@article{Anand2023,
  title   = {Causal Effect Identification in Cluster DAGs},
  volume  = {37},
  url     = {https://ojs.aaai.org/index.php/AAAI/article/view/26435},
  doi     = {10.1609/aaai.v37i10.26435},
  number  = {10},
  journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
  author  = {Anand, Tara V. and Ribeiro, Adele H. and Tian, Jin and Bareinboim, Elias},
  year    = {2023},
  pages   = {12172-12179}
}

@article{Antonoplis2022,
  title     = {Studying Socioeconomic Status: Conceptual Problems and an Alternative Path Forward},
  volume    = {18},
  url       = {http://dx.doi.org/10.1177/17456916221093615},
  doi       = {10.1177/17456916221093615},
  number    = {2},
  journal   = {Perspectives on Psychological Science},
  publisher = {SAGE Publications},
  author    = {Antonoplis,  Stephen},
  year      = {2022},
  pages     = {275–292}
}

@inproceedings{Argyriou2006,
  author    = {Argyriou, Andreas and Evgeniou, Theodoros and Pontil, Massimiliano},
  booktitle = {Advances in Neural Information Processing Systems},
  editor    = {B. Sch\"{o}lkopf and J. Platt and T. Hoffman},
  pages     = {},
  publisher = {MIT Press},
  title     = {Multi-Task Feature Learning},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2006/file/0afa92fc0f8a9cf051bf2961b06ac56b-Paper.pdf},
  volume    = {19},
  year      = {2006}
}

@book{Ash1975,
  author     = {Ash, Robert B. and Gardner, Melvin F.},
  mrclass    = {60-02},
  mrnumber   = {448463},
  mrreviewer = {Bennett\ Eisenberg},
  pages      = {viii+321},
  publisher  = {Academic Press [Harcourt Brace Jovanovich, Publishers], New
                York-London},
  series     = {Probability and Mathematical Statistics},
  title      = {Topics in stochastic processes},
  volume     = {Vol. 27},
  year       = {1975}
}

@book{Bollen1989,
  author     = {Bollen, Kenneth A.},
  title      = {Structural equations with latent variables},
  series     = {Wiley Series in Probability and Mathematical Statistics:
                Applied Probability and Statistics},
  note       = {A Wiley-Interscience Publication},
  publisher  = {John Wiley \& Sons, Inc., New York},
  year       = {1989},
  pages      = {xiv+514},
  mrclass    = {62-01 (62J05 62Pxx 92-01 92A25)},
  mrnumber   = {996025},
  mrreviewer = {Tom\ Wansbeek},
  doi        = {10.1002/9781118619179},
  url        = {https://doi.org/10.1002/9781118619179}
}


@article{Campbell1959,
  title     = {Convergent and discriminant validation by the multitrait-multimethod matrix.},
  volume    = {56},
  url       = {http://dx.doi.org/10.1037/h0046016},
  doi       = {10.1037/h0046016},
  number    = {2},
  journal   = {Psychological Bulletin},
  publisher = {American Psychological Association (APA)},
  author    = {Campbell,  Donald T. and Fiske,  Donald W.},
  year      = {1959},
  pages     = {81–105}
}

@inproceedings{Chalupka2016,
  title     = {Multi-Level Cause-Effect Systems},
  author    = {Chalupka, Krzysztof and Eberhardt, Frederick and Perona, Pietro},
  booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
  pages     = {361--369},
  year      = {2016},
  editor    = {Gretton, Arthur and Robert, Christian C.},
  volume    = {51},
  series    = {Proceedings of Machine Learning Research},
  address   = {Cadiz, Spain},
  publisher = {PMLR},
  pdf       = {http://proceedings.mlr.press/v51/chalupka16.pdf},
  url       = {https://proceedings.mlr.press/v51/chalupka16.html}
}
@incollection{Chickering2003,
  author     = {Chickering, David Maxwell},
  title      = {Optimal structure identification with greedy search},
  note       = {Computational learning theory},
  journal    = {J. Mach. Learn. Res.},
  fjournal   = {Journal of Machine Learning Research (JMLR)},
  volume     = {3},
  year       = {2003},
  number     = {3},
  pages      = {507--554},
  mrclass    = {68T05 (68Q32)},
  mrnumber   = {1991085},
  mrreviewer = {Tru\ Hoang\ Cao},
  doi        = {10.1162/153244303321897717},
  url        = {https://doi.org/10.1162/153244303321897717}
}

@article{Colombo2014,
  author   = {Colombo, Diego and Maathuis, Marloes H.},
  fjournal = {Journal of Machine Learning Research (JMLR)},
  journal  = {J. Mach. Learn. Res.},
  mrclass  = {68T05 (62H99 68R10 92D10)},
  mrnumber = {3291411},
  pages    = {3741--3782},
  title    = {Order-independent constraint-based causal structure learning},
  volume   = {15},
  year     = {2014}
}


@article{Cronbach1955,
  title     = {Construct validity in psychological tests.},
  volume    = {52},
  url       = {http://dx.doi.org/10.1037/h0040957},
  doi       = {10.1037/h0040957},
  number    = {4},
  journal   = {Psychological Bulletin},
  publisher = {American Psychological Association (APA)},
  author    = {Cronbach,  Lee J. and Meehl,  Paul E.},
  year      = {1955},
  pages     = {281–302}
}

@article{Drton2017,
  abstract = { A graphical model is a statistical model that is associated with a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models have computationally convenient factorization properties and have long been a valuable tool for tractable modeling of multivariate distributions. More recently, applications such as reconstructing gene regulatory networks from gene expression data have driven major advances in structure learning, that is, estimating the graph underlying a model. We review some of these advances and discuss methods such as the graphical lasso and neighborhood selection for undirected graphical models (or Markov random fields) and the PC algorithm and score-based search methods for directed graphical models (or Bayesian networks). We further review extensions that account for effects of latent variables and heterogeneous data sources. },
  author   = {Drton, Mathias and Maathuis, Marloes H.},
  doi      = {10.1146/annurev-statistics-060116-053803},
  eprint   = {

              https://doi.org/10.1146/annurev-statistics-060116-053803



              },
  journal  = {Annual Review of Statistics and Its Application},
  number   = {1},
  pages    = {365-393},
  title    = {Structure Learning in Graphical Modeling},
  url      = {

              https://doi.org/10.1146/annurev-statistics-060116-053803



              },
  volume   = {4},
  year     = {2017}
}

@inproceedings{Eigenmann2020,
  author    = {Eigenmann, Marco and Mukherjee, Sach and Maathuis, Marloes},
  booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)},
  pages     = {151--160},
  pdf       = {http://proceedings.mlr.press/v124/eigenmann20a/eigenmann20a.pdf},
  publisher = {PMLR},
  series    = {Proceedings of Machine Learning Research},
  title     = {Evaluation of Causal Structure Learning Algorithms via Risk Estimation},
  url       = {https://proceedings.mlr.press/v124/eigenmann20a.html},
  volume    = {124},
  year      = {2020}
}


@inproceedings{Entner2012,
  author    = {Entner, Doris
               and Hoyer, Patrik O.},
  editor    = {Villa, Alessandro E. P.
               and Duch, W{\l}odzis{\l}aw
               and {\'E}rdi, P{\'e}ter
               and Masulli, Francesco
               and Palm, G{\"u}nther},
  title     = {Estimating a Causal Order among Groups of Variables in Linear Models},
  booktitle = {Artificial Neural Networks and Machine Learning -- ICANN 2012},
  year      = {2012},
  publisher = {Springer Berlin Heidelberg},
  address   = {Berlin, Heidelberg},
  pages     = {84--91},
  abstract  = {The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize existing methods to apply to collections of multi-dimensional random vectors, focusing on techniques applicable to linear models. The performance of the resulting algorithms is evaluated and compared in simulations, which show that our methods can, in many cases, provide useful information on causal relationships even for relatively small sample sizes.}
}



@inbook{Erdos2011,
  title     = {On the evolution of random graphs},
  url       = {http://dx.doi.org/10.1515/9781400841356.38},
  doi       = {10.1515/9781400841356.38},
  booktitle = {The Structure and Dynamics of Networks},
  publisher = {Princeton University Press},
  author    = {Erd\"{o}s,  P. and Rényi,  A.},
  year      = {2011},
  pages     = {38-82}
}

@article{Fornasier2008,
  author   = {Fornasier, Massimo and Rauhut, Holger},
  title    = {Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints},
  journal  = {SIAM Journal on Numerical Analysis},
  volume   = {46},
  number   = {2},
  pages    = {577-613},
  year     = {2008},
  doi      = {10.1137/0606668909},
  url      = {

              https://doi.org/10.1137/0606668909



              },
  eprint   = {

              https://doi.org/10.1137/0606668909



              },
  abstract = { Vector-valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting coupling of nonvanishing components. These measures are typically constructed as weighted \$\ell\_1\$ norms of componentwise \$\ell\_q\$ norms of frame coefficients. We show how to compute solutions of linear inverse problems with such joint sparsity regularization constraints by fast thresholded Landweber algorithms. Next we discuss the adaptive choice of suitable weights appearing in the definition of sparsity measures. The weights are interpreted as indicators of the sparsity pattern and are iteratively updated after each new application of the thresholded Landweber algorithm. The resulting two-step algorithm is interpreted as a double-minimization scheme for a suitable target functional. We show its \$\ell\_2\$-norm convergence. An implementable version of the algorithm is also formulated, and its norm convergence is proven. Numerical experiments in color image restoration are presented. }
}

@misc{Foygel2010,
  title         = {Exact block-wise optimization in group lasso and sparse group lasso for linear regression},
  author        = {Rina Foygel and Mathias Drton},
  year          = {2010},
  eprint        = {1010.3320},
  archiveprefix = {arXiv},
  primaryclass  = {stat.ML},
  url           = {https://arxiv.org/abs/1010.3320}
}

@inproceedings{Fukumizu2007,
  author    = {Fukumizu, Kenji and Gretton, Arthur and Sun, Xiaohai and Sch\"{o}lkopf, Bernhard},
  booktitle = {Advances in Neural Information Processing Systems},
  editor    = {J. Platt and D. Koller and Y. Singer and S. Roweis},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {Kernel Measures of Conditional Dependence},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2007/file/3a0772443a0739141292a5429b952fe6-Paper.pdf},
  volume    = {20},
  year      = {2007}
}


@inproceedings{Gentzel2019,
  author    = {Gentzel, Amanda and Garant, Dan and Jensen, David},
  booktitle = {Advances in Neural Information Processing Systems},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2019/file/a87c11b9100c608b7f8e98cfa316ff7b-Paper.pdf},
  volume    = {32},
  year      = {2019}
}

@inproceedings{Goebler2024,
  title     = {$\texttt{causalAssembly}$: Generating Realistic Production Data for Benchmarking Causal Discovery},
  author    = {G\"obler, Konstantin and Windisch, Tobias and Drton, Mathias and Pychynski, Tim and Roth, Martin and Sonntag, Steffen},
  booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning},
  pages     = {609--642},
  year      = {2024},
  editor    = {Locatello, Francesco and Didelez, Vanessa},
  volume    = {236},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {https://proceedings.mlr.press/v236/gobler24a/gobler24a.pdf},
  url       = {https://proceedings.mlr.press/v236/gobler24a.html}
}


@inproceedings{Greenfeld2020,
  title     = {Robust Learning with the {H}ilbert-Schmidt Independence Criterion},
  author    = {Greenfeld, Daniel and Shalit, Uri},
  booktitle = {Proceedings of the 37th International Conference on Machine Learning},
  pages     = {3759--3768},
  year      = {2020},
  editor    = {III, Hal Daumé and Singh, Aarti},
  volume    = {119},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {http://proceedings.mlr.press/v119/greenfeld20a/greenfeld20a.pdf},
  url       = {https://proceedings.mlr.press/v119/greenfeld20a.html},
  abstract  = {We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by \citet{mooij2009regression} in the context of learning causal graphs. We adapt it to the task of learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain, but with the assumption that $p(y|x)$ (the conditional probability of labels given instances) remains the same in the target domain. We show that the proposed loss is expected to give rise to models that generalize well on a class of target domains characterised by the complexity of their description within a reproducing kernel Hilbert space. Experiments on unsupervised covariate shift tasks demonstrate that models learned with the proposed loss-function outperform models learned with standard loss functions, achieving state-of-the-art results on a challenging cell-microscopy unsupervised covariate shift task.}
}

@incollection{Gretton2005,
  author    = {Gretton, Arthur and Bousquet, Olivier and Smola, Alex and
               Sch\"olkopf, Bernhard},
  title     = {Measuring statistical dependence with {H}ilbert-{S}chmidt
               norms},
  booktitle = {Algorithmic learning theory},
  series    = {Lecture Notes in Comput. Sci.},
  volume    = {3734},
  pages     = {63--77},
  publisher = {Springer, Berlin},
  year      = {2005},
  mrclass   = {62J10 (46N30)},
  mrnumber  = {2255909},
  doi       = {10.1007/11564089\_7},
  url       = {https://doi.org/10.1007/11564089_7}
}

@book{Hastie2015,
  author     = {Hastie, Trevor and Tibshirani, Robert and Wainwright, Martin},
  title      = {Statistical learning with sparsity},
  series     = {Monographs on Statistics and Applied Probability},
  volume     = {143},
  note       = {The lasso and generalizations},
  publisher  = {CRC Press, Boca Raton, FL},
  year       = {2015},
  pages      = {xv+351},
  mrclass    = {62-02 (62F15 62G08 62H12 62J05 62J07 62J12 62M15)},
  mrnumber   = {3616141},
  mrreviewer = {Su-Yun\ Chen\ Huang}
}
@inproceedings{Henckel2024,
  title     = {Adjustment Identification Distance: A gadjid for Causal Structure Learning},
  author    = {Leonard Henckel and Theo W{\"u}rtzen and Sebastian Weichwald},
  booktitle = {The 40th Conference on Uncertainty in Artificial Intelligence},
  year      = {2024},
  url       = {https://openreview.net/forum?id=jO5UNNrjJr}
}

@inproceedings{Hoyer2009,
  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},
  editor    = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {Nonlinear causal discovery with additive noise models},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2008/file/f7664060cc52bc6f3d620bcedc94a4b6-Paper.pdf},
  volume    = {21},
  year      = {2008}
}

@inproceedings{Janzing2010,
  title        = {Telling cause from effect based on high-dimensional observations},
  author       = {Janzing, D. and Hoyer, P. and Sch{\"o}lkopf, B.},
  booktitle    = {Proceedings of the 27th International Conference on Machine Learning},
  pages        = {479-486},
  editors      = {J F{\"u}rnkranz and T Joachims},
  publisher    = {International Machine Learning Society},
  organization = {Max-Planck-Gesellschaft},
  school       = {Biologische Kybernetik},
  address      = {Madison, WI, USA},
  year         = {2010},
  doi          = {}
}

@inproceedings{Kikuchi2023,
  title     = {Structure Learning for Groups of Variables in
               Nonlinear Time-Series Data with
               Location-Scale Noise},
  author    = {Kikuchi, Genta and Shimizu, Shohei},
  booktitle = {Proceedings of the 2023 Causal Analysis Workshop
               Series},
  pages     = {20--39},
  year      = {2023},
  editor    = {Kummerfeld, Erich and Ma, Sisi and Rawls, Eric and Andrews, Bryan},
  volume    = {223},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {https://proceedings.mlr.press/v223/kikuchi23a/kikuchi23a.pdf},
  url       = {https://proceedings.mlr.press/v223/kikuchi23a.html}
}

@article{Kohn2020,
  title    = {Principles of Corticocortical Communication: Proposed Schemes and Design Considerations},
  journal  = {Trends in Neurosciences},
  volume   = {43},
  number   = {9},
  pages    = {725-737},
  year     = {2020},
  doi      = {https://doi.org/10.1016/j.tins.2020.07.001},
  url      = {https://www.sciencedirect.com/science/article/pii/S016622362030165X},
  author   = {Adam Kohn and Anna I. Jasper and João D. Semedo and Evren Gokcen and Christian K. Machens and Byron M. Yu},
  keywords = {interareal signaling, corticocortical communication, visual cortex, feedforward, feedback, pulvinar, synchrony, communication through coherence, communication subspace}
}

@inproceedings{Lachapelle2020,
  title     = {Gradient-Based Neural DAG Learning},
  author    = {Sébastien Lachapelle and Philippe Brouillard and Tristan Deleu and Simon Lacoste-Julien},
  booktitle = {International Conference on Learning Representations},
  year      = {2020},
  url       = {https://openreview.net/forum?id=rklbKA4YDS}
}

@article{Lee2022,
  author   = {Lee, Kuang-Yao and Li, Lexin},
  doi      = {10.1111/rssb.12471},
  fjournal = {Journal of the Royal Statistical Society. Series B.
              Statistical Methodology},
  journal  = {J. R. Stat. Soc. Ser. B. Stat. Methodol.},
  mrclass  = {62H11 (05C20 47N30 62-08 62A09 62P10 62R10 65Y20)},
  mrnumber = {4412999},
  number   = {2},
  pages    = {600--629},
  title    = {Functional structural equation model},
  url      = {https://doi.org/10.1111/rssb.12471},
  volume   = {84},
  year     = {2022}
}

@article{Li2020,
  title     = {Multi-task learning sparse group lasso: a method for quantifying antigenicity of influenza A(H1N1) virus using mutations and variations in glycosylation of Hemagglutinin},
  volume    = {21},
  url       = {http://dx.doi.org/10.1186/s12859-020-3527-5},
  doi       = {10.1186/s12859-020-3527-5},
  number    = {1},
  journal   = {BMC Bioinformatics},
  publisher = {Springer Science and Business Media LLC},
  author    = {Li,  Lei and Chang,  Deborah and Han,  Lei and Zhang,  Xiaojian and Zaia,  Joseph and Wan,  Xiu-Feng},
  year      = {2020}
}

@inproceedings{Liu2007,
  author    = {Liu, Han and Wasserman, Larry and Lafferty, John and Ravikumar, Pradeep},
  booktitle = {Advances in Neural Information Processing Systems},
  editor    = {J. Platt and D. Koller and Y. Singer and S. Roweis},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {SpAM: Sparse Additive Models},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2007/file/42e7aaa88b48137a16a1acd04ed91125-Paper.pdf},
  volume    = {20},
  year      = {2007}
}

@inproceedings{Liu2008,
  author    = {Liu, Han and Wasserman, Larry and Lafferty, John},
  booktitle = {Advances in Neural Information Processing Systems},
  editor    = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {Nonparametric regression and classification with joint sparsity constraints},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2008/file/6faa8040da20ef399b63a72d0e4ab575-Paper.pdf},
  volume    = {21},
  year      = {2008}
}


@inproceedings{Liu2009,
  author    = {Liu, Jun and Ji, Shuiwang and Ye, Jieping},
  title     = {Multi-task feature learning via efficient l2, 1-norm minimization},
  year      = {2009},
  booktitle = {Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence},
  pages     = {339--348},
  numpages  = {10},
  series    = {UAI '09}
}


@inproceedings{Liu2009a,
  series     = {ICML '09},
  title      = {Blockwise coordinate descent procedures for the multi-task lasso,  with applications to neural semantic basis discovery},
  url        = {http://dx.doi.org/10.1145/1553374.1553458},
  doi        = {10.1145/1553374.1553458},
  booktitle  = {Proceedings of the 26th Annual International Conference on Machine Learning},
  author     = {Liu, Han and Palatucci, Mark and Zhang, Jian},
  year       = {2009},
  pages      = {649--656},
  collection = {ICML '09}
}


@inproceedings{Mooij2009,
  author    = {Mooij, Joris and Janzing, Dominik and Peters, Jonas and Sch\"{o}lkopf, Bernhard},
  title     = {Regression by dependence minimization and its application to causal inference in additive noise models},
  year      = {2009},
  url       = {https://doi.org/10.1145/1553374.1553470},
  doi       = {10.1145/1553374.1553470},
  booktitle = {Proceedings of the 26th Annual International Conference on Machine Learning},
  pages     = {745-752},
  numpages  = {8},
  series    = {ICML '09}
}

@article{Negahban2012,
  author   = {Negahban, Sahand N. and Ravikumar, Pradeep and Wainwright,
              Martin J. and Yu, Bin},
  title    = {A unified framework for high-dimensional analysis of
              {$M$}-estimators with decomposable regularizers},
  journal  = {Statist. Sci.},
  fjournal = {Statistical Science. A Review Journal of the Institute of
              Mathematical Statistics},
  volume   = {27},
  year     = {2012},
  number   = {4},
  pages    = {538--557},
  mrclass  = {62J07},
  mrnumber = {3025133},
  doi      = {10.1214/12-STS400},
  url      = {https://doi.org/10.1214/12-STS400}
}

@article{Panzeri2017,
  title    = {Cracking the Neural Code for Sensory Perception by Combining Statistics, Intervention, and Behavior},
  journal  = {Neuron},
  volume   = {93},
  number   = {3},
  pages    = {491-507},
  year     = {2017},
  doi      = {https://doi.org/10.1016/j.neuron.2016.12.036},
  url      = {https://www.sciencedirect.com/science/article/pii/S0896627316310091},
  author   = {Stefano Panzeri and Christopher D. Harvey and Eugenio Piasini and Peter E. Latham and Tommaso Fellin},
  keywords = {neural coding, choice, information, optogenetics, population coding, behavior}
}

@article{Parviainen2017,
  author   = {Parviainen, Pekka and Kaski, Samuel},
  title    = {Learning structures of {B}ayesian networks for variable
              groups},
  journal  = {Internat. J. Approx. Reason.},
  fjournal = {International Journal of Approximate Reasoning},
  volume   = {88},
  year     = {2017},
  pages    = {110--127},
  mrclass  = {62H99 (62H12 68T05)},
  mrnumber = {3679140},
  doi      = {10.1016/j.ijar.2017.05.006},
  url      = {https://doi.org/10.1016/j.ijar.2017.05.006}
}

@inproceedings{Peters2011,
  author    = {Peters, Jonas and Mooij, Joris M. and Janzing, Dominik and Sch\"{o}lkopf, Bernhard},
  title     = {Identifiability of causal graphs using functional Models},
  year      = {2011},
  booktitle = {Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence},
  pages     = {589-598},
  numpages  = {10},
  series    = {UAI'11}
}

@article{Peters2014,
  author   = {Peters, Jonas and Mooij, Joris M. and Janzing, Dominik and
              Sch\"{o}lkopf, Bernhard},
  fjournal = {Journal of Machine Learning Research (JMLR)},
  journal  = {J. Mach. Learn. Res.},
  mrclass  = {62H12 (62G08 62H99)},
  mrnumber = {3231600},
  pages    = {2009--2053},
  title    = {Causal discovery with continuous additive noise models},
  volume   = {15},
  year     = {2014}
}


@article{Peters2015,
  author   = {Peters, Jonas and B\"{u}hlmann, Peter},
  doi      = {10.1162/neco\_a\_00708},
  fjournal = {Neural Computation},
  journal  = {Neural Comput.},
  mrclass  = {68R10 (05C12)},
  mrnumber = {3865898},
  number   = {3},
  pages    = {771--799},
  title    = {Structural intervention distance for evaluating causal graphs},
  url      = {https://doi.org/10.1162/neco_a_00708},
  volume   = {27},
  year     = {2015}
}


@article{Ravikumar2009,
  author   = {Ravikumar, Pradeep and Lafferty, John and Liu, Han and
              Wasserman, Larry},
  title    = {Sparse additive models},
  journal  = {J. R. Stat. Soc. Ser. B Stat. Methodol.},
  fjournal = {Journal of the Royal Statistical Society. Series B.
              Statistical Methodology},
  volume   = {71},
  year     = {2009},
  number   = {5},
  pages    = {1009--1030},
  mrclass  = {99-01},
  mrnumber = {2750255},
  doi      = {10.1111/j.1467-9868.2009.00718.x},
  url      = {https://doi.org/10.1111/j.1467-9868.2009.00718.x}
}

@inproceedings{Reisach2021,
  author    = {Reisach, {Alexander G.} and Christof Seiler and Sebastian Weichwald},
  booktitle = {Advances in Neural Information Processing Systems 34 (NeurIPS)},
  language  = {English},
  pages     = {1--13},
  publisher = {NeurIPS Proceedings},
  title     = {Beware of the Simulated {DAG}! {C}ausal Discovery Benchmarks May Be Easy to Game},
  year      = {2021}
}

@book{Rockafellar1998,
  author     = {Rockafellar, R. Tyrrell and Wets, Roger J.-B.},
  title      = {Variational analysis},
  series     = {Grundlehren der mathematischen Wissenschaften [Fundamental
                Principles of Mathematical Sciences]},
  volume     = {317},
  publisher  = {Springer-Verlag, Berlin},
  year       = {1998},
  pages      = {xiv+733},
  mrclass    = {49-02 (46N10 47N10 49J52 49K40 90C30)},
  mrnumber   = {1491362},
  mrreviewer = {Francis\ H.\ Clarke},
  doi        = {10.1007/978-3-642-02431-3},
  url        = {https://doi.org/10.1007/978-3-642-02431-3}
}

@inproceedings{Rolland2022,
  title     = {Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models},
  author    = {Rolland, Paul and Cevher, Volkan and Kleindessner, Matth{\"a}us and Russell, Chris and Janzing, Dominik and Sch{\"o}lkopf, Bernhard and Locatello, Francesco},
  booktitle = {Proceedings of the 39th International Conference on Machine Learning},
  pages     = {18741--18753},
  year      = {2022},
  editor    = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
  volume    = {162},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {https://proceedings.mlr.press/v162/rolland22a/rolland22a.pdf},
  url       = {https://proceedings.mlr.press/v162/rolland22a.html},
  abstract  = {This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score’s Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.}
}

@conference{Rubenstein2017,
  title     = {Causal Consistency of Structural Equation Models},
  author    = {Rubenstein*, P. K. and Weichwald*, S. and Bongers, S. and Mooij, J. M. and Janzing, D. and Grosse-Wentrup, M. and Sch{\"o}lkopf, B.},
  booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence (UAI)},
  pages     = {ID 11},
  editors   = {Gal Elidan, Kristian Kersting, and Alexander T. Ihler},
  year      = {2017},
  note      = {*equal contribution},
  doi       = {},
  url       = {http://auai.org/uai2017/proceedings/papers/11.pdf}
}

@article{Runge2015,
  title     = {Identifying causal gateways and mediators in complex spatio-temporal systems},
  volume    = {6},
  url       = {http://dx.doi.org/10.1038/ncomms9502},
  doi       = {10.1038/ncomms9502},
  number    = {1},
  journal   = {Nature Communications},
  publisher = {Springer Science and Business Media LLC},
  author    = {Runge,  Jakob and Petoukhov,  Vladimir and Donges,  Jonathan F. and Hlinka,  Jaroslav and Jajcay,  Nikola and Vejmelka,  Martin and Hartman,  David and Marwan,  Norbert and Paluš,  Milan and Kurths,  J\"{u}rgen},
  year      = {2015}
}

@inproceedings{Saengkyongam2022,
  title     = {Exploiting Independent Instruments: Identification and Distribution Generalization},
  author    = {Saengkyongam, Sorawit and Henckel, Leonard and Pfister, Niklas and Peters, Jonas},
  booktitle = {Proceedings of the 39th International Conference on Machine Learning},
  pages     = {18935--18958},
  year      = {2022},
  editor    = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
  volume    = {162},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {https://proceedings.mlr.press/v162/saengkyongam22a/saengkyongam22a.pdf},
  url       = {https://proceedings.mlr.press/v162/saengkyongam22a.html},
  abstract  = {Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$ and the hidden confounders are uncorrelated with the instruments $Z$. This is often motivated by a graphical separation, an argument that also justifies independence. Positing an independence restriction, however, leads to strictly stronger identifiability results. We connect to the existing literature in econometrics and provide a practical method called HSIC-X for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.}
}

@article{Semedo2020,
  title   = {Statistical methods for dissecting interactions between brain areas},
  journal = {Current Opinion in Neurobiology},
  volume  = {65},
  pages   = {59-69},
  year    = {2020},
  note    = {Whole-brain interactions between neural circuits},
  doi     = {https://doi.org/10.1016/j.conb.2020.09.009},
  url     = {https://www.sciencedirect.com/science/article/pii/S0959438820301367},
  author  = {João D Semedo and Evren Gokcen and Christian K Machens and Adam Kohn and Byron M Yu}
}

@article{Shi2022a,
  author   = {Shi, Hongjian and Drton, Mathias and Han, Fang},
  title    = {Distribution-free consistent independence tests via
              center-outward ranks and signs},
  journal  = {J. Amer. Statist. Assoc.},
  fjournal = {Journal of the American Statistical Association},
  volume   = {117},
  year     = {2022},
  number   = {537},
  pages    = {395--410},
  mrclass  = {99-01},
  mrnumber = {4399094},
  doi      = {10.1080/01621459.2020.1782223},
  url      = {https://doi.org/10.1080/01621459.2020.1782223}
}

@article{Shi2022b,
  author     = {Shi, Hongjian and Hallin, Marc and Drton, Mathias and Han,
                Fang},
  title      = {On universally consistent and fully distribution-free rank
                tests of vector independence},
  journal    = {Ann. Statist.},
  fjournal   = {The Annals of Statistics},
  volume     = {50},
  year       = {2022},
  number     = {4},
  pages      = {1933--1959},
  mrclass    = {62G10},
  mrnumber   = {4474478},
  mrreviewer = {Jesse\ C.\ Frey},
  doi        = {10.1214/21-aos2151},
  url        = {https://doi.org/10.1214/21-aos2151}
}



@article{Shimizu2006,
  author   = {Shimizu, Shohei and Hoyer, Patrik O. and Hyv\"arinen, Aapo and
              Kerminen, Antti},
  title    = {A linear non-{G}aussian acyclic model for causal discovery},
  journal  = {J. Mach. Learn. Res.},
  fjournal = {Journal of Machine Learning Research (JMLR)},
  volume   = {7},
  year     = {2006},
  pages    = {2003--2030},
  mrclass  = {68T05 (62H25)},
  mrnumber = {2274431}
}

@article{Shimizu2011,
  author  = {Shohei Shimizu and Takanori Inazumi and Yasuhiro Sogawa and Aapo Hyv{{\"a}}rinen and Yoshinobu Kawahara and Takashi Washio and Patrik O. Hoyer and Kenneth Bollen},
  title   = {DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model},
  journal = {Journal of Machine Learning Research},
  year    = {2011},
  volume  = {12},
  number  = {33},
  pages   = {1225--1248},
  url     = {http://jmlr.org/papers/v12/shimizu11a.html}
}

@book{Spirtes1993,
  author     = {Spirtes, Peter and Glymour, Clark and Scheines, Richard},
  doi        = {10.1007/978-1-4612-2748-9},
  mrclass    = {62-07 (62H05)},
  mrnumber   = {1227558},
  mrreviewer = {A.\ D.\ Gordon},
  pages      = {xxiv+526},
  publisher  = {Springer-Verlag, New York},
  series     = {Lecture Notes in Statistics},
  title      = {Causation, prediction, and search},
  url        = {https://doi.org/10.1007/978-1-4612-2748-9},
  volume     = {81},
  year       = {1993}
}

@book{Spirtes2000,
  author    = {Spirtes, Peter and Glymour, Clark and Scheines, Richard},
  title     = {Causation, prediction, and search},
  series    = {Adaptive Computation and Machine Learning},
  edition   = {Second},
  note      = {With additional material by David Heckerman, Christopher Meek,
               Gregory F. Cooper and Thomas Richardson,
               A Bradford Book},
  publisher = {MIT Press, Cambridge, MA},
  year      = {2000},
  pages     = {xxii+543},
  mrclass   = {62-07 (05C90 62H05)},
  mrnumber  = {1815675}
}


@misc{Teyssier2012,
  title         = {Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks},
  author        = {Marc Teyssier and Daphne Koller},
  year          = {2012},
  eprint        = {1207.1429},
  archiveprefix = {arXiv},
  primaryclass  = {cs.LG},
  url           = {https://arxiv.org/abs/1207.1429}
}

@article{Tukey1962,
  author     = {Tukey, John W.},
  title      = {The future of data analysis},
  journal    = {Ann. Math. Statist.},
  fjournal   = {Annals of Mathematical Statistics},
  volume     = {33},
  year       = {1962},
  pages      = {1--67},
  mrclass    = {62.00},
  mrnumber   = {133937},
  mrreviewer = {I.\ J.\ Good},
  doi        = {10.1214/aoms/1177704711},
  url        = {https://doi.org/10.1214/aoms/1177704711}
}

@inproceedings{Uemura2022,
  title     = {A Multivariate Causal Discovery based on Post-Nonlinear Model},
  author    = {Uemura, Kento and Takagi, Takuya and Takayuki, Kambayashi and Yoshida, Hiroyuki and Shimizu, Shohei},
  booktitle = {Proceedings of the First Conference on Causal Learning and Reasoning},
  pages     = {826--839},
  year      = {2022},
  editor    = {Schölkopf, Bernhard and Uhler, Caroline and Zhang, Kun},
  volume    = {177},
  series    = {Proceedings of Machine Learning Research},
  publisher = {PMLR},
  pdf       = {https://proceedings.mlr.press/v177/uemura22a/uemura22a.pdf},
  url       = {https://proceedings.mlr.press/v177/uemura22a.html}
}

@article{Vukovic2022,
  author         = {Vuković, Matej and Thalmann, Stefan},
  title          = {Causal Discovery in Manufacturing: A Structured Literature Review},
  journal        = {Journal of Manufacturing and Materials Processing},
  volume         = {6},
  year           = {2022},
  number         = {1},
  article-number = {10},
  url            = {https://www.mdpi.com/2504-4494/6/1/10},
  doi            = {10.3390/jmmp6010010}
}


@article{Wahl2023,
  title   = {Vector Causal Inference between Two Groups of Variables},
  volume  = {37},
  url     = {https://ojs.aaai.org/index.php/AAAI/article/view/26450},
  doi     = {10.1609/aaai.v37i10.26450},
  number  = {10},
  journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
  author  = {Wahl, Jonas and Ninad, Urmi and Runge, Jakob},
  year    = {2023},
  pages   = {12305-12312}
}


@article{Wahl2024,
  url     = {https://doi.org/10.1515/jci-2023-0041},
  title   = {Foundations of causal discovery on groups of variables},
  author  = {Jonas Wahl and Urmi Ninad and Jakob Runge},
  volume  = {12},
  number  = {1},
  journal = {Journal of Causal Inference},
  doi     = {doi:10.1515/jci-2023-0041},
  year    = {2024}
}


@article{Wang2011,
  author  = {Wang, Hua and Nie, Feiping and Huang, Heng and Kim, Sungeun and Nho, Kwangsik and Risacher, Shannon L. and Saykin, Andrew J. and Shen, Li and For the Alzheimer's Disease Neuroimaging Initiative},
  title   = {Identifying quantitative trait loci via group-sparse multitask regression and feature selection: an imaging genetics study of the ADNI cohort},
  journal = {Bioinformatics},
  volume  = {28},
  number  = {2},
  pages   = {229-237},
  year    = {2011},
  doi     = {10.1093/bioinformatics/btr649},
  url     = {https://doi.org/10.1093/bioinformatics/btr649},
  eprint  = {https://academic.oup.com/bioinformatics/article-pdf/28/2/229/48867063/bioinformatics\_28\_2\_229.pdf}
}

@article{Yan2015,
  title    = {Cortical surface biomarkers for predicting cognitive outcomes using group l2,1 norm},
  journal  = {Neurobiology of Aging},
  volume   = {36},
  pages    = {S185-S193},
  year     = {2015},
  note     = {Novel Imaging Biomarkers for Alzheimer's Disease and Related Disorders (NIBAD)},
  doi      = {https://doi.org/10.1016/j.neurobiolaging.2014.07.045},
  url      = {https://www.sciencedirect.com/science/article/pii/S0197458014005466},
  author   = {Jingwen Yan and Taiyong Li and Hua Wang and Heng Huang and Jing Wan and Kwangsik Nho and Sungeun Kim and Shannon L. Risacher and Andrew J. Saykin and Li Shen},
  keywords = {Alzheimer's disease neuroimaging initiative (ADNI), Magnetic resonance imaging (MRI), Cortical thickness, Sparse learning, Cognitive function prediction},
  abstract = {Regression models have been widely studied to investigate the prediction power of neuroimaging measures as biomarkers for inferring cognitive outcomes in the Alzheimer's disease study. Most of these models ignore the interrelated structures either within neuroimaging measures or between cognitive outcomes, and thus may have limited power to yield optimal solutions. To address this issue, we propose to use a new sparse multitask learning model called Group-Sparse Multi-task Regression and Feature Selection (G-SMuRFS) and demonstrate its effectiveness by examining the predictive power of detailed cortical thickness measures toward 3 types of cognitive scores in a large cohort. G-SMuRFS proposes a group-level l2,1-norm strategy to group relevant features together in an anatomically meaningful manner and use this prior knowledge to guide the learning process. This approach also takes into account the correlation among cognitive outcomes for building a more appropriate predictive model. Compared with traditional methods, G-SMuRFS not only demonstrates a superior performance but also identifies a small set of surface markers that are biologically meaningful.}
}

@inproceedings{Yang2022,
  author    = {Yang, Tianle and Suzuki, Joe},
  booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models},
  pages     = {25--36},
  pdf       = {https://proceedings.mlr.press/v186/yang22a/yang22a.pdf},
  publisher = {PMLR},
  series    = {Proceedings of Machine Learning Research},
  title     = {The Functional {LiNGAM}},
  url       = {https://proceedings.mlr.press/v186/yang22a.html},
  volume    = {186},
  year      = {2022}
}


@article{Yin2012,
  title    = {Group sparse additive models},
  author   = {Yin, Junming and Chen, Xi and Xing, Eric P},
  journal  = {Proc. Int. Conf. Mach. Learn.},
  volume   = {2012},
  pages    = {871--878},
  year     = {2012},
  language = {en}
}

@article{Yuan2006,
  author   = {Yuan, Ming and Lin, Yi},
  title    = {Model selection and estimation in regression with grouped
              variables},
  journal  = {J. R. Stat. Soc. Ser. B Stat. Methodol.},
  fjournal = {Journal of the Royal Statistical Society. Series B.
              Statistical Methodology},
  volume   = {68},
  year     = {2006},
  number   = {1},
  pages    = {49--67},
  mrclass  = {62H25 (62M20)},
  mrnumber = {2212574},
  doi      = {10.1111/j.1467-9868.2005.00532.x},
  url      = {https://doi.org/10.1111/j.1467-9868.2005.00532.x}
}

@inproceedings{Zhang2009,
  author    = {Zhang, Kun and Hyv\"{a}rinen, Aapo},
  title     = {On the identifiability of the post-nonlinear causal model},
  year      = {2009},
  booktitle = {Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence},
  pages     = {647-655},
  numpages  = {9},
  location  = {Montreal, Quebec, Canada},
  series    = {UAI '09}
}

@inproceedings{Zhang2011,
  author    = {Zhang, Kun and Peters, Jonas and Janzing, Dominik and Sch\"{o}lkopf, Bernhard},
  title     = {Kernel-based conditional independence test and application in causal discovery},
  year      = {2011},
  publisher = {AUAI Press},
  address   = {Arlington, Virginia, USA},
  abstract  = {Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.},
  booktitle = {Proceedings of the 27th Annual Conference on Uncertainty in Artificial Intelligence (UAI)},
  pages     = {804--813},
  numpages  = {10},
  location  = {Barcelona, Spain},
  series    = {UAI'11}
}

@inproceedings{Zheng2018,
  author    = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep K and Xing, Eric P},
  booktitle = {Advances in Neural Information Processing Systems},
  editor    = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
  pages     = {},
  publisher = {Curran Associates, Inc.},
  title     = {DAGs with NO TEARS: Continuous Optimization for Structure Learning},
  url       = {https://proceedings.neurips.cc/paper_files/paper/2018/file/e347c51419ffb23ca3fd5050202f9c3d-Paper.pdf},
  volume    = {31},
  year      = {2018}
}


@article{Zhou2023,
  author   = {Zhou, Fangting and He, Kejun and Wang, Kunbo and Xu, Yanxun
              and Ni, Yang},
  doi      = {10.1111/biom.13922},
  fjournal = {Biometrics. Journal of the International Biometric Society},
  journal  = {Biometrics},
  mrclass  = {99-01},
  mrnumber = {4680721},
  number   = {4},
  pages    = {3279--3293},
  title    = {Functional {B}ayesian networks for discovering causality from
              multivariate functional data},
  url      = {https://doi.org/10.1111/biom.13922},
  volume   = {79},
  year     = {2023}
}

@inproceedings{Zscheischler2011,
  author    = {Zscheischler, Jakob and Janzing, Dominik and Zhang, Kun},
  title     = {Testing whether linear equations are causal: a free probability theory approach},
  year      = {2011},
  booktitle = {Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence},
  pages     = {839-848},
  numpages  = {10},
  location  = {Barcelona, Spain},
  series    = {UAI'11}
}
