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@article{runge2019inferring,
  title={Inferring causation from time series in Earth system sciences},
  author={Runge, Jakob and Bathiany, Sebastian and Bollt, Erik and Camps-Valls, Gustau and Coumou, Dim and Deyle, Ethan and Glymour, Clark and Kretschmer, Marlene and Mahecha, Miguel D and Mu{\~n}oz-Mar{\'\i}, Jordi and others},
  journal={Nature Communications},
  volume={10},
  number={1},
  pages={1--13},
  year={2019},
}

@article{dawid1979conditional,
	author = {Dawid, A Philip},
	journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
	number = {1},
	pages = {1--15},
	publisher = {Wiley Online Library},
	title = {Conditional independence in statistical theory},
	volume = {41},
	year = {1979}}
	
@inproceedings{ijcai2021-491,
  title     = {Ordering-Based Causal Discovery with Reinforcement Learning},
  author    = {Wang, Xiaoqiang and Du, Yali and Zhu, Shengyu and Ke, Liangjun and Chen, Zhitang and Hao, Jianye and Wang, Jun},
  booktitle = {IJCAI},
  year      = {2021}
}

@article{daudin1980partial,
	author = {Daudin, JJ},
	journal = {Biometrika},
	number = {3},
	pages = {581--590},
	publisher = {Oxford University Press},
	title = {Partial association measures and an application to qualitative regression},
	volume = {67},
	year = {1980}}

@article{chickering2002optimal,
	author = {Chickering, David Maxwell},
	journal = {Journal of machine learning research},
	number = {Nov},
	pages = {507--554},
	title = {Optimal structure identification with greedy search},
	volume = {3},
	year = {2002}}

@article{shah2020,
	author = {Shah, Rajen D. and Peters, Jonas},
	fjournal = {Annals of Statistics},
	journal = {The Annals of Statistics},
	number = {3},
	pages = {1514--1538},
	publisher = {The Institute of Mathematical Statistics},
	title = {The hardness of conditional independence testing and the generalised covariance measure},
	volume = {48},
	year = {2020},}

@article{azadkia2019simple,
author = {Mona Azadkia and Sourav Chatterjee},
title = {{A simple measure of conditional dependence}},
volume = {49},
journal = {The Annals of Statistics},
number = {6},
pages = {3070 -- 3102},
year = {2021},
}

@article{buhlmann2014cam,
	author = {B{\"u}hlmann, Peter and Peters, Jonas and Ernest, Jan},
	journal = {The Annals of Statistics},
	number = {6},
	pages = {2526--2556},
	publisher = {Institute of Mathematical Statistics},
	title = {CAM: Causal additive models, high-dimensional order search and penalized regression},
	volume = {42},
	year = {2014}}

@article{schwarz1978estimating,
	author = {Schwarz, Gideon},
	journal = {The Annals of Statistics},
	pages = {461--464},
	publisher = {JSTOR},
	title = {Estimating the dimension of a model},
	year = {1978}}

@article{peters2015structural,
	author = {Peters, Jonas and B{\"u}hlmann, Peter},
	journal = {Neural Computation},
	number = {3},
	pages = {771--799},
	publisher = {MIT Press},
	title = {Structural intervention distance for evaluating causal graphs},
	volume = {27},
	year = {2015}}

@article{kalainathan2020causal,
	author = {Kalainathan, Diviyan and Goudet, Olivier and Dutta, Ritik},
	journal = {J. Mach. Learn. Res.},
	pages = {37--1},
	title = {Causal Discovery Toolbox: Uncovering causal relationships in Python.},
	volume = {21},
	year = {2020}}

@article{hornik1989multilayer,
	author = {Hornik, Kurt and Stinchcombe, Maxwell and White, Halbert},
	journal = {Neural Networks},
	number = {5},
	pages = {359--366},
	publisher = {Elsevier},
	title = {Multilayer feedforward networks are universal approximators},
	volume = {2},
	year = {1989}}

@article{jennrich1969asymptotic,
	author = {Jennrich, Robert I},
	journal = {The Annals of Mathematical Statistics},
	number = {2},
	pages = {633--643},
	publisher = {JSTOR},
	title = {Asymptotic properties of non-linear least squares estimators},
	volume = {40},
	year = {1969}}

@article{zhang2015estimation,
	author = {Zhang, Kun and Wang, Zhikun and Zhang, Jiji and Sch{\"o}lkopf, Bernhard},
	journal = {ACM Transactions on Intelligent Systems and Technology (TIST)},
	number = {2},
	pages = {1--22},
	publisher = {ACM New York, NY, USA},
	title = {On estimation of functional causal models: general results and application to the post-nonlinear causal model},
	volume = {7},
	year = {2015}}

@article{van2006syntren,
	author = {Van den Bulcke, Tim and Van Leemput, Koenraad and Naudts, Bart and van Remortel, Piet and Ma, Hongwu and Verschoren, Alain and De Moor, Bart and Marchal, Kathleen},
	journal = {BMC bioinformatics},
	number = {1},
	pages = {1--12},
	publisher = {Springer},
	title = {SynTReN: a generator of synthetic gene expression data for design and analysis of structure learning algorithms},
	volume = {7},
	year = {2006}}

@article{shimizu2006lingam,
	author = {Shimizu, Shohei and Hoyer, Patrik O and Hyv{\"a}rinen, Aapo and Kerminen, Antti},
	journal = {Journal of Machine Learning Research},
	number = {10},
	title = {A linear non-Gaussian acyclic model for causal discovery},
	volume = {7},
	year = {2006}}

@article{peters2014equal,
	author = {Peters, Jonas and B{\"u}hlmann, Peter},
	journal = {Biometrika},
	number = {1},
	pages = {219--228},
	publisher = {Oxford University Press},
	title = {Identifiability of Gaussian structural equation models with equal error variances},
	volume = {101},
	year = {2014}}

@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},
  number={2},
  pages={121--129},
  year={2017},
  publisher={Springer}
}

@article{bartlett2017integer,
  title={Integer linear programming for the Bayesian network structure learning problem},
  author={Bartlett, Mark and Cussens, James},
  journal={Artificial Intelligence},
  volume={244},
  pages={258--271},
  year={2017},
  publisher={Elsevier}
}

@inproceedings{miyato2018spectral,
	author = {Takeru Miyato and Toshiki Kataoka and Masanori Koyama and Yuichi Yoshida},
	booktitle = {International Conference on Learning Representations},
	title = {Spectral Normalization for Generative Adversarial Networks},
	url = {https://openreview.net/forum?id=B1QRgziT-},
	year = {2018},
	Bdsk-Url-1 = {https://openreview.net/forum?id=B1QRgziT-}}

@inproceedings{Hoyer2009anm,
	author = {Hoyer, Patrik and Janzing, Dominik and Mooij, Joris M and Peters, Jonas and Sch\"{o}lkopf, Bernhard},
	booktitle = {Advances in Neural Information Processing Systems},
	title = {Nonlinear causal discovery with additive noise models},
	year = {2009}}

@inproceedings{zheng2018dags,
	author = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P},
	booktitle = {Advances in Neural Information Processing Systems},
	title = {{DAGs with NO TEARS}: Continuous optimization for structure learning},
	year = {2018}}

@inproceedings{huang2018generalized,
	author = {Huang, Biwei and Zhang, Kun and Lin, Yizhu and Sch{\"o}lkopf, Bernhard and Glymour, Clark},
	booktitle = {Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
	title = {Generalized score functions for causal discovery},
	year = {2018}}

@inproceedings{fukumizu2007kernel,
	author = {Fukumizu, Kenji and Gretton, Arthur and Sun, Xiaohai and Sch{\"o}lkopf, Bernhard},
	booktitle = {Advances in Neural Information Processing Systems},
	title = {Kernel measures of conditional dependence.},
	year = {2007}}

@inproceedings{bach2002learning,
	author = {Bach, Francis R and Jordan, Michael I},
	booktitle = {Advances in Neural Information Processing Systems},
	title = {Learning graphical models with {Mercer} kernels},
	year = {2002}}

@inproceedings{gretton2005measuring,
	author = {Gretton, Arthur and Bousquet, Olivier and Smola, Alex and Sch{\"o}lkopf, Bernhard},
	booktitle = {International Conference on Algorithmic Learning Theory},
	title = {Measuring statistical dependence with {Hilbert-Schmidt} norms},
	year = {2005}}

@inproceedings{Zhang2011KernelbasedCI,
	author = {K. Zhang and J. Peters and D. Janzing and B. Sch{\"o}lkopf},
	booktitle = {UAI},
	title = {Kernel-based Conditional Independence Test and Application in Causal Discovery},
	year = {2011}}

@inproceedings{yu2019dag,
	author = {Yu, Yue and Chen, Jie and Gao, Tian and Yu, Mo},
	booktitle = {International Conference on Machine Learning},
	title = {{DAG-GNN}: {DAG} structure learning with graph neural networks},
	year = {2019}}

@inproceedings{lachapelle2019gradient,
	author = {Lachapelle, S{\'e}bastien and Brouillard, Philippe and Deleu, Tristan and Lacoste-Julien, Simon},
	booktitle = {International Conference on Learning Representations},
	title = {Gradient-based neural {DAG} learning},
	year = {2020}}

@inproceedings{Zhu2020Causal,
	author = {Shengyu Zhu and Ignavier Ng and Zhitang Chen},
	booktitle = {International Conference on Learning Representations},
	title = {Causal Discovery with Reinforcement Learning},
	year = {2020},}

@incollection{geiger1994learning,
	author = {Geiger, Dan and Heckerman, David},
	booktitle = {UAI},
	title = {Learning {Gaussian} networks},
	year = {1994}}

@inproceedings{zhang2012pnl,
	author = {Zhang, Kun and Hyvarinen, Aapo},
	booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence},
	title = {On the identifiability of the post-nonlinear causal model},
	year = {2009}}

@inproceedings{chickering2020statistically,
	author = {Chickering, David Maxwell},
	booktitle = {Conference on Uncertainty in Artificial Intelligence},
	title = {Statistically efficient greedy equivalence search},
	year = {2020}}

@article{neto2010causal,
  title={Causal graphical models in systems genetics: a unified framework for joint inference of causal network and genetic architecture for correlated phenotypes},
  author={Neto, Elias Chaibub and Keller, Mark P and Attie, Alan D and Yandell, Brian S},
  journal={The Annals of Applied Statistics},
  volume={4},
  number={1},
  pages={320},
  year={2010},
  publisher={NIH Public Access}
}

@article{nandy2018,
  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{arjovsky2019irm,
	author = {Arjovsky, Martin and Bottou, L{\'e}on and Gulrajani, Ishaan and Lopez-Paz, David},
	journal = {arXiv preprint arXiv:1907.02893},
	title = {Invariant risk minimization},
	year = {2019}}

@inproceedings{ng2019masked,
    author = {Ignavier Ng and Shengyu Zhu and Zhuangyan Fang and Haoyang Li and Zhitang Chen and Jun Wang},
    title = {Masked Gradient-Based Causal Structure Learning},
    booktitle = {Proceedings of the SIAM International Conference on Data Mining (SDM)},
	year = {2022}}

@book{spirtes2000causation,
	author = {Spirtes, Peter and Glymour, Clark N and Scheines, Richard and Heckerman, David},
	publisher = {MIT press},
	title = {Causation, Prediction, and Search},
	year = {2000}}

@book{koller2009probabilistic,
	author = {Koller, Daphne and Friedman, Nir},
	publisher = {MIT press},
	title = {Probabilistic Graphical Models: Principles and Techniques},
	year = {2009}}

@book{pearl2009causality,
  author = {Pearl, Judea},
  edition = {2nd},
  publisher = {Cambridge University Press},
  timestamp = {2016-11-26T13:20:49.000+0100},
  title = {Causality: Models, Reasoning and Inference},
  year = 2009
}

@book{peters2017elements,
	author = {Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
	publisher = {The MIT Press},
	title = {Elements of Causal Inference: Foundations and Learning Algorithms},
	year = {2017}}
