@article{https://doi.org/10.48550/arxiv.1112.2738,
  doi = {10.48550/ARXIV.1112.2738},
  
  url = {https://arxiv.org/abs/1112.2738},
  
  author = {Schölkopf, Bernhard and Janzing, Dominik and Peters, Jonas and Zhang, Kun},
  
  keywords = {Machine Learning (stat.ML), Machine Learning (cs.LG), FOS: Computer and information sciences, FOS: Computer and information sciences},
  
  title = {Robust Learning via Cause-Effect Models},
  
  publisher = {arXiv},
  
  year = {2011},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{Dua:2019,
author = "Dua, Dheeru and Graff, Casey",
year = "2017",
title = "{UCI} Machine Learning Repository",
url = "http://archive.ics.uci.edu/ml",
institution = "University of California, Irvine, School of Information and Computer Sciences" } 

@article{ding2021retiring,
  title={Retiring Adult: New Datasets for Fair Machine Learning},
  author={Ding, Frances and Hardt, Moritz and Miller, John and Schmidt, Ludwig},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  year={2021}
}

@inproceedings{subbaswamy2018counterfactual,
  title={Counterfactual Normalization: Proactively Addressing Dataset Shift Using Causal Mechanisms.},
  author={Subbaswamy, Adarsh and Saria, Suchi},
  booktitle={UAI},
  pages={947--957},
  year={2018}
}

@inproceedings{
sinha2018certifiable,
title={Certifiable Distributional Robustness with Principled Adversarial Training},
author={Aman Sinha and Hongseok Namkoong and John Duchi},
booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=Hk6kPgZA-},
}

@inproceedings{Croce_adv_eval_attacks,
author = {Croce, Francesco and Hein, Matthias},
title = {Reliable Evaluation of Adversarial Robustness with an Ensemble of Diverse Parameter-Free Attacks},
year = {2020},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
articleno = {206},
numpages = {11},
series = {ICML}
}

@article{leiner2022data,
  title={Data fission: splitting a single data point},
  author={Leiner, James and Duan, Boyan and Wasserman, Larry and Ramdas, Aaditya},
  journal={arXiv preprint arXiv:2112.11079},
  year={2022}
}

@inproceedings{oberst2021regularizing,
  title={Regularizing towards causal invariance: Linear models with proxies},
  author={Oberst, Michael and Thams, Nikolaj and Peters, Jonas and Sontag, David},
  booktitle={International Conference on Machine Learning},
  pages={8260--8270},
  year={2021},
  organization={PMLR}
}

@article{peters2016causal,
  title={Causal inference by using invariant prediction: identification and confidence intervals},
  author={Peters, Jonas and B{\"u}hlmann, Peter and Meinshausen, Nicolai},
  journal={Journal of the Royal Statistical Society. Series B (Statistical Methodology)},
  pages={947--1012},
  year={2016},
  publisher={JSTOR}
}

@inproceedings{invariant_feature_selection,
author = {Magliacane, Sara and van Ommen, Thijs and Claassen, Tom and Bongers, Stephan and Versteeg, Philip and Mooij, Joris M.},
title = {Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions},
year = {2018},
publisher = {Curran Associates Inc.},
address = {Red Hook, NY, USA},
abstract = {An important goal common to domain adaptation and causal inference is to make accurate predictions when the distributions for the source (or training) domain(s) and target (or test) domain(s) differ. In many cases, these different distributions can be modeled as different contexts of a single underlying system, in which each distribution corresponds to a different perturbation of the system, or in causal terms, an intervention. We focus on a class of such causal domain adaptation problems, where data for one or more source domains are given, and the task is to predict the distribution of a certain target variable from measurements of other variables in one or more target domains. We propose an approach for solving these problems that exploits causal inference and does not rely on prior knowledge of the causal graph, the type of interventions or the intervention targets. We demonstrate our approach by evaluating a possible implementation on simulated and real world data.},
booktitle = {Proceedings of the 32nd International Conference on Neural Information Processing Systems},
pages = {10869–10879},
numpages = {11},
location = {Montr\'{e}al, Canada},
series = {NIPS'18}
}

@article{rojas2018invariant,
  title={Invariant models for causal transfer learning},
  author={Rojas-Carulla, Mateo and Sch{\"o}lkopf, Bernhard and Turner, Richard and Peters, Jonas},
  journal={The Journal of Machine Learning Research},
  volume={19},
  number={1},
  pages={1309--1342},
  year={2018},
  publisher={JMLR. org}
}

@article{heinze2018invariant,
  title={Invariant causal prediction for nonlinear models},
  author={Heinze-Deml, Christina and Peters, Jonas and Meinshausen, Nicolai},
  journal={Journal of Causal Inference},
  volume={6},
  number={2},
  year={2018},
  publisher={De Gruyter}
}

@inproceedings{
gulrajani2021in,
title={In Search of Lost Domain Generalization},
author={Ishaan Gulrajani and David Lopez-Paz},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=lQdXeXDoWtI}
}

@article{storkey2009training,
  title={When training and test sets are different: characterizing learning transfer},
  author={Storkey, Amos and others},
  journal={Dataset shift in machine learning},
  volume={30},
  pages={3--28},
  year={2009},
  publisher={Citeseer}
}

@article{invariant_prediction,
 ISSN = {13697412, 14679868},
 URL = {http://www.jstor.org/stable/44682904},
 abstract = {What is the difference between a prediction that is made with a causal model and that with a non-causal model? Suppose that we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a causal model for causal inference: given different experimental settings (e.g. various interventions) we collect all models that do show invariance in their predictive accuracy across settings and interventions. The causal model will be a member of this set of models with high probability. This approach yields valid confidence intervals for the causal relationships in quite general scenarios. We examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable. We further investigate robustness properties of our approach under model misspecification and discuss possible extensions. The empirical properties are studied for various data sets, including large-scale gene perturbation experiments.},
 author = {Jonas Peters and Peter Bühlmann and Nicolai Meinshausen},
 journal = {Journal of the Royal Statistical Society. Series B (Statistical Methodology)},
 number = {5},
 pages = {947--1012},
 publisher = {[Royal Statistical Society, Wiley]},
 title = {Causal inference by using invariant prediction: identification and confidence intervals},
 urldate = {2023-02-13},
 volume = {78},
 year = {2016}
}

@book{quinonero2008dataset,
  title={Dataset shift in machine learning},
  author={Quinonero-Candela, Joaquin and Sugiyama, Masashi and Schwaighofer, Anton and Lawrence, Neil D},
  year={2008},
  publisher={Mit Press}
}





# summary: there are site-specific features in an image (e.g. how metallic tokens indicating laterality appeared in radiographs) but also others. They suggest that CNNs rely on these site indicators through differences in acquisition protocol, image processing / compression rather than on the pathology. 
@article{chest_xray_spurious,
    doi = {10.1371/journal.pmed.1002683},
    author = {Zech, John R. AND Badgeley, Marcus A. AND Liu, Manway AND Costa, Anthony B. AND Titano, Joseph J. AND Oermann, Eric Karl},
    journal = {PLOS Medicine},
    publisher = {Public Library of Science},
    title = {Variable generalization performance of a deep learning model to detect pneumonia in chest radiographs: A cross-sectional study},
    year = {2018},
    month = {11},
    volume = {15},
    url = {https://doi.org/10.1371/journal.pmed.1002683},
    pages = {1-17},
    number = {11},

}

@article{arjovsky2019invariant,
  title={Invariant risk minimization},
  author={Arjovsky, Martin and Bottou, L{\'e}on and Gulrajani, Ishaan and Lopez-Paz, David},
  journal={arXiv preprint arXiv:1907.02893},
  year={2019}
}

@article{bellot2020generalization,
  title={Generalization and invariances in the presence of unobserved confounding},
  author={Bellot, Alexis and van der Schaar, Mihaela},
  journal={arXiv preprint arXiv:2007.10653},
  volume={4},
  year={2020}
}

@inproceedings{krueger2021out,
  title={Out-of-distribution generalization via risk extrapolation (rex)},
  author={Krueger, David and Caballero, Ethan and Jacobsen, Joern-Henrik and Zhang, Amy and Binas, Jonathan and Zhang, Dinghuai and Le Priol, Remi and Courville, Aaron},
  booktitle={International Conference on Machine Learning},
  pages={5815--5826},
  year={2021},
  organization={PMLR}
}

@article{sagawa2019distributionally,
  title={Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization},
  author={Sagawa, Shiori and Koh, Pang Wei and Hashimoto, Tatsunori B and Liang, Percy},
  journal={arXiv preprint arXiv:1911.08731},
  year={2019}
}

@inproceedings{bareinboim2012controlling,
  title={Controlling selection bias in causal inference},
  author={Bareinboim, Elias and Pearl, Judea},
  booktitle={Artificial Intelligence and Statistics},
  pages={100--108},
  year={2012},
  organization={PMLR}
}

@book{peters2017elements,
  title={Elements of causal inference: foundations and learning algorithms},
  author={Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  year={2017},
  publisher={The MIT Press}
}

@article{hysi2018genome,
  title={Genome-wide association meta-analysis of individuals of European ancestry identifies new loci explaining a substantial fraction of hair color variation and heritability},
  author={Hysi, Pirro G and Valdes, Ana M and Liu, Fan and Furlotte, Nicholas A and Evans, David M and Bataille, Veronique and Visconti, Alessia and Hemani, Gibran and McMahon, George and Ring, Susan M and others},
  journal={Nature genetics},
  volume={50},
  number={5},
  pages={652--656},
  year={2018},
  publisher={Nature Publishing Group US New York}
}

@article{subbaswamy2022unifying,
  title={A unifying causal framework for analyzing dataset shift-stable learning algorithms},
  author={Subbaswamy, Adarsh and Chen, Bryant and Saria, Suchi},
  journal={Journal of Causal Inference},
  volume={10},
  number={1},
  pages={64--89},
  year={2022},
  publisher={De Gruyter}
}

@article{gordon2021identifying,
  title={Identifying mixtures of Bayesian network distributions},
  author={Gordon, Spencer L and Mazaheri, Bijan and Rabani, Yuval and Schulman, Leonard J},
  journal={arXiv preprint arXiv:2112.11602},
  year={2021}
}

@incollection{balke1994counterfactual,
  title={Counterfactual probabilities: Computational methods, bounds and applications},
  author={Balke, Alexander and Pearl, Judea},
  booktitle={Uncertainty Proceedings 1994},
  pages={46--54},
  year={1994},
  publisher={Elsevier}
}

@book{pearl1988probabilistic,
  title={Probabilistic reasoning in intelligent systems: networks of plausible inference},
  author={Pearl, Judea},
  year={1988},
  publisher={Morgan kaufmann}
}

@article{schweikert2008empirical,
  title={An empirical analysis of domain adaptation algorithms for genomic sequence analysis},
  author={Schweikert, Gabriele and R{\"a}tsch, Gunnar and Widmer, Christian and Sch{\"o}lkopf, Bernhard},
  journal={Advances in neural information processing systems},
  volume={21},
  year={2008}
}

@article{shimodaira2000improving,
  title={Improving predictive inference under covariate shift by weighting the log-likelihood function},
  author={Shimodaira, Hidetoshi},
  journal={Journal of statistical planning and inference},
  volume={90},
  number={2},
  pages={227--244},
  year={2000},
  publisher={Elsevier}
}

@article{sugiyama2008direct,
  title={Direct importance estimation for covariate shift adaptation},
  author={Sugiyama, Masashi and Suzuki, Taiji and Nakajima, Shinichi and Kashima, Hisashi and B nau, Paul and Kawanabe, Motoaki},
  journal={Annals of the Institute of Statistical Mathematics},
  volume={60},
  number={4},
  pages={699--746},
  year={2008},
  publisher={Springer-Verlag, Berlin/Heidelberg}
}

@inproceedings{muandet2013domain,
  title={Domain generalization via invariant feature representation},
  author={Muandet, Krikamol and Balduzzi, David and Sch{\"o}lkopf, Bernhard},
  booktitle={International conference on machine learning},
  pages={10--18},
  year={2013},
  organization={PMLR}
}

@book{pearl2009causality,
  title={Causality},
  author={Pearl, Judea},
  year={2009},
  publisher={Cambridge university press}
}

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

@article{castanedo2013review,
  title={A review of data fusion techniques},
  author={Castanedo, Federico},
  journal={The scientific world journal},
  volume={2013},
  year={2013},
  publisher={Hindawi}
}

@article{bareinboim2016causal,
  title={Causal inference and the data-fusion problem},
  author={Bareinboim, Elias and Pearl, Judea},
  journal={Proceedings of the National Academy of Sciences},
  volume={113},
  number={27},
  pages={7345--7352},
  year={2016},
  publisher={National Acad Sciences}
}

@article{feldman2008learning,
  title={Learning mixtures of product distributions over discrete domains},
  author={Feldman, Jon and O'Donnell, Ryan and Servedio, Rocco A},
  journal={SIAM Journal on Computing},
  volume={37},
  number={5},
  pages={1536--1564},
  year={2008},
  publisher={SIAM}
}

@inproceedings{chen2019beyond,
  title={Beyond the low-degree algorithm: mixtures of subcubes and their applications},
  author={Chen, Sitan and Moitra, Ankur},
  booktitle={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
  pages={869--880},
  year={2019}
}

@article{scholkopf2012causal,
  title={On causal and anticausal learning},
  author={Sch{\"o}lkopf, Bernhard and Janzing, Dominik and Peters, Jonas and Sgouritsa, Eleni and Zhang, Kun and Mooij, Joris},
  journal={arXiv preprint arXiv:1206.6471},
  year={2012}
}

@article{dexter2020generalization,
  title={Generalization of machine learning approaches to identify notifiable conditions from a statewide health information exchange},
  author={Dexter, Gregory P and Grannis, Shaun J and Dixon, Brian E and Kasthurirathne, Suranga N},
  journal={AMIA Summits on Translational Science Proceedings},
  volume={2020},
  pages={152},
  year={2020},
  publisher={American Medical Informatics Association}
}

@article{janzing2013quantifying,
  title={Quantifying causal influences},
  author={Janzing, Dominik and Balduzzi, David and Grosse-Wentrup, Moritz and Sch{\"o}lkopf, Bernhard},
  journal={The Annals of Statistics},
  volume={41},
  number={5},
  pages={2324--2358},
  year={2013},
  publisher={Institute of Mathematical Statistics}
}

@book{cover1999elements,
  title={Elements of information theory},
  author={Cover, Thomas M},
  year={1999},
  publisher={John Wiley \& Sons}
}

@article{colnet2020causal,
  title={Causal inference methods for combining randomized trials and observational studies: a review},
  author={Colnet, B{\'e}n{\'e}dicte and Mayer, Imke and Chen, Guanhua and Dieng, Awa and Li, Ruohong and Varoquaux, Ga{\"e}l and Vert, Jean-Philippe and Josse, Julie and Yang, Shu},
  journal={arXiv preprint arXiv:2011.08047},
  year={2020}
}

@article{horvitz1952generalization,
  title={A generalization of sampling without replacement from a finite universe},
  author={Horvitz, Daniel G and Thompson, Donovan J},
  journal={Journal of the American statistical Association},
  volume={47},
  number={260},
  pages={663--685},
  year={1952},
  publisher={Taylor \& Francis}
}

@inproceedings{pearl2011transportability,
  title={Transportability of causal and statistical relations: A formal approach},
  author={Pearl, Judea and Bareinboim, Elias},
  booktitle={Twenty-fifth AAAI conference on artificial intelligence},
  year={2011}
}

@misc{CounterfactuallyInvPredictors,
  doi = {10.48550/ARXIV.2207.09768},
  
  url = {https://arxiv.org/abs/2207.09768},
  
  author = {Quinzan, Francesco and Casolo, Cecilia and Muandet, Krikamol and Kilbertus, Niki and Luo, Yucen},
  
  keywords = {Machine Learning (cs.LG), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Computer and information sciences},
  
  title = {Learning Counterfactually Invariant Predictors},
  
  publisher = {arXiv},
  
  year = {2022},
  
  copyright = {Creative Commons Attribution Share Alike 4.0 International}
}

@inproceedings{vorburger2006entropy,
  title={Entropy-based concept shift detection},
  author={Vorburger, Peter and Bernstein, Abraham},
  booktitle={Sixth International Conference on Data Mining (ICDM'06)},
  pages={1113--1118},
  year={2006},
  organization={IEEE}
}



@inproceedings{
veitch2021counterfactual,
title={Counterfactual Invariance to Spurious Correlations in Text Classification},
author={Victor Veitch and Alexander D'Amour and Steve Yadlowsky and Jacob Eisenstein},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=BdKxQp0iBi8}
}

@inproceedings{gordon2021source,
  title={Source identification for mixtures of product distributions},
  author={Gordon, Spencer and Mazaheri, Bijan H and Rabani, Yuval and Schulman, Leonard},
  booktitle={Conference on Learning Theory},
  pages={2193--2216},
  year={2021},
  organization={PMLR}
}