Papers and Books

This page collects key references for the theory and algorithms implemented in Tetrad.
It is not exhaustive, but covers some foundational papers, major algorithmic developments, and software-related publications most relevant to users and developers.

This is a first draft; we’ll expand this list as time permits. Please submit missing papers if you note them.

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Andrews, B., Ramsey, J., Sanchez-Romero, R., Camchong, J., & Kummerfeld, E. (2023). Fast scalable and accurate discovery of DAGs using the best order score search and grow shrink trees. In Advances in Neural Information Processing Systems (NeurIPS 36), 63945–63956.

Bai, X., Padman, R., Ramsey, J., & Spirtes, P. (2008). Tabu search-enhanced graphical models for classification in high dimensions. INFORMS Journal on Computing, 20(3), 423–437.

Bello, K., Aragam, B., & Ravikumar, P. (2022). DAGMA: Learning DAGs via M-matrices and a log-determinant acyclicity characterization. In Advances in Neural Information Processing Systems (NeurIPS 35), 8226–8239.

Bollen, K. A. (1989). Structural Equations with Latent Variables. Wiley.

Bühlmann, P., Peters, J., & Ernest, J. (2014). CAM: Causal additive models, high-dimensional order search and penalized regression. Annals of Statistics, 42(6), 2526–2556.

Colombo, D., Maathuis, M. H., Kalisch, M., & Richardson, T. S. (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables. Annals of Statistics, 40(1), 294–321.

Glymour, C. (2007). Learning the structure of deterministic systems. In Causal Learning: Psychology, Philosophy, and Computation (pp. 231–240).

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

Hyvärinen, A., & Smith, S. (2013). Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. Journal of Machine Learning Research, 14(1), 111–152.

Jolliffe, I. T. (2002). Principal Component Analysis (2nd ed.). Springer.

Kummerfeld, E., & Ramsey, J. (2016). Causal clustering for 1-factor measurement models. In Proceedings of KDD.

Lacerda, G., Spirtes, P., Ramsey, J., & Hoyer, P. (2008). Discovering cyclic causal models by independent component analysis. In UAI 2008.

Lam, W. Y., Andrews, B., & Ramsey, J. (2022). Greedy relaxations of the sparsest permutation algorithm. In Uncertainty in Artificial Intelligence (UAI), 1052–1062.

Liu, H., Roeder, K., & Wasserman, L. (2010). Stability approach to regularization selection (StARS) for high-dimensional graphical models. Annals of Applied Statistics.

Meek, C. (1995). Causal inference and the construction of graphical models with background knowledge. In Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence (UAI-95), 403–411.

Meinshausen, N., & Bühlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series B, 72(4), 417–473.

Murray-Watters, A., & Glymour, C. (2015). What is going on inside the arrows? Discovering the hidden springs in causal models. Philosophy of Science, 82(4), 556–586.

Nandy, P., Hauser, A., & Maathuis, M. H. (2018). High-dimensional consistency in score-based and hybrid structure learning. Annals of Statistics, 46(6A), 3151–3183.

Ogarrio, J. M., Spirtes, P., & Ramsey, J. (2016). A hybrid causal search algorithm for latent variable models. In PGM 2016, 368–379.

Raghu, V. K., Ramsey, J. D., Morris, A., Manatakis, D. V., Sprites, P., Chrysanthis, P. K., … & Benos, P. V. (2018). Comparison of strategies for scalable causal discovery of latent variable models from mixed data. International Journal of Data Science and Analytics, 6(1), 33–45.

Ramsey, J. (2016). Improving accuracy and scalability of the PC algorithm by maximizing p-value. arXiv:1610.00378.

Ramsey, J. D., Hanson, S. J., & Glymour, C. (2011). Multi-subject search correctly identifies causal connections and most causal directions in DCM models: the Smith et al. simulation study. NeuroImage, 58(3), 838–848.

Ramsey, J., Andrews, B., & Spirtes, P. (2025). Efficient latent variable causal discovery: Combining score search and targeted testing. arXiv:2510.04263.

Ramsey, J., Glymour, M., Sanchez-Romero, R., & Glymour, C. (2017). A million variables and more: The fast greedy equivalence search algorithm for learning high-dimensional graphical causal models. International Journal of Data Science and Analytics, 3(2), 121–129.

Ramsey, J., Zhang, J., & Spirtes, P. (2006). Adjacency-faithfulness and conservative causal inference. In UAI-06, 401–408.

Ramsey, J., Zhang, J., & Spirtes, P. (2012). Adjacency-faithfulness and conservative causal inference. arXiv:1206.6843.

Raskutti, G., & Uhler, C. (2018). Learning directed acyclic graph models based on sparsest permutations. Stat, 7(1), e183.

Richardson, T. S. (2013). A discovery algorithm for directed cyclic graphs. arXiv:1302.3599.

Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., & Sejdinovic, D. (2019). Detecting causal associations in large nonlinear time series datasets. Science Advances, 5(11).

Sanchez-Romero, R., Ramsey, J., Zhang, K., Glymour, C., Huang, B., & Spirtes, P. (2019). Causal discovery of feedback networks with functional interventions. In Causal Learning and Reasoning (CLeaR).

Shimizu, S., Hoyer, P. O., Hyvärinen, A., & Kerminen, A. (2011). DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. Journal of Machine Learning Research, 12, 1225–1248.

Shimizu, S., Hoyer, P. O., Hyvärinen, A., & Kerminen, A. (2006). A Linear Non-Gaussian Acyclic Model for causal discovery. Journal of Machine Learning Research, 7, 2003–2030.

Silva, R. (2006). Learning the structure of linear latent variable models. Journal of Machine Learning Research.

Spirtes, P., Glymour, C. N., & Scheines, R. (2000). Causation, Prediction, and Search (2nd ed.). MIT Press.

Stekhoven, D. J., Moraes, I., Sveinbjörnsson, G., Hennig, L., Maathuis, M. H., & Bühlmann, P. (2012). Causal stability ranking. Bioinformatics, 28(21), 2819–2823.

Tillman, R., & Spirtes, P. (2011). Learning equivalence classes of acyclic models with latent and selection variables from multiple datasets with overlapping variables. In AISTATS, 3–15.

Zhang, J. (2008). On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence, 172(16–17), 1873–1896.

Zhang, K., Huang, B., Zhang, J., Glymour, C., & Schölkopf, B. (2017). Causal discovery from nonstationary and heterogeneous data: Causal invariance and CD-NOD. In NeurIPS 31.