hilton Hotel, Chicago, Illinois February 18–20, 2010. Bulletin of Symbolic Logic 16 (3).
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  26. Clark Glymour, David Danks, Bruce Glymour, Frederick Eberhardt, Joseph Ramsey, Richard Scheines, Peter Spirtes, Choh Man Teng & Jiji Zhang (2010). Actual Causation: A Stone Soup Essay. Synthese 175 (2):169 - 192.
    We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) "neuron" and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are relevant, but (...)
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  27. Peter Spirtes, A Tutorial On Causal Inference.
    The goal of this tutorial is twofold: to provide a description of some basic causal inference problems, models, algorithms, and assumptions in enough detail to understand recent developments in these areas; and to compare and contrast these with machine learning problems, models, algorithms, and assumptions.
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  28. Jiji Zhang & Peter Spirtes (2008). Detection of Unfaithfulness and Robust Causal Inference. Minds and Machines 18 (2):239-271.
    Much of the recent work on the epistemology of causation has centered on two assumptions, known as the Causal Markov Condition and the Causal Faithfulness Condition. Philosophical discussions of the latter condition have exhibited situations in which it is likely to fail. This paper studies the Causal Faithfulness Condition as a conjunction of weaker conditions. We show that some of the weaker conjuncts can be empirically tested, and hence do not have to be assumed a priori. Our results lead to (...)
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  29. Peter Spirtes (2005). Graphical Models, Causal Inference, and Econometric Models. Journal of Economic Methodology 12 (1):3-34.
    A graphical model is a graph that represents a set of conditional independence relations among the vertices (random variables). The graph is often given a causal interpretation as well. I describe how graphical causal models can be used in an algorithm for constructing partial information about causal graphs from observational data that is reliable in the large sample limit, even when some of the variables in the causal graph are unmeasured. I also describe an algorithm for estimating from observational data (...)
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  30. Jiji Zhang & Peter Spirtes, A Characterization of Markov Equivalence Classes for Ancestral Graphical Models.
    JiJi Zhang and Peter Spirtes. A Characterization of Markov Equivalence Classes for Ancestral Graphical Models.
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  31. Jiji Zhang & Peter Spirtes, A Transformational Characterization of Markov Equivalence Between DAGs with Latent Variables.
    JiJi Zhang and Peter Spirtes. A Transformational Characterization of Markov Equivalence between DAGs with Latent Variables.
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  32. Peter Spirtes & Richard Scheines (2004). Causal Inference of Ambiguous Manipulations. Philosophy of Science 71 (5):833-845.
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  33. David Danks, Clark Glymour & Peter Spirtes (2003). The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search. In W. H. Hsu, R. Joehanes & C. D. Page (eds.), Proceedings of IJCAI-2003 workshop on learning graphical models for computational genomics.
    Various algorithms have been proposed for learning (partial) genetic regulatory networks through systematic measurements of differential expression in wild type versus strains in which expression of specific genes has been suppressed or enhanced, as well as for determining the most informative next experiment in a sequence. While the behavior of these algorithms has been investigated for toy examples, the full computational complexity of the problem has not received sufficient attention. We show that finding the true regulatory network requires (in the (...)
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  34. Nicoleta Serban, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Daniel Handley, Richard Scheines & Clark Glymour, Analysis of Microarray Data for Treated Fat Cells.
    DNA microarrays are perfectly suited for comparing gene expression in different populations of cells. An important application of microarray techniques is identifying genes which are activated by a particular drug of interest. This process will allow biologists to identify therapies targeted to particular diseases, and, eventually, to gain more knowledge about the biological processes in organisms. Such an application is described in this paper. It is focused on diabetes and obesity, which is a genetically heterogeneous disease, meaning that multiple defective (...)
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  35. Ricardo Silva, Richard Scheines, Clark Glymour & Peter Spirtes, Learning Measurement Models for Unobserved Variables.
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  36. Peter Spirtes & Richard Scheines, Causal Inference and Ambiguous Manipulations.
    Peter Spirtes and Richard Scheines. Causal Inference and Ambiguous Manipulations.
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  37. 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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  38. Thomas Richardson & Peter Spirtes, Scoring Ancestral Graph Models.
    Thomas Richardson and Peter Spirtes. Scoring Ancestral Graph Models.
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  39. James M. Robins, Richard Scheines, Peter Spirtes & Larry Wasserman, The Limits of Causal Knowledge.
    James M. Robins, Richard Scheines, Peter Spirtes, and Larry Wasserman. The Limits of Causal Knowledge.
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  40. 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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  41. Peter Spirtes, Calrk Glymour & Richard Scheines, Reply to Humphreys and Freedman's Review of Causation, Prediction, and Search.
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  42. Peter Spirtes, Clark Glymour & Richard Scheines (1997). Reply to Humphreys and Freedman's Review of Causation, Prediction, and Search. British Journal for the Philosophy of Science 48 (4):555-568.
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  43. Peter Spirtes, Discovering Causal Relations Among Latent Variables in Directed Acyclical Graphical Models.
    Peter Spirtes. Discovering Causal Relations Among Latent Variables in Directed Acyclical Graphical Models.
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  44. Stephen E. Fienberg, Clark Glymour & Peter Spirtes, Discussion of Causal Diagrams for Empirical Research by J. Pearl.
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  45. Clark Glymour, Richard Scheines, Peter Spirtes & Christopher Meek, Regression and Causation.
    Clark Glymour, Richard Scheines, Peter Spirtes, and Christopher Meek. Regression and Causation.
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  46. Peter Spirtes, Conditional Independence in Directed Cyclical Graphical Models Representing Feedback or Mixtures.
    Peter Spirtes. Conditional Independence in Directed Cyclical Graphical Models Representing Feedback or Mixtures.
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  47. Peter Spirtes, Conditional Independence in Directed Cyclic Graphical Models for Feedback.
    Peter Spirtes. Conditional Independence in Directed Cyclic Graphical Models for Feedback.
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  48. Peter Spirtes, Directed Cyclic Graphs, Conditional Independence, and Non-Recursive Linear Structural Equation Models.
    : "Recursive linear structural equation models can be represented by directed acyclic graphs. When represented in this way, they satisfy the Markov Condition. Hence it is possible to use the graphical d-separation to determine what conditional independence relations are entailed by a given linear structural equation model. I prove in this paper that it is also possible to use the graphical d-separation applied to a cyclic graph to determine what conditional independence relations are entailed to hold by a given non-recursive (...)
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  49. Peter Spirtes, Clark Glymour, Richard Scheines, Christopher Meek, S. Fineberg & E. Slate, Prediction and Experimental Design with Graphical Causal Models.
    Peter Spirtes, Clark Glymour, Richard Scheines, Christopher Meek, S. Fineberg, E. Slate. Prediction and Experimental Design with Graphical Causal Models.
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