@book{pearl1988probabilistic,
  title={Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference},
  author={Pearl, Judea},
  year={1988},
  publisher={Morgan kaufmann}
}
@book{spirtes2000causation,
  title={Causation, Prediction, and Search},
  author={Spirtes, Peter and Glymour, Clark N and Scheines, Richard},
  year={2000},
  publisher={MIT press}
}
@article{chickering2002optimal,
  title={Optimal structure identification with greedy search},
  author={Chickering, David Maxwell},
  journal={Journal of Machine Learning Research},
  volume={3},
  number={Nov},
  pages={507--554},
  year={2002}
}
@article{chickering2002learning,
  title={Learning equivalence classes of Bayesian-network structures},
  author={Chickering, David Maxwell},
  journal={Journal of Machine Learning Research},
  volume={2},
  pages={445--498},
  year={2002},
}
@article{hauser2012characterization,
  title={Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs},
  author={Hauser, Alain and B{\"u}hlmann, Peter},
  journal={Journal of Machine Learning Research},
  volume={13},
  pages={2409--2464},
  year={2012},
}
@inproceedings{verma1991equivalence,
  title={Equivalence and Synthesis of Causal Models},
  author={Verma, T. and Pearl, J.},
  booktitle={Uncertainty in Artificial Intelligence},
  year={1991},
}
@article{haughton1988choice,
  title={On the choice of a model to fit data from an exponential family},
  author={Haughton, Dominique MA},
  journal={Annals of Statistics},
  pages={342--355},
  year={1988},
}
@article{schwarz1978estimating,
  title={Estimating the dimension of a model},
  author={Schwarz, Gideon},
  journal={Annals of Statistics},
  pages={461--464},
  year={1978},
}
# meek rules
@article{meek1995causal,
  title={Causal inference and causal explanation with background knowledge},
  author={Meek, Christopher},
  journal={Uncertainty in Artificial Intelligence},
  pages={403--410},
  year={1995}
}
@article{kalisch2012causal,
  title={Causal inference using graphical models with the R package pcalg},
  author={Kalisch, Markus and M{\"a}chler, Martin and Colombo, Diego and Maathuis, Marloes H and B{\"u}hlmann, Peter},
  journal={Journal of Statistical Software},
  volume={47},
  pages={1--26},
  year={2012}
}
@article{ramsey2017million,
  title={A million variables and more: the fast greedy equivalence search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images},
  author={Ramsey, Joseph and Glymour, Madelyn and Sanchez-Romero, Ruben and Glymour, Clark},
  journal={International Journal of Data Science and Analytics},
  volume={3},
  pages={121--129},
  year={2017},
}

@article{zheng2018dags,
  title={DAGs with NO TEARS: Continuous Optimization for Structure Learning},
  author={Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep K and Xing, Eric P},
  journal={Neural Information Processing Systems},
  year={2018}
}

@article{brouillard2020differentiable,
  title={Differentiable causal discovery from interventional data},
  author={Brouillard, Philippe and Lachapelle, S{\'e}bastien and Lacoste, Alexandre and Lacoste-Julien, Simon and Drouin, Alexandre},
  journal={Neural Information Processing Systems},
  year={2020}
}

@inproceedings{nazaret2023stable,
  title={Stable Differentiable Causal Discovery},
  author={Nazaret, Achille and Hong, Justin and Azizi, Elham and Blei, David},
  booktitle={International Conference on Machine Learning},
  year={2024},
}

@article{liu2023improving,
  title={Improving greedy local search methods by switching the search space},
  author={Liu, Xiaohan and Gao, Xiaoguang and Ru, Xinxin and Tan, Xiangyuan and Wang, Zidong},
  journal={Applied Intelligence},
  pages={1--18},
  year={2023},
}

@article{alonso2018use,
  title={On the use of local search heuristics to improve GES-based Bayesian network learning},
  author={Alonso, Juan I and de la Ossa, Luis and Gamez, Jose A and Puerta, Jose M},
  journal={Applied Soft Computing},
  volume={64},
  pages={366--376},
  year={2018},
}

@article{glymour2019review,
  title={Review of causal discovery methods based on graphical models},
  author={Glymour, Clark and Zhang, Kun and Spirtes, Peter},
  journal={Frontiers in Genetics},
  volume={10},
  year={2019},
}

@inproceedings{chickering2015selective,
  title={Selective Greedy Equivalence Search: finding optimal Bayesian networks using a polynomial number of score evaluations},
  author={Chickering, David Maxwell and Meek, Christopher},
  booktitle={Uncertainty in Artificial Intelligence},
  year={2015}
}

@article{he2015counting,
  title={Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs},
  author={He, Yangbo and Jia, Jinzhu and Yu, Bin},
  journal={Journal of Machine Learning Research},
  volume={16},
  number={1},
  pages={2589--2609},
  year={2015},
}


@inproceedings{zhang2011kernel,
  title={Kernel-based conditional independence test and application in causal discovery},
  author={Zhang, Kun and Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  booktitle={Uncertainty in Artificial Intelligence},
  year={2011}
}

@article{fang2023low,
  title={On Low-Rank Directed Acyclic Graphs and Causal Structure Learning},
  author={Fang, Zhuangyan and Zhu, Shengyu and Zhang, Jiji and Liu, Yue and Chen, Zhitang and He, Yangbo},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  year={2023},
  publisher={IEEE}
}
@article{buhlmann2014cam,
  title={CAM: CAUSAL ADDITIVE MODELS, HIGH-DIMENSIONAL ORDER SEARCH AND PENALIZED REGRESSION},
  author={B{\"u}hlmann, Peter and Peters, Jonas and Ernest, Jan},
  journal={Annals of Statistics},
  pages={2526--2556},
  year={2014},
  publisher={JSTOR}
}
@article{scholkopf2021toward,
  title={Toward causal representation learning},
  author={Sch{\"o}lkopf, Bernhard and Locatello, Francesco and Bauer, Stefan and Ke, Nan Rosemary and Kalchbrenner, Nal and Goyal, Anirudh and Bengio, Yoshua},
  journal={Proceedings of the IEEE},
  volume={109},
  number={5},
  pages={612--634},
  year={2021},
  publisher={IEEE}
}
@article{nandy2018high,
  title={High-dimensional consistency in score-based and hybrid structure learning},
  author={Nandy, Preetam and Hauser, Alain and Maathuis, Marloes H},
  journal={The Annals of Statistics},
  volume={46},
  number={6A},
  pages={3151--3183},
  year={2018},
  publisher={JSTOR}
}

@article{peters2014causal,
  title={Causal Discovery with Continuous Additive Noise Models},
  author={Peters, Jonas and Mooij, Joris M and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  journal={Journal of Machine Learning Research},
  volume={15},
  pages={2009--2053},
  year={2014}
}

@article{reisach2021beware,
  title={Beware of the simulated dag! causal discovery benchmarks may be easy to game},
  author={Reisach, Alexander and Seiler, Christof and Weichwald, Sebastian},
  journal={Neural Information Processing Systems},
  volume={34},
  pages={27772--27784},
  year={2021}
}

@article{peters2014identifiability,
  title={Identifiability of Gaussian structural equation models with equal error variances},
  author={Peters, Jonas and B{\"u}hlmann, Peter},
  journal={Biometrika},
  volume={101},
  number={1},
  pages={219--228},
  year={2014},
  publisher={Oxford University Press}
}

@article{waskom2021seaborn,
  title={Seaborn: statistical data visualization},
  author={Waskom, Michael L},
  journal={Journal of Open Source Software},
  volume={6},
  number={60},
  pages={3021},
  year={2021}
}

@article{schultheiss2023pitfalls,
  title={On the pitfalls of Gaussian likelihood scoring for causal discovery},
  author={Schultheiss, Christoph and B{\"u}hlmann, Peter},
  journal={Journal of Causal Inference},
  volume={11},
  number={1},
  year={2023}
}