# 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*.