@article{drton2018,
	title        = {Structure learning in graphical models},
	author       = {Drton, Mathias and Maathuis, Marloes H.},
	year         = 2018,
	journal      = {Annual Review of Statistics and Its Application},
	publisher    = {Annual Reviews},
	volume       = 5,
	pages        = {365--393}
}
@article{shah2020,
	title        = {Hardness results for conditional independence testing and related problems},
	author       = {Shah, Rajen D. and Peters, Jonas and Bühlmann, Peter},
	year         = 2020,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 48,
	number       = 3,
	pages        = {1514--1538}
}
@book{anderson1958,
	title        = {An Introduction to Multivariate Statistical Analysis},
	author       = {Anderson, T. W.},
	year         = 1958,
	publisher    = {John Wiley \& Sons}
}
@book{golub1996,
	title        = {Matrix Computations},
	author       = {Golub, Gene H. and Van Loan, Charles F.},
	year         = 1996,
	publisher    = {Johns Hopkins University Press},
	edition      = {3rd}
}
@article{hoerl1970,
	title        = {Ridge regression: Biased estimation for nonorthogonal problems},
	author       = {Hoerl, Arthur E. and Kennard, Robert W.},
	year         = 1970,
	journal      = {Technometrics},
	publisher    = {Taylor \& Francis},
	volume       = 12,
	number       = 1,
	pages        = {55--67}
}
@article{hotelling1936,
	title        = {Relations between two sets of variates},
	author       = {Hotelling, Harold},
	year         = 1936,
	journal      = {Biometrika},
	publisher    = {Oxford University Press},
	volume       = 28,
	number       = {3/4},
	pages        = {321--377}
}
@article{olson1976,
	title        = {On choosing a test statistic in multivariate analysis of variance},
	author       = {Olson, Clark L.},
	year         = 1976,
	journal      = {Psychological Bulletin},
	publisher    = {American Psychological Association},
	volume       = 83,
	number       = 4,
	pages        = {579--586}
}
@book{roy1957,
	title        = {Some Aspects of Multivariate Analysis},
	author       = {Roy, S.~N.},
	year         = 1957,
	publisher    = {John Wiley \& Sons}
}
@article{schatzoff1968,
	title        = {Sensitivity comparisons among tests for the general linear hypothesis in multivariate analysis},
	author       = {Schatzoff, M., Tsao, R., and Roy, S.~N.},
	year         = 1968,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor \& Francis},
	volume       = 63,
	number       = 322,
	pages        = {415--436}
}
@article{shah2018,
	title        = {The hardness of conditional independence testing and the generalized covariance measure},
	author       = {Shah, Rajen D. and Peters, Jonas},
	year         = 2018,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 46,
	number       = 3,
	pages        = {1516--1553}
}
@article{vinod1976,
	title        = {Canonical ridge and econometrics of joint production},
	author       = {Vinod, H.~D.},
	year         = 1976,
	journal      = {Journal of Econometrics},
	publisher    = {Elsevier},
	volume       = 4,
	number       = 2,
	pages        = {147--166}
}
@article{lindquist2008statistical,
	title        = {The statistical analysis of fMRI data},
	author       = {Lindquist, Martin A.},
	year         = 2008,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 23,
	number       = 4,
	pages        = {439--464}
}
@article{runge2019inferring,
	title        = {Inferring causation from time series in Earth system sciences},
	author       = {Runge, Jakob and Nowack, Peer and Kretschmer, Marlene and Flaxman, Seth and Sejdinovic, Dino},
	year         = 2019,
	journal      = {Nature communications},
	publisher    = {Nature Publishing Group},
	volume       = 10,
	number       = 1,
	pages        = 255
}
@book{Kay1998Detection,
	title        = {Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory},
	author       = {Kay, Steven M.},
	year         = 1998,
	publisher    = {Prentice Hall}
}
@book{Muirhead1982Aspects,
	title        = {Aspects of Multivariate Statistical Theory},
	author       = {Muirhead, Robb J.},
	year         = 1982,
	publisher    = {John Wiley \& Sons}
}
@article{Roy1953OnAH,
	title        = {On a heuristic method of test construction and its use in multivariate analysis},
	author       = {Roy, S. N.},
	year         = 1953,
	journal      = {The Annals of Mathematical Statistics},
	volume       = 24,
	number       = 2,
	pages        = {220--238},
	url          = {https://api.semanticscholar.org/CorpusID:122974856}
}
@book{VanTrees1968Detection,
	title        = {Detection, Estimation, and Modulation Theory, Part I},
	author       = {Van Trees, Harry L.},
	year         = 1968,
	publisher    = {John Wiley \& Sons}
}
@article{Wilks1938,
	title        = {The large-sample distribution of the likelihood ratio for testing composite hypotheses},
	author       = {Wilks, S. S.},
	year         = 1938,
	journal      = {The Annals of Mathematical Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 9,
	number       = 1,
	pages        = {60--62}
}
@article{chetty2014geography,
	title        = {Where is the land of opportunity? The geography of intergenerational mobility in the United States},
	author       = {Chetty, Raj and Hendren, Nathaniel and Kline, Patrick and Saez, Emmanuel},
	year         = 2014,
	journal      = {The Quarterly Journal of Economics},
	publisher    = {Oxford University Press},
	volume       = 129,
	number       = 4,
	pages        = {1553--1623}
}
@inproceedings{gretton2005measuring,
	title        = {Measuring statistical dependence with Hilbert-Schmidt norms},
	author       = {Gretton, Arthur and Bousquet, Olivier and Smola, Alexander and Sch{\"o}lkopf, Bernhard},
	year         = 2005,
	booktitle    = {International Conference on Algorithmic Learning Theory},
	pages        = {63--77},
	organization = {Springer}
}
@article{zhang2012,
	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},
	year         = 2012,
	journal      = {Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI)},
	pages        = {804--813}
}
@article{li2022kernel,
	title        = {Kernel dependence regularizers and Gaussian processes with applications to algorithmic fairness},
	author       = {Li, Zhu and P{\'e}rez-Suay, Adri{\'a}n and Camps-Valls, Gustau and Sejdinovic, Dino},
	year         = 2022,
	journal      = {Pattern Recognition},
	publisher    = {Elsevier},
	volume       = 132,
	pages        = 108922
}
@book{hastie2009elements,
	title        = {The elements of statistical learning: data mining, inference, and prediction},
	author       = {Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome H and Friedman, Jerome H},
	year         = 2009,
	publisher    = {Springer},
	volume       = 2
}
@article{girosi1995regularisation,
	title        = {Regularization theory and neural networks architectures},
	author       = {Girosi, Federico and Jones, Michael and Poggio, Tomaso},
	year         = 1995,
	journal      = {Neural computation},
	publisher    = {MIT Press},
	volume       = 7,
	number       = 2,
	pages        = {219--269}
}
@article{cortes2022physics,
	title        = {Physics-aware nonparametric regression models for Earth data analysis},
	author       = {Cort{\'e}s-Andr{\'e}s, Jordi and Camps-Valls, Gustau and Sippel, Sebastian and Sz{\'e}kely, Enik{\H{o}} and Sejdinovic, Dino and Diaz, Emiliano and P{\'e}rez-Suay, Adri{\'a}n and Li, Zhu and Mahecha, Miguel and Reichstein, Markus},
	year         = 2022,
	journal      = {Environmental Research Letters},
	publisher    = {IOP Publishing},
	volume       = 17,
	number       = 5,
	pages        = {054034}
}
@article{bergsma2004testing,
	title        = {Testing conditional independence for continuous random variables},
	author       = {Bergsma, Wicher Pieter},
	year         = 2004,
	journal      = {},
	publisher    = {Eurandom}
}
@book{thomas2006elements,
	title        = {Elements of information theory},
	author       = {Thomas, MTCAJ and Joy, A Thomas},
	year         = 2006,
	publisher    = {Wiley-Interscience}
}
@article{sugiyama2007covariate,
	title        = {Covariate shift adaptation by importance weighted cross validation.},
	author       = {Sugiyama, Masashi and Krauledat, Matthias and M{\"u}ller, Klaus-Robert},
	year         = 2007,
	journal      = {Journal of Machine Learning Research},
	volume       = 8,
	number       = 5
}
@article{sugiyama2008direct,
	title        = {Direct importance estimation for covariate shift adaptation},
	author       = {Sugiyama, Masashi and Suzuki, Taiji and Nakajima, Shinichi and Kashima, Hisashi and Von B{\"u}nau, Paul and Kawanabe, Motoaki},
	year         = 2008,
	journal      = {Annals of the Institute of Statistical Mathematics},
	publisher    = {Springer},
	volume       = 60,
	pages        = {699--746}
}
@article{hocking1976biometrics,
	title        = {A Biometrics invited paper. The analysis and selection of variables in linear regression},
	author       = {Hocking, Ronald R},
	year         = 1976,
	journal      = {Biometrics},
	publisher    = {JSTOR},
	pages        = {1--49}
}
@article{Rao1969,
	title        = {Partial canonical correlations},
	author       = {Rao, B. Raja},
	year         = 1969,
	month        = {Jun},
	day          = {01},
	journal      = {Trabajos de estadistica y de investigacion operativa},
	volume       = 20,
	number       = 2,
	pages        = {211--219},
	doi          = {10.1007/BF03028532},
	issn         = {0041-0241},
	url          = {https://doi.org/10.1007/BF03028532}
}
@article{bartlett1941statistical,
	title        = {The statistical significance of canonical correlations},
	author       = {Bartlett, Maurice S},
	year         = 1941,
	journal      = {Biometrika},
	publisher    = {JSTOR},
	volume       = 32,
	number       = 1,
	pages        = {29--37}
}
@misc{kay1993fundamentals,
	title        = {Fundamentals of Statistical Signal Processing: Estimation Theory},
	author       = {Kay, Steven M},
	year         = 1993,
	publisher    = {Prentice Hall}
}
@article{Mises1929,
	title        = {Praktische Verfahren der Gleichungsauflösung .},
	author       = {Mises, R. V. and Pollaczek-Geiringer, H.},
	year         = 1929,
	journal      = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik},
	volume       = 9,
	number       = 2,
	pages        = {152--164},
	doi          = {https://doi.org/10.1002/zamm.19290090206},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19290090206},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/zamm.19290090206}
}
@article{macmillan2002signal,
	title        = {Signal detection theory},
	author       = {Macmillan, Neil A},
	year         = 2002,
	journal      = {Stevens' handbook of experimental psychology: Methodology in experimental psychology},
	volume       = 4,
	pages        = {43--90}
}
@article{nogueira2022methods,
	title        = {Methods and tools for causal discovery and causal inference},
	author       = {Nogueira, Ana Rita and Pugnana, Andrea and Ruggieri, Salvatore and Pedreschi, Dino and Gama, Jo{\~a}o},
	year         = 2022,
	journal      = {Wiley interdisciplinary reviews: data mining and knowledge discovery},
	publisher    = {Wiley Online Library},
	volume       = 12,
	number       = 2,
	pages        = {e1449}
}
@article{chow1960tests,
	title        = {Tests of equality between sets of coefficients in two linear regressions},
	author       = {Chow, Gregory C},
	year         = 1960,
	journal      = {Econometrica: Journal of the Econometric Society},
	publisher    = {JSTOR},
	pages        = {591--605}
}
@article{janzing2013quantifying,
	title        = {Quantifying causal influences},
	author       = {Janzing, Dominik and Balduzzi, David and Grosse-Wentrup, Moritz and Sch{\"o}lkopf, Bernhard},
	year         = 2013,
	journal      = {}
}
@book{sugiyama2012machine,
	title        = {Machine learning in non-stationary environments: Introduction to covariate shift adaptation},
	author       = {Sugiyama, Masashi and Kawanabe, Motoaki},
	year         = 2012,
	publisher    = {MIT press}
}
@book{bowden1990instrumental,
	title        = {Instrumental variables},
	author       = {Bowden, Roger J and Turkington, Darrell A},
	year         = 1990,
	publisher    = {Cambridge university press}
}
@article{Arenas-Garcia1015,
	title        = {Sparse and kernel {OPLS} feature extraction based on eigenvalue problem solving},
	author       = {Arenas-García, Jerónimo and Gómez-Verdejo, Vanessa},
	year         = 2015,
	month        = {05},
	journal      = {Pattern Recognition},
	volume       = 48,
	pages        = {},
	doi1         = {10.1016/j.patcog.2014.12.002}
}
@article{Rothenhäusler2018,
	title        = {Anchor Regression: Heterogeneous Data Meet Causality},
	author       = {Rothenhäusler, Dominik and Bühlmann, Peter and Meinshausen, Nicolai and Peters, Jonas},
	year         = 2018,
	month        = {01},
	journal      = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	volume       = 83,
	pages        = {},
	doi1         = {10.1111/rssb.12398}
}
@article{Po-Chedley2022,
	title        = {Internal variability and forcing influence model-satellite differences in the rate of tropical tropospheric warming},
	author       = {Po-Chedley, Stephen and Fasullo, John and Siler, Nicholas and Labe, Zachary and Barnes, Elizabeth and Bonfils, Céline and Santer, Benjamin},
	year         = 2022,
	month        = 11,
	journal      = {Proceedings of the National Academy of Sciences of the United States of America},
	volume       = 119,
	pages        = {e2209431119},
	doi1         = {10.1073/pnas.2209431119}
}
@article{Sun2011,
	title        = {Canonical Correlation Analysis for Multilabel Classification: A Least-Squares Formulation, Extensions, and Analysis},
	author       = {Sun, Liang and Ji, Shuiwang and Ye, Jieping},
	year         = 2011,
	month        = {01},
	journal      = {IEEE transactions on pattern analysis and machine intelligence},
	volume       = 33,
	pages        = {194--200},
	doi1         = {10.1109/TPAMI.2010.160}
}
@article{Arenas-Garcia2013,
	title        = {Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods},
	author       = {Arenas-Garcia, Jeronimo and Petersen, Kaare Brandt and Camps-Valls, Gustavo and Hansen, Lars Kai},
	year         = 2013,
	journal      = {IEEE Signal Processing Magazine},
	volume       = 30,
	number       = 4,
	pages        = {16--29},
	doi1         = {10.1109/MSP.2013.2250591}
}
@article{Borga1998,
	title        = {A Unified Approach to {PCA}, {PLS}, {MLR} and {CCA}},
	author       = {Borga, Magnus and Landelius, Tomas and Knutsson, Hans},
	year         = 1998,
	month        = {02},
	journal      = {},
	pages        = {}
}
@article{Chen2012,
	title        = {Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection},
	author       = {Chen, Lisha and Huang, Jianhua},
	year         = 2012,
	month        = 12,
	journal      = {JASA. Journal of the American Statistical Association},
	volume       = 107,
	pages        = {},
	doi1         = {10.1080/01621459.2012.734178}
}
@article{Yang2021,
	title        = {A Survey on Canonical Correlation Analysis},
	author       = {Yang, Xinghao and Liu, Weifeng and Liu, Wei and Tao, Dacheng},
	year         = 2021,
	journal      = {IEEE Transactions on Knowledge and Data Engineering},
	volume       = 33,
	number       = 6,
	pages        = {2349--2368},
	doi1         = {10.1109/TKDE.2019.2958342}
}
@article{Arenas-Garcia2008,
	title        = {Efficient Kernel Orthonormalized {PLS} for Remote Sensing Applications},
	author       = {Arenas-Garcia, Jeronimo and Camps-Valls, Gustau},
	year         = 2008,
	month        = 11,
	journal      = {Geoscience and Remote Sensing, IEEE Transactions on},
	volume       = 46,
	pages        = {2872--2881},
	doi1         = {10.1109/TGRS.2008.918765}
}
@article{Brian2015,
	title        = {Dynamical Adjustment of the Northern Hemisphere Surface Air Temperature Field: Methodology and Application to Observations},
	author       = {Brian V. Smoliak and John M. Wallace and Pu Lin and Qiang Fu},
	year         = 2015,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 28,
	number       = 4,
	pages        = {1613--1629},
	doi1         = {https://%doi.org/10.1175/JCLI-D-14-00111.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/28/4/jcli-d-14-00111.1.xml}
}
@inproceedings{Shi2023,
	title        = {Learning Nonlinear Causal Effect via Kernel Anchor Regression},
	author       = {Shi, Wenqi and Xu, Wenkai},
	year         = 2023,
	month        = {31 Jul--04 Aug},
	booktitle    = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 216,
	pages        = {1942--1952},
	url1         = {https://proceedings.mlr.press/v216/shi23a.html},
	editor1      = {Evans, Robin J. and Shpitser, Ilya},
	pdf1         = {https://proceedings.mlr.press/v216/shi23a/shi23a.pdf}
}
@article{Sippel2019,
	title        = {Uncovering the Forced Climate Response from a Single Ensemble Member Using Statistical Learning},
	author       = {Sebastian Sippel and Nicolai Meinshausen and Anna Merrifield and Flavio Lehner and Angeline G. Pendergrass and Erich Fischer and Reto Knutti},
	year         = 2019,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 32,
	number       = 17,
	pages        = {5677--5699},
	doi1         = {https://%doi.org/10.1175/JCLI-D-18-0882.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/32/17/jcli-d-18-0882.1.xml}
}
@article{Smoliak2015,
	title        = {Dynamical Adjustment of the Northern Hemisphere Surface Air Temperature Field: Methodology and Application to Observations},
	author       = {Brian V. Smoliak and John M. Wallace and Pu Lin and Qiang Fu},
	year         = 2015,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 28,
	number       = 4,
	pages        = {1613--1629},
	doi1         = {https://%doi.org/10.1175/JCLI-D-14-00111.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/28/4/jcli-d-14-00111.1.xml}
}
@inproceedings{Oberst2021,
	title        = {Regularizing towards causal invariance: Linear models with proxies},
	author       = {Oberst, Michael and Thams, Nikolaj and Peters, Jonas and Sontag, David},
	year         = 2021,
	booktitle    = {International Conference on Machine Learning},
	pages        = {8260--8270},
	organization = {PMLR}
}
@book{Peters2017,
	title        = {Elements of Causal Inference: Foundations and Learning Algorithms},
	author       = {Peters, Jonas and Janzing, Dominik and Schlkopf, Bernhard},
	year         = 2017,
	publisher    = {The MIT Press},
	isbn         = {0262037319}
}
@article{Shen2021,
	title        = {Towards Out-Of-Distribution Generalization: A Survey},
	author       = {Zheyan Shen and Jiashuo Liu and Yue He and Xingxuan Zhang and Renzhe Xu and Han Yu and Peng Cui},
	year         = 2021,
	journal      = {ArXiv},
	volume       = {abs/2108.13624},
	url1         = {https://api.semanticscholar.org/CorpusID:237364121}
}
@misc{Arjovsky2019,
	title        = {Invariant Risk Minimization},
	author       = {Martin Arjovsky and Léon Bottou and Ishaan Gulrajani and David Lopez-Paz},
	year         = 2020,
	eprint       = {1907.02893},
	archiveprefix = {arXiv},
	primaryclass = {stat.ML}
}
@inproceedings{Meinshausen2018,
	title        = {CAUSALITY FROM A DISTRIBUTIONAL ROBUSTNESS POINT OF VIEW},
	author       = {Meinshausen, Nicolai},
	year         = 2018,
	booktitle    = {2018 IEEE Data Science Workshop (DSW)},
	volume       = {},
	number       = {},
	pages        = {6--10},
	doi1         = {10.1109/DSW.2018.8439889}
}
@article{Peters2016,
	title        = {Causal Inference by using Invariant Prediction: {I}dentification and Confidence Intervals},
	author       = {Peters, Jonas and Bühlmann, Peter and Meinshausen, Nicolai},
	year         = 2016,
	month        = 10,
	journal      = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
	volume       = 78,
	number       = 5,
	pages        = {947--1012},
	issn         = {1369-7412},
	doi1         = {10.1111/rssb.12167},
	url1         = {https://%doi.org/10.1111/rssb.12167},
	eprint1      = {https://academic.oup.com/jrsssb/article-pdf/78/5/947/49235444/jrsssb\_78\_5\_947.pdf}
}
@article{Buhlmann2020,
	title        = {Invariance, causality and robustness},
	author       = {B{\"u}hlmann, Peter},
	year         = 2020,
	journal      = {ArXiv}
}
@inproceedings{Xu2008,
	title        = {Robust Regression and Lasso},
	author       = {Xu, Huan and Caramanis, Constantine and Mannor, Shie},
	year         = 2008,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 21,
	pages        = {},
	url1         = {https://proceedings.neurips.cc/paper_files/paper/2008/file/24681928425f5a9133504de568f5f6df-Paper.pdf},
	editor1      = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou}
}
@article{Newey2003,
	title        = {Instrumental Variable Estimation of Nonparametric Models},
	author       = {Newey, Whitney K. and Powell, James L.},
	year         = 2003,
	journal      = {Econometrica},
	volume       = 71,
	number       = 5,
	pages        = {1565--1578},
	doi1         = {https://%doi.org/10.1111/1468-0262.00459},
	url1         = {https://onlinelibrary.wiley.com/%doi/abs/10.1111/1468-0262.00459}
}
@article{Abdi2010,
	title        = {Partial least squares regression and projection on latent structure regression ({PLS} Regression)},
	author       = {Abdi, Hervé},
	year         = 2010,
	month        = {01},
	journal      = {Wiley Interdisciplinary Reviews: Computational Statistics},
	volume       = 2,
	pages        = {97--106},
	doi1         = {10.1002/wics.51}
}
@article{Barker2003,
	title        = {Partial least squares for discrimination},
	author       = {Barker, Matthew and Rayens, William},
	year         = 2003,
	journal      = {Journal of Chemometrics},
	volume       = 17,
	number       = 3,
	pages        = {166--173},
	doi1         = {https://%doi.org/10.1002/cem.785},
	url1         = {https://analyticalsciencejournals.onlinelibrary.wiley.com/%doi/abs/10.1002/cem.785}
}
@article{Izenman1975,
	title        = {Reduced-rank regression for the multivariate linear model},
	author       = {Alan Julian Izenman},
	year         = 1975,
	journal      = {Journal of Multivariate Analysis},
	volume       = 5,
	number       = 2,
	pages        = {248--264},
	doi1         = {https://%doi.org/10.1016/0047-259X(75)90042-1},
	issn1        = {0047-259X},
	url1         = {https://www.sciencedirect.com/science/article/pii/0047259X75900421}
}
@article{Sippel2021,
	title        = {Robust detection of forced warming in the presence of potentially large climate variability},
	author       = {Sebastian Sippel  and Nicolai Meinshausen  and Enikő Székely  and Erich Fischer  and Angeline G. Pendergrass  and Flavio Lehner  and Reto Knutti},
	year         = 2021,
	journal      = {Science Advances},
	volume       = 7,
	number       = 43,
	pages        = {eabh4429},
	doi1         = {10.1126/sciadv.abh4429},
	url1         = {https://www.science.org/%doi/abs/10.1126/sciadv.abh4429}
}
@article{Mukherjee2011,
	title        = {Reduced rank ridge regression and its kernel extensions},
	author       = {Mukherjee, Ashin and Zhu, Ji},
	year         = 2011,
	journal      = {Statistical Analysis and Data Mining: The ASA Data Science Journal},
	volume       = 4,
	number       = 6,
	pages        = {612--622},
	doi1         = {https://%doi.org/10.1002/sam.10138},
	url1         = {https://onlinelibrary.wiley.com/%doi/abs/10.1002/sam.10138}
}
@misc{Szekely2022,
	title        = {Robust detection and attribution of climate change under interventions},
	author       = {Székely, Enikő and Sippel, Sebastian and Meinshausen, Nicolai and Obozinski, Guillaume and Knutti, Reto},
	year         = 2022,
	month        = 12,
	pages        = {},
	archiveprefix = {arXiv},
	doi1         = {10.48550/arXiv.2212.04905}
}
@article{Deser2020,
	title        = {Insights from Earth system model initial-condition large ensembles and future prospects},
	author       = {Deser, C. and Lehner, F. and Rodgers, K. and Ault, Toby and Delworth, T. and DiNezio, P. and Fiore, A. and Frankignoul, Claude and Fyfe, J. and Horton, Daniel and Kay, Jennifer and Knutti, Reto and Lovenduski, N. and Marotzke, J. and McKinnon, K. and Minobe, S. and Randerson, James and Screen, J. and Simpson, Isla and Ting, Miao},
	year         = 2020,
	month        = {04},
	journal      = {Nature Climate Change},
	volume       = 10,
	pages        = {277--286},
	doi1         = {10.1038/s41558-020-0731-2}
}
@article{Baiocchi2014,
	title        = {Instrumental variable methods for causal inference},
	author       = {Baiocchi, Michael and Cheng, Jing and Small, Dylan S.},
	year         = 2014,
	journal      = {Statistics in Medicine},
	volume       = 33,
	number       = 13,
	pages        = {2297--2340},
	doi1         = {https://%doi.org/10.1002/sim.6128},
	url1         = {https://onlinelibrary.wiley.com/%doi/abs/10.1002/sim.6128}
}
@article{Hoerl2000,
	title        = {Ridge Regression: Biased Estimation for Nonorthogonal Problems},
	year         = 2000,
	journal      = {Technometrics},
	publisher    = {[Taylor & Francis, Ltd., American Statistical Association, American Society for Quality]},
	volume       = 42,
	number       = 1,
	pages        = {80--86},
	issn1        = {00401706},
	url1         = {http://www.jstor.org/stable/1271436}
}
@article{Tibshirani1996,
	title        = {Regression Shrinkage and Selection via the Lasso},
	author       = {Robert Tibshirani},
	year         = 1996,
	journal      = {Journal of the Royal Statistical Society. Series B (Methodological)},
	publisher    = {[Royal Statistical Society, Wiley]},
	volume       = 58,
	number       = 1,
	pages        = {267--288},
	issn1        = {00359246},
	url1         = {http://www.jstor.org/stable/2346178}
}
@article{Hegerl1996,
	title        = {Detecting Greenhouse-Gas-Induced Climate Change with an Optimal Fingerprint Method},
	author       = {Gabriele C.  Hegerl and Hans  von Storch and Klaus  Hasselmann and Benjamin D.  Santer and Ulrich  Cubasch and Philip D.  Jones},
	year         = 1996,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 9,
	number       = 10,
	pages        = {2281--2306},
	doi1         = {10.1175/1520-0442(1996)009<2281:DGGICC>2.0.CO;2},
	url1         = {https://journals.ametsoc.org/view/journals/clim/9/10/1520-0442_1996_009_2281_dggicc_2_0_co_2.xml}
}
@article{kook2021,
	title        = {Distributional anchor regression},
	author       = {Kook, Lucas and Sick, Beate and B{\"u}hlmann, Peter},
	year         = 2022,
	journal      = {Statistics and Computing},
	publisher    = {Springer}
}
@article{Yuan2006,
	title        = {Model Selection and Estimation in Regression With Grouped Variables},
	author       = {Yuan, Ming and Lin, Yi},
	year         = 2006,
	month        = {02},
	journal      = {Journal of the Royal Statistical Society Series B},
	volume       = 68,
	pages        = {49--67},
	doi1         = {10.1111/j.1467-9868.2005.00532.x}
}
@article{Zou2005,
	title        = {Regularization and variable selection via the elastic net},
	author       = {Zou, Hui and Hastie, Trevor},
	year         = 2005,
	journal      = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	volume       = 67,
	number       = 2,
	pages        = {301--320},
	doi1         = {https://%doi.org/10.1111/j.1467-9868.2005.00503.x},
	url1         = {https://rss.onlinelibrary.wiley.com/%doi/abs/10.1111/j.1467-9868.2005.00503.x}
}
@article{Eyring2016,
	title        = {Overview of the {Coupled} {Model} {Intercomparison} {Project} {Phase} 6 ({CMIP}6) experimental design and organization},
	author       = {Eyring, Veronika and Bony, Sandrine and Meehl, Gerald A. and Senior, Catherine A. and Stevens, Bjorn and Stouffer, Ronald J. and Taylor, Karl E.},
	year         = 2016,
	month        = may,
	journal      = {Geoscientific Model Development},
	volume       = 9,
	number       = 5,
	pages        = {1937--1958},
	doi1         = {10.5194/gmd-9-1937-2016},
	url1         = {https://www.geosci-model-dev.net/9/1937/2016/}
}
@article{Taylor2011,
	title        = {An overview of {CMIP}5 and the experiment design},
	author       = {Taylor, Karl E and Stouffer, Ronald J and Meehl, Gerald A},
	year         = 2011,
	journal      = {Bulletin of the American Meteorological Society},
	volume       = 93,
	number       = 4,
	pages        = {485--498},
	note         = {Publisher: American Meteorological Society},
	doi1         = {10.1175/BAMS-D-11-00094.1},
	issn1        = {0003-0007},
	url1         = {http://dx.%doi.org/10.1175/BAMS-D-11-00094.1}
}
@article{Salcedo2020,
	title        = {Machine learning information fusion in Earth observation: A comprehensive review of methods, applications and data sources},
	author       = {S. Salcedo-Sanz and P. Ghamisi and M. Piles and M. Werner and L. Cuadra and A. Moreno-Martínez and E. Izquierdo-Verdiguier and J. Muñoz-Marí and Amirhosein Mosavi and G. Camps-Valls},
	year         = 2020,
	journal      = {Information Fusion},
	volume       = 63,
	pages        = {256--272},
	doi1         = {https://%doi.org/10.1016/j.inffus.2020.07.004},
	issn1        = {1566-2535},
	url1         = {https://www.sciencedirect.com/science/article/pii/S1566253520303171}
}
@article{Parsons2020,
	title        = {Magnitudes and Spatial Patterns of Interdecadal Temperature Variability in {CMIP}6},
	author       = {Parsons, Luke A. and Brennan, M. Kathleen and Wills, Robert C.J. and Proistosescu, Cristian},
	year         = 2020,
	journal      = {Geophysical Research Letters},
	volume       = 47,
	number       = 7,
	pages        = {e2019GL086588},
	doi1         = {https://%doi.org/10.1029/2019GL086588},
	url1         = {https://agupubs.onlinelibrary.wiley.com/%doi/abs/10.1029/2019GL086588},
	note1        = {e2019GL086588 2019GL086588}
}
@article{Chernozhukov2017,
	title        = {Double/Debiased/Neyman Machine Learning of Treatment Effects},
	author       = {Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney},
	year         = 2017,
	month        = may,
	journal      = {American Economic Review},
	volume       = 107,
	number       = 5,
	pages        = {261--65},
	doi1         = {10.1257/aer.p20171038},
	url1         = {https://www.aeaweb.org/articles?id=10.1257/aer.p20171038}
}
@article{Zhou2023,
	title        = {Domain Generalization: A Survey},
	author       = {Zhou, Kaiyang and Liu, Ziwei and Qiao, Yu and Xiang, Tao and Loy, Chen Change},
	year         = 2023,
	month        = apr,
	journal      = {IEEE Trans. Pattern Anal. Mach. Intell.},
	publisher    = {IEEE Computer Society},
	address      = {USA},
	volume       = 45,
	number       = 4,
	pages        = {4396–4415},
	doi1         = {10.1109/TPAMI.2022.3195549},
	issn1        = {0162-8828},
	url1         = {https://%doi.org/10.1109/TPAMI.2022.3195549}
}
@inproceedings{Namkoong2016,
	title        = {Stochastic Gradient Methods for Distributionally Robust Optimization with f-divergences},
	author       = {Namkoong, Hongseok and Duchi, John C},
	year         = 2016,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 29,
	pages        = {},
	url2         = {https://proceedings.neurips.cc/paper_files/paper/2016/file/4588e674d3f0faf985047d4c3f13ed0d-Paper.pdf},
	editor1      = {D. Lee and M. Sugiyama and U. Luxburg and I. Guyon and R. Garnett}
}
@article{Esfahani2015,
	title        = {Data-Driven Distributionally Robust Optimization Using the {W}asserstein Metric: Performance Guarantees and Tractable Reformulations},
	author       = {Esfahani, Peyman and Kuhn, Daniel},
	year         = 2015,
	month        = {05},
	journal      = {Mathematical Programming},
	volume       = 171,
	pages        = {},
	doi1         = {10.1007/s10107-017-1172-1}
}
@article{Zhuang2021,
	title        = {A Comprehensive Survey on Transfer Learning},
	author       = {Fuzhen Zhuang and Zhiyuan Qi and Keyu Duan and Dongbo Xi and Yongchun Zhu and Hengshu Zhu and Hui Xiong and Qing He},
	year         = 2021,
	month        = jan,
	journal      = {Proceedings of the IEEE},
	publisher    = {Institute of Electrical and Electronics Engineers Inc.},
	volume       = 109,
	number       = 1,
	pages        = {43--76},
	doi1         = {10.1109/JPROC.2020.3004555},
	issn1        = {0018-9219}
}
@article{Desole2006,
	title        = {Low-Frequency Variations of Surface Temperature in Observations and Simulations},
	author       = {Timothy DelSole},
	year         = 2006,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 19,
	number       = 18,
	pages        = {4487--4507},
	doi1         = {10.1175/JCLI3879.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/19/18/jcli3879.1.xml}
}
@article{Kociuba2015,
	title        = {Inability of {CMIP}5 Models to Simulate Recent Strengthening of the Walker Circulation: Implications for Projections},
	author       = {Greg Kociuba and Scott B. Power},
	year         = 2015,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 28,
	number       = 1,
	pages        = {20--35},
	doi1         = {10.1175/JCLI-D-13-00752.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/28/1/jcli-d-13-00752.1.xml}
}
@article{Anson2017,
	title        = {Comparison of Low-Frequency Internal Climate Variability in {CMIP}5 Models and Observations},
	author       = {Anson H. Cheung and Michael E. Mann and Byron A. Steinman and Leela M. Frankcombe and Matthew H. England and Sonya K. Miller},
	year         = 2017,
	journal      = {Journal of Climate},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 30,
	number       = 12,
	pages        = {4763--4776},
	doi1         = {10.1175/JCLI-D-16-0712.1},
	url1         = {https://journals.ametsoc.org/view/journals/clim/30/12/jcli-d-16-0712.1.xml}
}
@article{Mcgregor2018,
	title        = {Model tropical Atlantic biases underpin diminished Pacific decadal variability},
	author       = {Mcgregor, Shayne and Stuecker, Malte and Kajtar, Jules and England, Matthew and Collins, M.},
	year         = 2018,
	month        = {06},
	journal      = {Nature Climate Change},
	volume       = 8,
	pages        = {},
	doi1         = {10.1038/s41558-018-0163-4}
}
@article{Borchani2015,
	title        = {A survey on multi-output regression},
	author       = {Borchani, Hanen and Varando, Gherardo and Bielza, Concha and Larranaga, Pedro},
	year         = 2015,
	month        = {07},
	journal      = {Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery},
	volume       = 5,
	pages        = {},
	doi          = {10.1002/widm.1157}
}
@book{Csurka2022,
	title        = {Domain Generalization},
	author       = {Csurka, Gabriela and Hospedales, Timothy M. and Salzmann, Mathieu and Tommasi, Tatiana},
	year         = 2022,
	booktitle    = {Visual Domain Adaptation in the Deep Learning Era},
	publisher    = {Springer International Publishing},
	address      = {Cham},
	pages        = {85--97},
	doi1         = {10.1007/978-3-031-79175-8_7},
	isbn1        = {978-3-031-79175-8},
	url1         = {https://%doi.org/10.1007/978-3-031-79175-8_7}
}
@book{Csurka2017,
	title        = {Domain Adaptation in Computer Vision Applications},
	author       = {Csurka, Gabriela},
	year         = 2017,
	month        = {01},
	publisher    = {Springer},
	pages        = {},
	doi1         = {10.1007/978-3-319-58347-1},
	isbn1        = {978-3-319-58346-4}
}
@inproceedings{Zhang2021,
	title        = {An empirical framework for domain generalization in clinical settings},
	author       = {Zhang, Haoran and Dullerud, Natalie and Seyyed-Kalantari, Laleh and Morris, Quaid and Joshi, Shalmali and Ghassemi, Marzyeh},
	year         = 2021,
	booktitle    = {Proceedings of the Conference on Health, Inference, and Learning},
	location     = {Virtual Event, USA},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	series       = {CHIL '21},
	pages        = {279–290},
	doi1         = {10.1145/3450439.3451878},
	isbn1        = 9781450383592,
	url1         = {https://%doi.org/10.1145/3450439.3451878}
}
@article{Tuia2016,
	title        = {Domain Adaptation for the Classification of Remote Sensing Data: An Overview of Recent Advances},
	author       = {Tuia, Devis and Persello, Claudio and Bruzzone, Lorenzo},
	year         = 2016,
	journal      = {IEEE Geoscience and Remote Sensing Magazine},
	volume       = 4,
	number       = 2,
	pages        = {41--57},
	doi2         = {10.1109/MGRS.2016.2548504}
}
@inbook{Kellenberger2021,
	title        = {Deep Domain Adaptation in Earth Observation},
	author       = {Kellenberger, Benjamin and Tasar, Onur and Bhushan Damodaran, Bharath and Courty, Nicolas and Tuia, Devis},
	year         = 2021,
	booktitle    = {Deep Learning for the Earth Sciences},
	publisher    = {John Wiley \& Sons, Ltd},
	pages        = {90--104},
	chapter      = 7,
	doi1         = {https://%doi.org/10.1002/9781119646181.ch7},
	isbn1        = 9781119646181,
	url1         = {https://onlinelibrary.wiley.com/%doi/abs/10.1002/9781119646181.ch7}
}
@book{buhlmann2011statistics,
	title        = {Statistics for high-dimensional data: methods, theory and applications},
	author       = {B{\"u}hlmann, Peter and Van De Geer, Sara},
	year         = 2011,
	publisher    = {Springer Science \& Business Media}
}
@article{candes2007dantzig,
	title        = {The Dantzig selector: Statistical estimation when p is much larger than n},
	author       = {Emmanuel Candes and Terence Tao},
	year         = 2007,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 35,
	number       = 6,
	pages        = {2313 -- 2351},
	keywords     = {geometry in high dimensions, ideal estimation, ℓ_1-minimization, linear programming, Model selection, Oracle inequalities, random matrices, restricted orthonormality, sparse solutions to underdetermined systems, Statistical linear model},
	doi2         = {10.1214/009053606000001523},
	url2         = {https://doi.org/10.1214/009053606000001523}
}
@inproceedings{Sun2009,
	title        = {On the equivalence between canonical correlation analysis and orthonormalized partial least squares},
	author       = {Sun, Liang and Ji, Shuiwang and Yu, Shipeng and Ye, Jieping},
	year         = 2009,
	booktitle    = {Proceedings of the 21st International Joint Conference on Artificial Intelligence},
	location     = {Pasadena, California, USA},
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	series       = {IJCAI'09},
	pages        = {1230–1235},
	abstract     = {Canonical correlation analysis (CCA) and partial least squares (PLS) are well-known techniques for feature extraction from two sets of multi-dimensional variables. The fundamental difference between CCA and PLS is that CCA maximizes the correlation while PLS maximizes the covariance. Although both CCA and PLS have been applied successfully in various applications, the intrinsic relationship between them remains unclear. In this paper, we attempt to address this issue by showing the equivalence relationship between CCA and orthonormalized partial least squares (OPLS), a variant of PLS. We further extend the equivalence relationship to the case when regularization is employed for both sets of variables. In addition, we show that the CCA projection for one set of variables is independent of the regularization on the other set of variables. We have performed experimental studies using both synthetic and real data sets and our results confirm the established equivalence relationship. The presented analysis provides novel insights into the connection between these two existing algorithms as well as the effect of the regularization.},
	numpages     = 6
}
@article{Christiansen2022,
	title        = {A Causal Framework for Distribution Generalization},
	author       = {Christiansen, Rune and Pfister, Niklas and Jakobsen, Martin Emil and Gnecco, Nicola and Peters, Jonas},
	year         = 2022,
	month        = {oct},
	journal      = {IEEE Trans. Pattern Anal. Mach. Intell.},
	publisher    = {IEEE Computer Society},
	address      = {USA},
	volume       = 44,
	number       = 10,
	pages        = {6614–6630},
	doi          = {10.1109/TPAMI.2021.3094760},
	issn         = {0162-8828},
	url          = {https://doi.org/10.1109/TPAMI.2021.3094760},
	issue_date   = {Oct. 2022},
	numpages     = 17
}
@article{Jakobsen2021,
	title        = {{Distributional robustness of K-class estimators and the PULSE}},
	author       = {Jakobsen, Martin Emil and Peters, Jonas},
	year         = 2021,
	month        = 10,
	journal      = {The Econometrics Journal},
	volume       = 25,
	number       = 2,
	pages        = {404--432},
	doi          = {10.1093/ectj/utab031},
	issn         = {1368-4221},
	url          = {https://doi.org/10.1093/ectj/utab031},
	eprint       = {https://academic.oup.com/ectj/article-pdf/25/2/404/43772884/utab031.pdf}
}
@article{Haavelmo1943TheSI,
	title        = {The Statistical Implications of a System of Simultaneous Equations},
	author       = {Trygve Haavelmo},
	year         = 1943,
	journal      = {Econometrica},
	volume       = 11,
	pages        = 1,
	url          = {https://api.semanticscholar.org/CorpusID:155386145}
}
@article{SSB19,
	title        = {Transfer learning of deep neural network representations for fMRI decoding},
	author       = {Svanera, Michele and Savardi, Mattia and Benini, Sergio and Signoroni, Alberto and Raz, Gal and Hendler, Talma and Muckli, Lars and Goebel, Rainer and Valente, Giancarlo},
	year         = 2019,
	journal      = {bioRxiv},
	publisher    = {Cold Spring Harbor Laboratory},
	doi          = {10.1101/535377},
	url          = {https://www.biorxiv.org/content/early/2019/02/04/535377},
	elocation-id = 535377,
	eprint       = {https://www.biorxiv.org/content/early/2019/02/04/535377.full.pdf}
}
@article{scikit-learn,
	title        = {Scikit-learn: Machine Learning in {P}ython},
	author       = {Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
	year         = 2011,
	journal      = {Journal of Machine Learning Research},
	volume       = 12,
	pages        = {2825--2830}
}
@article{Schatzoff1966SensitivityCA,
	title        = {Sensitivity Comparisons among Tests of the General Linear Hypothesis},
	author       = {Martin Schatzoff},
	year         = 1966,
	journal      = {Journal of the American Statistical Association},
	volume       = 61,
	pages        = {415--435},
	url          = {https://api.semanticscholar.org/CorpusID:120953066}
}
@article{Olson1974ComparativeRO,
	title        = {Comparative Robustness of Six Tests in Multivariate Analysis of Variance},
	author       = {C. L. Olson},
	year         = 1974,
	journal      = {Journal of the American Statistical Association},
	volume       = 69,
	pages        = {894--908},
	url          = {https://api.semanticscholar.org/CorpusID:122378412}
}
@article{Shah2018TheHO,
	title        = {The hardness of conditional independence testing and the generalised covariance measure},
	author       = {Rajen Dinesh Shah and J. Peters},
	year         = 2018,
	journal      = {The Annals of Statistics},
	url          = {https://api.semanticscholar.org/CorpusID:88516900}
}
@inproceedings{Madow1959AnIT,
	title        = {An Introduction to Multivariate Statistical Analysis},
	author       = {William G. Madow and T. Anderson},
	year         = 1959,
	booktitle    = {An Introduction to Multivariate Statistical Analysis},
	url          = {https://api.semanticscholar.org/CorpusID:121297223}
}
@inproceedings{Johnson1983AppliedMS,
	title        = {Applied Multivariate Statistical Analysis},
	author       = {Richard A. Johnson and Dean W. Wichern},
	year         = 1983,
	booktitle    = {Applied Multivariate Statistical Analysis},
	url          = {https://api.semanticscholar.org/CorpusID:122308290}
}
@inproceedings{Bilodeau1999TheoryOM,
	title        = {Theory of multivariate statistics},
	author       = {Martin Bilodeau and David Brenner},
	year         = 1999,
	booktitle    = {Theory of multivariate statistics},
	url          = {https://api.semanticscholar.org/CorpusID:117047324}
}
@article{Fujikoshi1988ComparisonOP,
	title        = {Comparison of powers of a class of tests for multivariate linear hypothesis and independence},
	author       = {Yasunori Fujikoshi},
	year         = 1988,
	journal      = {Journal of Multivariate Analysis},
	volume       = 26,
	pages        = {48--58},
	url          = {https://api.semanticscholar.org/CorpusID:120587656}
}
@book{pearl2009causality,
	title        = {Causality},
	author       = {Pearl, J},
	year         = 2009,
	publisher    = {Cambridge university press}
}
@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{Dawid1979ConditionalII,
	title        = {Conditional Independence in Statistical Theory},
	author       = {A. Philip Dawid},
	year         = 1979,
	journal      = {Journal of the royal statistical society series b-methodological},
	volume       = 41,
	pages        = {1--15},
	url          = {https://api.semanticscholar.org/CorpusID:115903686}
}
@article{bengio2013representation,
	title        = {Representation learning: A review and new perspectives},
	author       = {Bengio, Yoshua and Courville, Aaron and Vincent, Pascal},
	year         = 2013,
	journal      = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	publisher    = {IEEE},
	volume       = 35,
	number       = 8,
	pages        = {1798--1828}
}
@article{lecun2015deep,
	title        = {Deep learning},
	author       = {LeCun, Yann and Bengio, Yoshua and Hinton, Geoffrey},
	year         = 2015,
	journal      = {Nature},
	publisher    = {Nature Publishing Group},
	volume       = 521,
	number       = 7553,
	pages        = {436--444}
}
@inproceedings{krizhevsky2012imagenet,
	title        = {ImageNet classification with deep convolutional neural networks},
	author       = {Krizhevsky, Alex and Sutskever, Ilya and Hinton, Geoffrey E},
	year         = 2012,
	booktitle    = {Advances in Neural Information Processing Systems},
	pages        = {1097--1105}
}
@article{libbrecht2015machine,
	title        = {Machine learning applications in genetics and genomics},
	author       = {Libbrecht, Maxwell W and Noble, William Stafford},
	year         = 2015,
	journal      = {Nature Reviews Genetics},
	publisher    = {Nature Publishing Group},
	volume       = 16,
	number       = 6,
	pages        = {321--332}
}
@article{miotto2017deep,
	title        = {Deep learning for healthcare: review, opportunities and challenges},
	author       = {Miotto, Riccardo and Wang, Fei and Wang, Shuang and Jiang, Xiaoqian and Dudley, Joel T},
	year         = 2017,
	journal      = {Briefings in Bioinformatics},
	publisher    = {Oxford University Press},
	volume       = 19,
	number       = 6,
	pages        = {1236--1246}
}
@article{scholkopf1998nonlinear,
	title        = {Nonlinear component analysis as a kernel eigenvalue problem},
	author       = {Sch{\"o}lkopf, Bernhard and Smola, Alexander and M{\"u}ller, Klaus-Robert},
	year         = 1998,
	journal      = {Neural Computation},
	publisher    = {MIT Press},
	volume       = 10,
	number       = 5,
	pages        = {1299--1319}
}
@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},
	year         = 2021,
	journal      = {Proceedings of the IEEE},
	publisher    = {IEEE},
	volume       = 109,
	number       = 5,
	pages        = {612--634}
}
@inproceedings{parascandolo2018learning,
	title        = {Learning independent causal mechanisms},
	author       = {Parascandolo, Giambattista and Kilbertus, Niki and Rojas-Carulla, Mariana and Sch{\"o}lkopf, Bernhard},
	year         = 2018,
	booktitle    = {International Conference on Machine Learning},
	pages        = {4036--4044},
	organization = {PMLR}
}
@article{locatello2019challenging,
	title        = {Challenging common assumptions in the unsupervised learning of disentangled representations},
	author       = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Gelly, Sylvain and Sch{\"o}lkopf, Bernhard and Bachem, Olivier},
	year         = 2019,
	journal      = {International Conference on Machine Learning},
	pages        = {4114--4124},
	organization = {PMLR}
}
@book{bollen1989structural,
	title        = {Structural Equations with Latent Variables},
	author       = {Bollen, Kenneth A},
	year         = 1989,
	publisher    = {John Wiley \& Sons}
}
@book{hoyle1995structural,
	title        = {Structural Equation Modeling: Concepts, Issues, and Applications},
	author       = {Hoyle, Rick H},
	year         = 1995,
	publisher    = {Sage Publications}
}
@book{jolliffe2016principal,
	title        = {Principal Component Analysis},
	author       = {Jolliffe, Ian T and Cadima, Jorge},
	year         = 2016,
	publisher    = {Springer}
}
@incollection{wold1985partial,
	title        = {Partial Least Squares},
	author       = {Wold, Herman},
	year         = 1985,
	booktitle    = {Encyclopedia of Statistical Sciences},
	publisher    = {Wiley},
	volume       = 6,
	pages        = {581--591}
}
@article{trygg2002orthogonal,
	title        = {Orthogonal projections to latent structures (O-PLS)},
	author       = {Trygg, Johan and Wold, Svante},
	year         = 2002,
	journal      = {Journal of Chemometrics},
	publisher    = {Wiley Online Library},
	volume       = 16,
	number       = 3,
	pages        = {119--128}
}
@article{rosipal2006overview,
	title        = {Overview and recent advances in partial least squares},
	author       = {Rosipal, Roman and Kramer, Nicole},
	year         = 2006,
	journal      = {Subspace, Latent Structure and Feature Selection},
	publisher    = {Springer},
	pages        = {34--51}
}
@article{chernozhukov2018double,
	title        = {Double/debiased machine learning for treatment and structural parameters},
	author       = {Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James},
	year         = 2018,
	journal      = {The Econometrics Journal},
	publisher    = {Oxford University Press},
	volume       = 21,
	number       = 1,
	pages        = {C1--C68}
}
@article{tibshirani1996regression,
	title        = {Regression shrinkage and selection via the lasso},
	author       = {Tibshirani, Robert},
	year         = 1996,
	journal      = {Journal of the Royal Statistical Society: Series B (Methodological)},
	publisher    = {Wiley Online Library},
	volume       = 58,
	number       = 1,
	pages        = {267--288}
}
@inproceedings{johansson2016learning,
	title        = {Learning representations for counterfactual inference},
	author       = {Johansson, Fredrik D and Shalit, Uri and Sontag, David},
	year         = 2016,
	booktitle    = {International Conference on Machine Learning},
	pages        = {3020--3029},
	organization = {PMLR}
}
@book{stewart1990matrix,
	title        = {Matrix Perturbation Theory},
	author       = {Stewart, G.W. and Sun, Ji-guang},
	year         = 1990,
	publisher    = {Academic Press}
}
@article{magnus1985differentiating,
	title        = {Differentiating Eigenvalues and Eigenvectors of Symmetric Matrices},
	author       = {Magnus, Jan R.},
	year         = 1985,
	journal      = {Econometric Theory},
	publisher    = {Cambridge University Press},
	volume       = 1,
	number       = 2,
	pages        = {179--191}
}
@article{davis1970rotation,
	title        = {The Rotation of Eigenvectors by a Perturbation. III},
	author       = {Davis, Chandler and Kahan, William M.},
	year         = 1970,
	journal      = {SIAM Journal on Numerical Analysis},
	publisher    = {SIAM},
	volume       = 7,
	number       = 1,
	pages        = {1--46}
}
@book{anderson2003introduction,
	title        = {An Introduction to Multivariate Statistical Analysis},
	author       = {Anderson, T.W.},
	year         = 2003,
	publisher    = {Wiley}
}
@article{smola1998learning,
	title        = {Learning with Kernels},
	author       = {Smola, Alex and Sch{\"o}lkopf, Bernhard},
	year         = 1998,
	journal      = {Advances in Kernel Methods—Support Vector Learning},
	publisher    = {MIT Press},
	pages        = {169--184}
}
@article{caponnetto2007optimal,
	title        = {Optimal rates for the regularized least-squares algorithm},
	author       = {Caponnetto, Andrea and De Vito, Ernesto},
	year         = 2007,
	journal      = {Foundations of Computational Mathematics},
	publisher    = {Springer},
	volume       = 7,
	number       = 3,
	pages        = {331--368}
}
@article{bartlett2002rademacher,
	title        = {Rademacher and Gaussian complexities: Risk bounds and structural results},
	author       = {Bartlett, Peter L and Mendelson, Shahar},
	year         = 2002,
	journal      = {Journal of Machine Learning Research},
	volume       = 3,
	number       = {Nov},
	pages        = {463--482}
}
@book{kato1995perturbation,
	title        = {Perturbation Theory for Linear Operators},
	author       = {Kato, Tosio},
	year         = 1995,
	publisher    = {Springer}
}
@article{smale2007learning,
	title        = {Learning theory estimates via integral operators and their approximations},
	author       = {Smale, Steve and Zhou, Ding-Xuan},
	year         = 2007,
	journal      = {Constructive Approximation},
	publisher    = {Springer},
	volume       = 26,
	number       = 2,
	pages        = {153--172}
}
@article{bickel2008covariance,
	title        = {Covariance Regularization by Thresholding},
	author       = {Bickel, Peter J. and Levina, Elizaveta},
	year         = 2008,
	journal      = {Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 36,
	number       = 6,
	pages        = {2577--2604}
}
@book{fisher1925statistical,
	title        = {Statistical Methods for Research Workers},
	author       = {Fisher, Ronald A},
	year         = 1925,
	publisher    = {Oliver and Boyd}
}
@book{mardia1979multivariate,
	title        = {Multivariate Analysis},
	author       = {Mardia, Kanti V and Kent, John T and Bibby, John},
	year         = 1979,
	publisher    = {Academic Press}
}
@book{abramowitz1965handbook,
	title        = {Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables},
	author       = {Abramowitz, Milton and Stegun, Irene A},
	year         = 1965,
	publisher    = {Dover Publications}
}
@book{scholkopf2002learning,
	title        = {Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond},
	author       = {Sch{\"o}lkopf, Bernhard and Smola, Alexander J},
	year         = 2002,
	publisher    = {MIT Press}
}
@book{brillinger2001time,
	title        = {Time Series: Data Analysis and Theory},
	author       = {Brillinger, David R},
	year         = 2001,
	publisher    = {SIAM}
}
@article{donoho2000high,
	title        = {High-dimensional data analysis: The curses and blessings of dimensionality},
	author       = {Donoho, David L},
	year         = 2000,
	journal      = {AMS Math Challenges Lecture},
	publisher    = {American Mathematical Society},
	volume       = 1,
	pages        = 32
}
@article{hofmann2008kernel,
	title        = {Kernel Methods in Machine Learning},
	author       = {Hofmann, Thomas and Sch{\"o}lkopf, Bernhard and Smola, Alexander J},
	year         = 2008,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 36,
	number       = 3,
	pages        = {1171--1220}
}
@inproceedings{louizos2017causal,
	title        = {Causal effect inference with deep latent-variable models},
	author       = {Louizos, Christos and Shalit, Uri and Mooij, Joris M and Sontag, David and Zemel, Rich and Welling, Max},
	year         = 2017,
	booktitle    = {Advances in Neural Information Processing Systems},
	pages        = {6446--6456}
}
@book{scholkopf2012causal,
	title        = {Causal Inference for Machine Learning},
	author       = {Sch{\"o}lkopf, Bernhard and Perona, Pietro},
	year         = 2012,
	publisher    = {MIT Press}
}
@article{pawlowski2020deep,
	title        = {Deep structural causal models for tractable counterfactual inference},
	author       = {Pawlowski, Nick and Coeurdoux, Frank and Glocker, Ben},
	year         = 2020,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 33,
	pages        = {857--869}
}
@article{greenland1999confounding,
	title        = {Confounding and collapsibility in causal inference},
	author       = {Greenland, Sander and Robins, James M},
	year         = 1999,
	journal      = {Statistical Science},
	publisher    = {JSTOR},
	pages        = {29--46}
}
@article{belloni2014inference,
	title        = {Inference on treatment effects after selection among high-dimensional controls},
	author       = {Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian},
	year         = 2014,
	journal      = {The Review of Economic Studies},
	publisher    = {Oxford University Press},
	volume       = 81,
	number       = 2,
	pages        = {608--650}
}
@article{farrell2015robust,
	title        = {Robust inference on average treatment effects with possibly more covariates than observations},
	author       = {Farrell, Max H},
	year         = 2015,
	journal      = {Journal of Econometrics},
	publisher    = {Elsevier},
	volume       = 189,
	number       = 1,
	pages        = {1--23}
}
@article{li2014novel,
	title        = {A novel approach to detect urban expansion by using high-resolution remotely sensed imagery},
	author       = {Li, Jie and Chen, Ying and Hu, Bin and Li, Wei and He, Ming},
	year         = 2014,
	journal      = {Remote Sensing},
	publisher    = {MDPI},
	volume       = 6,
	number       = 1,
	pages        = {768--789}
}
@article{schmidt2015remote,
	title        = {Remote sensing of vegetation using hyperspectral imaging},
	author       = {Schmidt, Kerstin S and Skidmore, Andrew K},
	year         = 2015,
	journal      = {Encyclopedia of Remote Sensing},
	publisher    = {Springer},
	pages        = {427--439}
}
@article{tran2019deep,
	title        = {Deep learning in weather forecasting: A review},
	author       = {Tran, Ngoc Cuong and Song, Xianfang},
	year         = 2019,
	journal      = {Atmosphere},
	publisher    = {MDPI},
	volume       = 10,
	number       = 11,
	pages        = 741
}
@article{smith2011network,
	title        = {Network modelling methods for FMRI},
	author       = {Smith, Stephen M and Miller, Karla L and Salimi-Khorshidi, Gholamreza and Webster, Matthew and Beckmann, Christian F and Nichols, Thomas E and Ramsey, Joseph D and Woolrich, Mark W},
	year         = 2011,
	journal      = {NeuroImage},
	publisher    = {Elsevier},
	volume       = 54,
	number       = 2,
	pages        = {875--891}
}
@article{reid2019advancing,
	title        = {Advancing functional connectivity research from association to causation},
	author       = {Reid, Andrew T and Headley, Drew B and Mill, Ren{\'e} D and Sanchez-Romero, Rodrigo and Uddin, Lucina Q and Marinazzo, Daniele and Lurie, Daniel J and Vald{\'e}s-Sosa, Pedro A and Hanson, Stephen J and Biswal, Bharat B and others},
	year         = 2019,
	journal      = {Nature Neuroscience},
	publisher    = {Nature Publishing Group},
	volume       = 22,
	number       = 11,
	pages        = {1751--1760}
}
@article{shaha2020,
	title        = {{The hardness of conditional independence testing and the generalised covariance measure}},
	author       = {Rajen D. Shah and Jonas Peters},
	year         = 2020,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 48,
	number       = 3,
	pages        = {1514 -- 1538},
	doi          = {10.1214/19-AOS1857},
	url          = {https://doi.org/10.1214/19-AOS1857},
	keywords     = {Conditional independence, Hypothesis testing, kernel ridge regression, testability, wild bootstrap}
}
@article{Chernozhukov2018dml,
	title        = {{Double/debiased machine learning for treatment and structural parameters}},
	author       = {Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James},
	year         = 2018,
	month        = {01},
	journal      = {The Econometrics Journal},
	volume       = 21,
	number       = 1,
	pages        = {C1-C68},
	doi          = {10.1111/ectj.12097},
	issn         = {1368-4221},
	url          = {https://doi.org/10.1111/ectj.12097},
	eprint       = {https://academic.oup.com/ectj/article-pdf/21/1/C1/27684918/ectj00c1.pdf}
}
@article{Zhang2023,
	title        = {Instrumental variable regression via kernel maximum moment loss},
	title        = {},
	author       = {Rui Zhang and Masaaki Imaizumi and Bernhard Schölkopf and Krikamol Muandet},
	year         = 2023,
	journal      = {Journal of Causal Inference},
	volume       = 11,
	number       = 1,
	pages        = 20220073,
	doi          = {doi:10.1515/jci-2022-0073},
	url          = {https://doi.org/10.1515/jci-2022-0073},
	lastchecked  = {2023-11-20}
}
@inproceedings{runge2018conditional,
	title        = {Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information},
	author       = {Runge, Jakob},
	year         = 2018,
	booktitle    = {Proceedings of the 35th International Conference on Machine Learning (ICML)},
	pages        = {5381--5390}
}
@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},
	year         = 2011,
	booktitle    = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI)},
	pages        = {804--813}
}
@inproceedings{fukumizu2008kernel,
	title        = {Kernel measures of conditional dependence},
	author       = {Fukumizu, Kenji and Gretton, Arthur and Sun, Xiaohai and Sch{\"o}lkopf, Bernhard},
	year         = 2008,
	booktitle    = {Advances in Neural Information Processing Systems (NeurIPS)},
	pages        = {489--496}
}
@book{woodward2005making,
	title        = {Making things happen: A theory of causal explanation},
	author       = {Woodward, James},
	year         = 2005,
	publisher    = {Oxford university press}
}
@article{globerson2003sufficient,
	title        = {Sufficient dimensionality reduction},
	author       = {Globerson, Amir and Tishby, Naftali},
	year         = 2003,
	journal      = {Journal of Machine Learning Research},
	volume       = 3,
	number       = {Mar},
	pages        = {1307--1331}
}
@article{fukumizu2009kernel,
	title        = {Kernel dimension reduction in regression},
	author       = {Fukumizu, Kenji and Bach, Francis R and Jordan, Michael I},
	year         = 2009
}
@article{hasselmann1993optimal,
	title        = {Optimal fingerprints for the detection of time-dependent climate change},
	author       = {Hasselmann, Klaus},
	year         = 1993,
	journal      = {Journal of Climate},
	volume       = 6,
	number       = 10,
	pages        = {1957--1971}
}
@inproceedings{varando2022learning,
	title        = {Learning Causal Representations with Granger PCA},
	author       = {Varando, Gherardo and Fern{\'a}ndez-Torres, Miguel-{\'A}ngel and Mu{\~n}oz-Mar{\'\i}, Jordi and Camps-Valls, Gustau},
	year         = 2022,
	booktitle    = {UAI 2022 Workshop on Causal Representation Learning}
}
@article{pearl2014interpretation,
	title        = {Interpretation and identification of causal mediation.},
	author       = {Pearl, Judea},
	year         = 2014,
	journal      = {Psychological methods},
	publisher    = {American Psychological Association},
	volume       = 19,
	number       = 4,
	pages        = 459
}
@incollection{pearl2022direct,
	title        = {Direct and indirect effects},
	author       = {Pearl, Judea},
	year         = 2022,
	booktitle    = {Probabilistic and causal inference: the works of Judea Pearl},
	pages        = {373--392}
}
@article{heinze2018causal,
	title        = {Causal structure learning},
	author       = {Heinze-Deml, Christina and Maathuis, Marloes H and Meinshausen, Nicolai},
	year         = 2018,
	journal      = {Annual Review of Statistics and Its Application},
	publisher    = {Annual Reviews},
	volume       = 5,
	number       = 1,
	pages        = {371--391}
}
@inproceedings{squires2023linear,
	title        = {Linear causal disentanglement via interventions},
	author       = {Squires, Chandler and Seigal, Anna and Bhate, Salil S and Uhler, Caroline},
	year         = 2023,
	booktitle    = {International Conference on Machine Learning},
	pages        = {32540--32560},
	organization = {PMLR}
}
@article{yao2018representation,
	title        = {Representation learning for treatment effect estimation from observational data},
	author       = {Yao, Liuyi and Li, Sheng and Li, Yaliang and Huai, Mengdi and Gao, Jing and Zhang, Aidong},
	year         = 2018,
	journal      = {Advances in neural information processing systems},
	volume       = 31
}
@inproceedings{lachapelle2022disentanglement,
	title        = {Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA},
	author       = {Lachapelle, S{\'e}bastien and Rodriguez, Pau and Sharma, Yash and Everett, Katie E and Le Priol, R{\'e}mi and Lacoste, Alexandre and Lacoste-Julien, Simon},
	year         = 2022,
	booktitle    = {Conference on Causal Learning and Reasoning},
	pages        = {428--484},
	organization = {PMLR}
}
@article{lippe2022causal,
	title        = {Causal representation learning for instantaneous and temporal effects in interactive systems},
	author       = {Lippe, Phillip and Magliacane, Sara and L{\"o}we, Sindy and Asano, Yuki M and Cohen, Taco and Gavves, Efstratios},
	year         = 2022,
	journal      = {arXiv preprint arXiv:2206.06169}
}
@article{granger1969investigating,
	title        = {Investigating causal relations by econometric models and cross-spectral methods},
	author       = {Granger, Clive WJ},
	year         = 1969,
	journal      = {Econometrica: journal of the Econometric Society},
	publisher    = {JSTOR},
	pages        = {424--438}
}
@article{kalisch2007estimating,
	title        = {Estimating high-dimensional directed acyclic graphs with the PC-algorithm.},
	author       = {Kalisch, Markus and B{\"u}hlman, Peter},
	year         = 2007,
	journal      = {Journal of Machine Learning Research},
	volume       = 8,
	number       = 3
}
@book{lehmann2006theory,
	title        = {Theory of point estimation},
	author       = {Lehmann, Erich L and Casella, George},
	year         = 2006,
	publisher    = {Springer Science \& Business Media}
}
@article{danabasoglu2020community,
	title        = {The community earth system model version 2 (CESM2)},
	author       = {Danabasoglu, Gokhan and Lamarque, J-F and Bacmeister, J and Bailey, DA and DuVivier, AK and Edwards, Jim and Emmons, LK and Fasullo, John and Garcia, R and Gettelman, Andrew and others},
	year         = 2020,
	journal      = {Journal of Advances in Modeling Earth Systems},
	publisher    = {Wiley Online Library},
	volume       = 12,
	number       = 2,
	pages        = {e2019MS001916}
}
@article{lean2008natural,
	title        = {How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006},
	author       = {Lean, Judith L and Rind, David H},
	year         = 2008,
	journal      = {Geophysical Research Letters},
	publisher    = {Wiley Online Library},
	volume       = 35,
	number       = 18
}
@article{ledoit2004well,
	title        = {A well-conditioned estimator for large-dimensional covariance matrices},
	author       = {Ledoit, Olivier and Wolf, Michael},
	year         = 2004,
	journal      = {Journal of multivariate analysis},
	publisher    = {Elsevier},
	volume       = 88,
	number       = 2,
	pages        = {365--411}
}
@article{fisher1915frequency,
	title        = {Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population},
	author       = {Fisher, Ronald A},
	year         = 1915,
	journal      = {Biometrika},
	publisher    = {JSTOR},
	volume       = 10,
	number       = 4,
	pages        = {507--521}
}
@incollection{hotelling1992relations,
	title        = {Relations between two sets of variates},
	author       = {Hotelling, Harold},
	year         = 1992,
	booktitle    = {Breakthroughs in statistics: methodology and distribution},
	publisher    = {Springer},
	pages        = {162--190}
}

@article{saengkyongam2023identifying,
  title={Identifying representations for intervention extrapolation},
  author={Saengkyongam, Sorawit and Rosenfeld, Elan and Ravikumar, Pradeep and Pfister, Niklas and Peters, Jonas},
  journal={arXiv preprint arXiv:2310.04295},
  year={2023}
}