The TETRAD Project:

Causal Models and Statistical Data

Publications

Books

Discovering Causal Structure: Artificial Intelligence, Philosophy of Science, and Statistical Modeling

Spirtes, P., Glymour, C. and Scheines, R. (1993). Causation, Prediction, and Search, New York, N.Y.: Springer-Verlag. 2nd Edition, MIT Press (2001)

Glymour, C. and G. Cooper, Causation, Computation and Discovery (1999), MIT/AAAI Press.

Glymour, C. The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology (2001), MIT Press.

TETRAD II program and manual

TETRAD II: Tools for Discovery

Articles

G. Lacerda, P. Spirtes, J. Ramsey, P.O. Hoyer. "Discovering Cyclic Causal Models by Independent Components Analysis." Submitted, Feb. 2008. [code]

R. Ali, T. Richardson, P. Spirtes and J, Zhang. “Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graph Models with Latent Variables”, Uncertainty in Artificial Intelligence 2005, Edinboro, Scotland. [ps]

T. Chu, C. Glymour, R. Scheines, P. Spirtes. “A Statistical Problem for Inference to Regulatory Structure from Associations of Gene Expression Measurements with Microarrays”, Bioinformatics, 2003, 19, pp. 1147-1152.

G. Cooper, C. Aliferis, R. Ambrosino, J. Aronis, B. Buchanan, R. Caruana, M. Fine, C. Glymour, G. Gordon, B. Hanusa, J. Janosky, C. Meek, T. Mitchell, T. Richardson, P. Spirtes. (1996). "An Evaluation of Machine-Learning Methods for Predicting Pneumonia Mortality," Artificial Intelligence in Medicine, to appear.

C. Glymour, R. Scheines, P. Spirtes, & K. Kelly (1987). Discovering Causal Structure. Academic Press, San Diego, CA.

C. Glymour and P. Spirtes (1988). "Causality, Latent Variables and Overidentifying Constraints", Journal of Econometrics, vol. 39, pp. 175-197.

C. Glymour and P. Spirtes (1993). "Comment: Conditional Independence and Causal Inference," Statistical Science, vol. 9, August, pp. 250-257.

C. Glymour, P. Spirtes, and R. Scheines (1994). "In Place of Regression," in Patrick Suppes: Scientific Philosopher, Paul Humphreys (editor), Vol. 1, Kluwer Academic Publishers, Dordrecht, Holland.

C. Glymour, P. Spirtes, and R. Scheines.(1990), "Independence Relations Produced by Parameter Values in Causal Models," Philosophical Topics, Vol. 18, No. 2, pp. 55-70.

C. Glymour, P. Spirtes, and R. Scheines. (1993). "Inferring Causal Structures in Mixed Populations", in Artificial Intelligence in Statistics: Ai and statistics III, D. Hand, ed., Chapman and Hall, pp. 141-155.

C. Glymour, P. Spirtes, and R. Scheines. (1994). "Causal Inference", Erkenntnis, vol. 35, July, pp. 151-189.

C. Meek, (1995) Causal inference and causal explanation with background knowledge. Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, Philippe Besnard and Steve Hanks (Eds.), Morgan Kaufmann Publishers, Inc., San Mateo, CA, 403-410.

C. Meek (1995). "Strong Completeness and Faithfulness in Bayesian Networks" Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers, Inc., San Mateo, pp 411-418..

C. Meek (1997) Graphical Models: Selecting Causal and Statistical Models. Ph.D. Thesis, Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA.

C. Meek, and C. Glymour. (1994). "Conditioning and intervening," British Journal for the Philosophy of Science.

J. Ramsey, P. Gazis,, T. Roush, P. Spirtes and C. Glymour. “Automated Classification of Carbonates from Near Infrared Reflectance Spectra”, Data Mining and Knowledge Discover, 2003, 6, pp. 275-291.

J. Ramsey, J. Zhang and P. Spirtes. “Adjacency-Faithfulness and Conservative Causal Inference”, Uncertainty in Artificial Intelligence 2006, Boston, MA. [ps]

T. Richardson (1994). "Equivalence in Non-Recursive Structural Equation Models," Proceedings of The 11th Symposium on Computational Statistics, COMPSTAT, 20-26 August 1994, Vienna, Austria. R. Dutter ed., Physica Verlag, Vienna, Austria.

T. Richardson. (1996). Feedback Models: Interpretation and Discovery. Ph.D. Thesis, Dept. of Philosophy, Carnegie Mellon University, Pgh., PA, 15213.

T. Richardson (1996). "A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models," Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, Portland, Oregon, 1996. E. Horvitz and F. Jensen eds., Morgan Kaufmann, San Francisco, CA.

T. Richardson (1996). "A Discovery Algorithm for Directed Cyclic Graphs," Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, Portland, Oregon, 1996. E. Horvitz and F. Jensen eds., Morgan Kaufmann, San Francisco, CA.

T. Richardson (1996) Chain Graphs and Symmetric Associations. In Learning in Graphical Models, M. I. Jordan (Ed.), Kluwer Academic Press.

T. Richardson (1997) A Characterization of Markov Equivalence for Directed Cyclic Graphs. International Journal of Approximate Reasoning, 1997, vol. 17, 2/3 (Aug-Oct. 97), pp.107-162.

T. Richardson (1997) Extensions of Undirected and Acyclic, Directed Graphical Models. In Preliminary Papers, 6th International Workshop on Artificial Intelligence and Statistics, D. Madigan, ed., January 1997.

T. Richardson, P. Spirtes. “Ancestral Graph Markov Models”, Annals of Statistics, 2002, 30 pp. 962-1030.

T. Richardson, and P. Spirtes. “Ancestral graph Markov models”, in Highly Structured Stochastic Systems ed. by Peter J. Green, Nils Lid Hjort and Sylvia Richardson, Oxford University Press, 2003, Oxford, UK., pp. 83-103.

T. Richardson, P. Spirtes., C. Glymour. (1997) A Note on Cyclic Graphs and Dynamical Feedback Systems. In Preliminary Papers, 6th International Workshop on Artificial Intelligence and Statistics, D. Madigan, ed., January 1997.

J. Robins, R, Scheines, P. Spirtes and L. Wasserman. “Uniform Consistency In Causal Inference”, Biometrika, September, 2003, 90, pp. 491-515.

R. Scheines, (1994). "Inferring Causal Structure Among Unmeasured Variables," in Selecting Models from Data: AI and Statistics IV, P. Chessman and R. W. Oldford (editors), Springer-Verlag, pp. 197-204.

R. Scheines (1994). "Causation, Indistinguishability, and Regression," in Sofstat '93: Advances in Statistial Software 4, Frank Faulbaum (editor), Gustav Fischer Verlag, pp. 89-98.

R. Scheines (1996). "Estimating Structural Equation Models with the Gibbs Sampler," in SoftStat 95, Advances in Statistical Software 5, ed. by Frank Faulbaum and Wolfgang Bandilla, Lucious & Lucious, Stuttgart, Germany, 183-194.

R. Scheines (1996). ÒEstimating Underidentified Structural Models,Ó (1996). R. Scheines, in Compstat Ô96: Proceedings in Computational Statistics, Short Communications and Posters ed., by A. Prat and E. Ripoll, 109-111.

R. Scheines (1996). "Estimating Latent Causal Influence: TETRAD II Model Selection and Bayesian Parameter Estimation." Proceedings of the 6th International Workshop on Artificial Intelligence and Statistics.

R. Scheines, Spirtes, P., Glymour, C., Meek, C., and Richardson, T. (to appear). The TETRAD Project: Constraint Based Aids to Causal Model Specification, Multivariate Behavioral Research. [ps]

R. Scheines (1997) An Introduction to Causal Inference, in Causality in Crisis, ed. by Steven Turner and Vaughan McKim, University of Notre Dame Press. [ps]

R. Scheines, P. Spirtes, and C. Glymour. (1993). "Prediction and Causation," in Advanded Technology for Developers, Jane Klimasauskas (editor), Vol. 2, August, High-Tech Communications, Sewickley, PA, pp. 1-12.

R. da Silva, C. Glymour, R. Scheines, P. Spirtes“Learning the structure of latent linear structure models”, Journal of Machine Learning Research, 7(Feb):191--246, 2006. [ps]

P. Spirtes, R. Scheines, and C. Glymour (1990). "Simulation Studies of the Reliability of Computer Aided Model Specification using the TETRAD, EQS,and LISREL Programs," (1990), Sociological Methods and Research, Vol. 19, No. 1, pp. 3-66.

P., Spirtes (1991). "Detecting Causal Relations in the Presence of Unmeasured Variables", in Uncertainty in Artificial Intelligence, Proceedings of the Seventh Conference, Morgan Kaufman Publishers.

P. Spirtes. “Graphical Models, Causal Inference, and Econometric Models”, Journal of Economic Methodology. 2005 12:1, pp. 1–33.

P. Spirtes (1995). Directed Cyclic Graphical Representation of Feedback Models, Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, ed. by Philippe Besnard and Steve Hanks, Morgan Kaufmann Publishers, Inc., San Mateo, 1995. [ps]

P. Spirtes (1994). "Building Causal Graphs from Statistical Data in the Presence of Latent Variables", in Logic, Methodology, and the Philosophy of Scienc IX, ed. by D. Prawitz, B. Skyrms, and D. Westerstahl, Elsevier Science, pp. 813-829.

P. Spirtes, C. Glymour and R. Scheines. (1991). "An Algorithm for Fast Recovery of Sparse Causal Graphs", Social Science Computer Review, vol. 9, pp. 62-72.

P. Spirtes, and R. Scheines. “Causal Inference of Ambiguous Manipulations”, PSA 2002 Contributed Papers, 2--5. [ps]

P. Spirtes, R. Scheines, C. Glymour, T. Richardson, and C. Meek. “Causal Inference”, The SAGE Handbook of Quantitative Methodology for the Social Sciences, D. Kaplan, ed., SAGE Publications, Thousand Oaks, CA., 2004, pp. 447-477. [ps]

Spirtes, P., C. Glymour, C. Meek (1996). "Learning Bayesian Networks from Data," AISB Quarterly, to appear

P. Spirtes, C. Glymour, and R. Scheines.(1994). "Inference, Intervention, and Prediction", in Selecting Models from Data: Artificial Intelligence and Statistics IV, ed. by P. Cheesman and R. Oldford, Springer Verlag, Lecture Notes in Statistics 89, pp. 215-223.

P. Spirtes, C. Glymour, and R. Scheines (forthcoming) Reply to Humphrey's and Freedman's Review of Causation, Prediction, and Search. British Journal for Philosophy of Science.

P. Spirtes and C. Meek (1995). "Learning Bayesian Networks with Discrete Variables from Data", in Proceedings of The First International Conference on Knowledge Discovery and Data Mining, ed. by Usama M. Fayyad and Ramasamy Uthurusamy, AAI Press, pp. 294-299.

P. Spirtes, C. Meek and T. Richardson (1995). Causal inference in the presence of latent variables and selection bias , in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence , ed P. Besnard and S. Hanks, Morgan Kaufmann Publishers, Inc., San Mateo, pp 499-506. [ps]

P. Spirtes and T. Richardson (1996). A Polynomial Time Algorithm For Determining DAG Equivalence in the Presence of Latent Variables and Selection Bias, Proceedings of the 6th International Workshop on Artificial Intelligence and Statistics. [ps]

P. Spirtes, T. Richardson and C. Meek (1996). Heuristic Greedy Search Algorithms for Latent Variable Models, Proceedings of the 6th International Workshop on Artificial Intelligence and Statistics. [ps]

P. Spirtes and R. Scheines (forthcoming). Reply to Freedman, in Causality in Crisis, ed. by Steven Turner and Vaughan McKim, University of Notre Dame Press. [ps]

J. Zhang. "Generalized Do-Calculus with Testable Causal Assumptions." AI & Stat, 2007. Submitted, UAI 2007. [ps]

J. Zhang. "A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables."

J. Zhang, and P. Spirtes. “A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables”, Uncertainty in Artificial Intelligence 2005, Edinboro, Scotland. [ps]

J. Zhang and P. Spirtes. "Detection of Unfaithfulness and Robust Causal Inference." Draft. [ps]

Tech Reports

J. Ramsey (2006). A PC-style Markov blanket search for high-dimensional datasets. Technical Report, CMU-PHIL-177, Carnegie Mellon University, Department of Philosophy. [ps]

T. Richardson (1996). Fast Re-Calculation of the Covariance Matrix Implied by a Recursive Structural Equation Model, Tech Report CMU-PHIL-67, Dept. of Philosophy, Carnegie Mellon Univ., Pittsburgh, PA. January.

T. Richardson and P. Spirtes (1996). Automated discovery of linear feedback models, Technical Report CMU-75-Phil. [ps]

R. Scheines (1993). "Unidimensional Linear Latent Variable Models," Tech Report CMU-PHIL-39, Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA.

R. Scheines, H. Hoijtink and A. Boomsma, (1995). "Bayesian Estimation and Testing of Structural Equation Models," Technical Report CMU-PHIL-66, Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA.

P. Spirtes and C. Glymour (1990). "Causal Structure among Measured Variables Preserved with Unmeasured Variables", Technical Report CMU-PHIL-14, Department of Philosophy, Carnegie Mellon University, April.

P. Spirtes (1993)."Directed Cyclic Graphs, Conditional Independence, and Non-Recursive Linear Structual Equation Models." Technical Report CMU-PHIL-35, Department of Philosophy, Carnegie Mellon University, April.

P. Spirtes (1994)."Conditional Independence in Directed Cyclic Graphical Models for Feedback." Technical Report CMU-PHIL-54, Department of Philosophy, Carnegie Mellon University, May.

P. Spirtes and T. Verma (1992). "Equivalence of Causal Models with Latent Variables." Technical Report CMU-PHIL-33, Department of Philosophy, Carnegie Mellon University, October.

P. Spirtes, T. Richardson, C. Meek, R. Scheines, and C. Glymour, (1996). Using D-separation to Calculate Zero Partial Correlations in Linear Models with Correlated Errors, Technical Report CMU-72-Phil, Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA, 15213. [ps]

P. Spirtes, C. Meek, and T. Richardson (1996). Causal Inference in the Presence of Latent Variables and Selection Bias (with proofs), Technical Report CMU-77-Phil. Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA, 15213. [ps]

P. Spirtes, T. Richardson, C. Meek, R. Scheines, and C. Glymour, (1997). Using Path Diagrams as a Structural Equation Modelling Tool, Technical Report CMU-82-Phil. Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA, 15213. [ps]

P. Spirtes, T. Richardson, and C. Meek (1997). The Dimensionality of Mixed Ancestral Graphs. Technical Report CMU- Phil. Dept. of Philosophy, Carnegie Mellon University, Pittsburgh, PA, 15213.

scheines@andrew.cmu.edu