%%%%%%%%%%%%%%%%%%% Identifiability
@article{lanne2017identification,
    title={{Identification and estimation of non-Gaussian structural vector autoregressions}},
    author={Lanne, Markku and Meitz, Mika and Saikkonen, Pentti},
    journal={Journal of Econometrics},
    volume={196},
    number={2},
    pages={288--304},
    year={2017},
    publisher={Elsevier}
}

%%%%%%%%%%%%%%%%%%%% Large scale causal discovery
@article{lopez2022largefactorgraphs,
  title={{Large-scale Differentiable Causal Discovery of Factor Graphs}},
  author={Lopez, Romain and H{\"u}tter, Jan-Christian and Pritchard, Jonathan and Regev, Aviv},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={19290--19303},
  year={2022}
}

@inproceedings{lippe2021ENCO_no_acyclicity,
  title={Efficient Neural Causal Discovery without Acyclicity Constraints},
  author={Lippe, Phillip and Cohen, Taco and Gavves, Efstratios},
  booktitle={International Conference on Learning Representations},
  year={2021}
}

%%%%%%%%%%%%%%%%%%%% Root cause Analysis RCA
root cause analysis for microservices murat
@article{murat2022rootcause,
  title={{Root Cause Analysis of Failures in Microservices through Causal Discovery}},
  author={Ikram, Azam and Chakraborty, Sarthak and Mitra, Subrata and Saini, Shiv and Bagchi, Saurabh and Kocaoglu, Murat},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={31158--31170},
  year={2022}
}

@article{xin2023causalrca,
  title={{CausalRCA: Causal Inference based Precise Fine-grained Root Cause Localization for Microservice Applications}},
  author={Xin, Ruyue and Chen, Peng and Zhao, Zhiming},
  journal={Journal of Systems and Software},
  volume={203},
  pages={111724},
  year={2023},
  publisher={Elsevier}
}


@article{lin2024GrangerRCA, 
title={{Root Cause Analysis in Microservice Using Neural Granger Causal Discovery}}, 
author={Lin, Cheng-Ming and Chang, Ching and Wang, Wei-Yao and Wang, Kuang-Da and Peng, Wen-Chih}, 
volume={38},
number={1}, 
journal={Proceedings of the AAAI Conference on Artificial Intelligence}, 
year={2024}, 
month={Mar.}, 
pages={206-213} 
}

%%%%%%%%%%%%% Control systems, Z-transform 
@book{skogestad2005multivariablecontrol,
  title={{Multivariable Feedback Control: Analysis and Design}},
  author={Skogestad, Sigurd and Postlethwaite, Ian},
  year={2005},
  publisher={john Wiley \& sons}
}

%%%%%%%%%%%%%%%%%% Benchmarks, datasets, surveys
@article{marbach2009dream3,
  title={Generating realistic in silico gene networks for performance assessment of reverse engineering methods},
  author={Marbach, Daniel and Schaffter, Thomas and Mattiussi, Claudio and Floreano, Dario},
  journal={Journal of computational biology},
  volume={16},
  number={2},
  pages={229--239},
  year={2009},
  publisher={Mary Ann Liebert, Inc. 2 Madison Avenue Larchmont, NY 10538 USA}
}

@article{prill2010dream3,
  title={Towards a rigorous assessment of systems biology models: the DREAM3 challenges},
  author={Prill, Robert J and Marbach, Daniel and Saez-Rodriguez, Julio and Sorger, Peter K and Alexopoulos, Leonidas G and Xue, Xiaowei and Clarke, Neil D and Altan-Bonnet, Gregoire and Stolovitzky, Gustavo},
  journal={PloS one},
  volume={5},
  number={2},
  pages={e9202},
  year={2010},
  publisher={Public Library of Science San Francisco, USA}
}
@misc{mehta2023nvidia,
    author = {Reuters},
    title = {Nvidia shares soar nearly 30\% as sales forecast jumps and AI booms},
    howpublished = {\url{https://www.reuters.com/technology/nvidia-forecasts-second-quarter-revenue-above-estimates-2023-05-24/}},
    year = {2023},
    note = {Accessed: 2024-05-21}
}

@misc{paul2024facebook,
    author = {Reuters},
    title = {Facebook parent Meta declares first dividend, shares soar},
    howpublished = {\url{https://www.reuters.com/technology/facebook-parent-meta-declares-first-ever-dividend-2024-02-01/}},
    year = {2024},
    note = {Accessed: 2024-05-21}
}

@misc{meteoswiss_climate,
  author = {{MeteoSwiss}},
  title = {The Climate of Switzerland},
  howpublished = {\url{https://www.meteoswiss.admin.ch/climate/the-climate-of-switzerland.html}},
  year = {2024},
  note = {Accessed: 2024-05-17}
}


@inproceedings{cheng2024causaltimebench,
title={{CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery}},
author={Yuxiao Cheng and Ziqian Wang and Tingxiong Xiao and Qin Zhong and Jinli Suo and Kunlun He},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=iad1yyyGme}
}

@article{runge2023causalsurveynature,
  title={{Causal inference for time series}},
  author={Runge, Jakob and Gerhardus, Andreas and Varando, Gherardo and Eyring, Veronika and Camps-Valls, Gustau},
  journal={Nature Reviews Earth \& Environment},
  volume={4},
  number={7},
  pages={487--505},
  year={2023},
  publisher={Nature Publishing Group UK London}
}


@inproceedings{causal2023temporaloverview,
author = {Gong, Chang and Yao, Di and Zhang, Chuzhe and Li, Wenbin and Bi, Jingping and Du, Lun and Wang, Jin},
title = {{Causal Discovery from Temporal Data: An Overview and New Perspectives}},
year = {2023},
booktitle = {Association for Computing Machinery},
pages = {5803–5804},
numpages = {2},
keywords = {temporal data analysis, relational learning, causal discovery},
series = {KDD '23}
}

@article{hasan2023causalsurvey,
  title={{A Survey on Causal Discovery Methods for I.I.D. and Time Series Data
}},
  author={Hasan, Uzma and Hossain, Emam and Gani, Md Osman},
  journal={Transactions on Machine Learning Research},
  year={2023}
}

@article{assaad2022survey,
  title={{Survey and Evaluation of Causal Discovery Methods for Time Series}},
  author={Assaad, Charles K. and Devijver, Emilie and Gaussier, Eric},
  journal={Journal of Artificial Intelligence Research},
  volume={73},
  pages={767--819},
  year={2022}
}

% FMRI simulated dataset
@article{smith2011FMRI,
  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},
  journal={Neuroimage},
  volume={54},
  number={2},
  pages={875--891},
  year={2011},
  publisher={Elsevier}
}

% simulated financial series
@book{kleinberg2013finance,
  title={{Causality, Probability, and Time}},
  author={Kleinberg, Samantha},
  year={2013},
  publisher={Cambridge University Press}
}

@article{fama1970efficient,
  title={{Efficient Capital Markets: A Review of Theory and Empirical Work}},
  author={Fama, Eugene F},
  journal={Journal of finance},
  volume={25},
  number={2},
  pages={383--417},
  year={1970}
}

@article{yang2023precipitationUS,
  title={{Finding Causal Gateways of Precipitation Over the Contiguous United States}},
  author={Yang, Xueli and Wang, Zhi-Hua and Wang, Chenghao and Lai, Ying-Cheng},
  journal={Geophysical Research Letters},
  volume={50},
  number={4},
  pages={e2022GL101942},
  year={2023},
  publisher={Wiley Online Library}
}

@article{yang2022heatUS,
  title={{Detecting the causal influence of thermal environments among climate regions in the United States}},
  author={Yang, Xueli and Wang, Zhi-Hua and Wang, Chenghao and Lai, Ying-Cheng},
  journal={Journal of Environmental Management},
  volume={322},
  pages={116001},
  year={2022},
  publisher={Elsevier}
}

%%%%%%%%%%%% DAG learning methods
@article{misiakos2024fewrootcauses,
  title={{Learning DAGs from Data with Few Root Causes}},
  author={Misiakos, Panagiotis and Wendler, Chris and P{\"u}schel, Markus},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2023}
}

%%%%%%%%%%%%%%%%%%%%%% Time series DAG learning methods %%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% Functional causal model %%%%%%%%%%
@article{hyvarinen2010varlingam,
  title={{Estimation of a Structural Vector Autoregression Model
Using Non-Gaussianity}},
  author={Hyv{\"a}rinen, Aapo and Zhang, Kun and Shimizu, Shohei and Hoyer, Patrik O},
  journal={Journal of Machine Learning Research},
  volume={11},
  number={5},
  year={2010}
}

@article{peters2013timino,
  title={{Causal Inference on Time Series using Structural Equation Models}},
  author={Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  journal={Advances in neural information processing systems},
  volume={26},
  year={2013}
}

% Functional causal model based, learns summary graph.
@inproceedings{assaad2021NBCB,
  title={{A Mixed Noise and Constraint-Based Approach to Causal Inference in Time Series}},
  author={Assaad, Charles K. and Devijver, Emilie and Gaussier, Eric and Ait-Bachir, Ali},
  booktitle={Machine Learning and Knowledge Discovery in Databases. Research Track: European Conference, ECML PKDD 2021, Bilbao, Spain, September 13--17, 2021, Proceedings, Part I 21},
  pages={453--468},
  year={2021},
  organization={Springer}
}

%%%%%%%%%%%% Score-based %%%%%%%%%%
@inproceedings{sun2023ntsnotears,
  title={{NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge}},
  author={Sun, Xiangyu and Schulte, Oliver and Liu, Guiliang and Poupart, Pascal},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1942--1964},
  year={2023},
  organization={PMLR}
}

@inproceedings{pamfil2020dynotears,
  title={{DYNOTEARS: Structure Learning from Time-Series Data}},
  author={Pamfil, Roxana and Sriwattanaworachai, Nisara and Desai, Shaan and Pilgerstorfer, Philip and Georgatzis, Konstantinos and Beaumont, Paul and Aragam, Bryon},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1595--1605},
  year={2020},
  organization={PMLR}
}

% works with interventions 
% (similar performance with DYNOTEARS in observational dataset)
@inproceedings{gao2022idyno,
  title={{IDYNO: Learning Nonparametric DAGs from Interventional Dynamic Data}},
  author={Gao, Tian and Bhattacharjya, Debarun and Nelson, Elliot and Liu, Miao and Yu, Yue},
  booktitle={International Conference on Machine Learning},
  pages={6988--7001},
  year={2022},
  organization={PMLR}
}

%%%%%%%%%%%% Constraint-based %%%%%%%%%%
% The constraint-based method $\text{PCMCI}_Ω$ \cite{gao2024PCMCI_Om} extends PCMCI for periodically changing time series model. 
@article{gao2024PCMCI_Om,
  title={{Causal Discovery in Semi-Stationary Time Series}},
  author={Gao, Shanyun and Addanki, Raghavendra and Yu, Tong and Rossi, Ryan and Kocaoglu, Murat},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2024}
}

%PAG
@article{entner2010tsFCI,
  title={{On Causal Discovery from Time Series Data using FCI}},
  author={Entner, Doris and Hoyer, Patrik O},
  journal={Probabilistic graphical models},
  pages={121--128},
  year={2010}
}

@article{runge2019PCMCI,
  title={{Detecting and quantifying causal associations in large nonlinear time series datasets}},
  author={Runge, Jakob and Nowack, Peer and Kretschmer, Marlene and Flaxman, Seth and Sejdinovic, Dino},
  journal={Science advances},
  volume={5},
  number={11},
  pages={eaau4996},
  year={2019},
  publisher={American Association for the Advancement of Science}
}

@inproceedings{runge2020pcmci+,
  title={{Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets}},
  author={Runge, Jakob},
  booktitle={Conference on Uncertainty in Artificial Intelligence},
  pages={1388--1397},
  year={2020},
  organization={PMLR}
}

@article{gerhardus2020lpcmci,
  title={{High-recall causal discovery for autocorrelated time series with latent confounders}},
  author={Gerhardus, Andreas and Runge, Jakob},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={12615--12625},
  year={2020}
}

@inproceedings{assaad2022PC-GCE,
  title={{Discovery of extended summary graphs in time series}},
  author={Assaad, Charles K. and Devijver, Emilie and Gaussier, Eric},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={96--106},
  year={2022},
  organization={PMLR}
}

@inproceedings{malinsky2018SVAR-FCI,
  title={{Causal Structure Learning from Multivariate Time Series in
Settings with Unmeasured Confounding}},
  author={Malinsky, Daniel and Spirtes, Peter},
  booktitle={Proceedings of 2018 ACM SIGKDD workshop on causal discovery},
  pages={23--47},
  year={2018},
  organization={PMLR}
}
%%%%%%%%%%%%%%%%%%% Convergent cross mapping 
% This category detects causality between two variables (pairwise) in a deterministic dynamical system 
@article{sugihara2012CCM,
  title={{Detecting Causality in Complex Ecosystems}},
  author={Sugihara, George and May, Robert and Ye, Hao and Hsieh, Chih-hao and Deyle, Ethan and Fogarty, Michael and Munch, Stephan},
  journal={science},
  volume={338},
  number={6106},
  pages={496--500},
  year={2012},
  publisher={American Association for the Advancement of Science}
}

@article{ye2015distingdelayCCM,
  title={{Distinguishing time-delayed causal interactions using convergent cross mapping}},
  author={Ye, Hao and Deyle, Ethan R and Gilarranz, Luis J and Sugihara, George},
  journal={Scientific reports},
  volume={5},
  number={1},
  pages={14750},
  year={2015},
  publisher={Nature Publishing Group UK London}
}

@article{benkHo2018CCM,
  title={{Complete Inference of Causal Relations between Dynamical Systems}},
  author={Benk{\H{o}}, Zsigmond and Zlatniczki, Ad{\'a}m and Stippinger, Marcell and Fab{\'o}, D{\'a}niel and S{\'o}lyom, Andr{\'a}s and Er{\H{o}}ss, Lor{\'a}nd and Telcs, Andr{\'a}s and Somogyv{\'a}ri, Zolt{\'a}n},
  journal={arXiv preprint arXiv:1808.10806},
  year={2018}
}

@inproceedings{de2020latentCCM,
  title={{Latent Convergent Cross Mapping}},
  author={De Brouwer, Edward and Arany, Adam and Simm, Jaak and Moreau, Yves},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

%%%%%%%%%%%% Granger causality %%%%%%%%%%
% summary graph
@inproceedings{marcinkevivcs2020GVAR,
  title={{Interpretable Models for Granger Causality Using Self-explaining Neural Networks}},
  author={Marcinkevi{\v{c}}s, Ri{\v{c}}ards and Vogt, Julia E},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

% summary graph
% Adds up outputs of d neural networks (MLPs). Inputs are the individual pasts of variables and output is a selected variable present. If a NN is constant on a variable, then that variable does not Granger-cause the selected variable.
@inproceedings{bussmann2021NAVAR,
  title={{Neural Additive Vector Autoregression Models for Causal Discovery in Time Series}},
  author={Bussmann, Bart and Nys, Jannes and Latr{\'e}, Steven},
  booktitle={Discovery Science: 24th International Conference, DS 2021, Halifax, NS, Canada, October 11--13, 2021, Proceedings 24},
  pages={446--460},
  year={2021},
  organization={Springer}
}

% uses MLPs and RNNs to learn non-linear Autoregressive models
@article{tank2021neuralGranger,
  title={{Neural Granger Causality}},
  author={Tank, Alex and Covert, Ian and Foti, Nicholas and Shojaie, Ali and Fox, Emily B},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  volume={44},
  number={8},
  pages={4267--4279},
  year={2021},
  publisher={IEEE}
}

% fewer trainable parameters -> less prone to overfitting
@inproceedings{khanna2019eSRU,
  title={{Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality}},
  author={Khanna, Saurabh and Tan, Vincent YF},
  booktitle={International Conference on Learning Representations},
  year={2019}
}

% GrID-Net used for single cell analysis
% Observations are not time-series but have a partial order
% It generalizes Granger causality from time domain to DAG domain. A variable Granger causes another if the past (ancestors) helps for the prediction of the other.
@inproceedings{wu2021grangerGenomicLoci,
  title={{Granger causal inference on DAGs identifies genomic loci regulating transcription}},
  author={Wu, Alexander P and Singh, Rohit and Berger, Bonnie},
  booktitle={International Conference on Learning Representations},
  year={2021}
}

% Copula-based granger causality
@article{hu2014copulaGranger,
  title={{A copula approach to assessing Granger causality}},
  author={Hu, Meng and Liang, Hualou},
  journal={NeuroImage},
  volume={100},
  pages={125--134},
  year={2014},
  publisher={Elsevier}
}

% employs kernel functions for non-linear granger causality
@article{marinazzo2008kernelGranger,
  title={{Kernel-Granger causality and the analysis of dynamical networks}},
  author={Marinazzo, Daniele and Pellicoro, Mario and Stramaglia, Sebastiano},
  journal={Physical review E},
  volume={77},
  number={5},
  pages={056215},
  year={2008},
  publisher={APS}
}

%%%%%%%%%%%% Neural networks %%%%%%%%%%
@article{gong2022rhino,
  title={Rhino: Deep causal temporal relationship learning with history-dependent noise},
  author={Gong, Wenbo and Jennings, Joel and Zhang, Cheng and Pawlowski, Nick},
  journal={arXiv preprint arXiv:2210.14706},
  year={2022}
}

@article{nauta2019TCDF,
  title={{Causal Discovery with Attention-Based Convolutional Neural Networks}},
  author={Nauta, Meike and Bucur, Doina and Seifert, Christin},
  journal={Machine Learning and Knowledge Extraction},
  volume={1},
  number={1},
  pages={19},
  year={2019},
  publisher={MDPI}
}

@inproceedings{xu2019SCGL,
  title={{Scalable Causal Graph Learning through a Deep Neural Network}},
  author={Xu, Chenxiao and Huang, Hao and Yoo, Shinjae},
  booktitle={Proceedings of the 28th ACM international conference on information and knowledge management},
  pages={1853--1862},
  year={2019}
}

% examines continuous-time data
@inproceedings{bellot2021neuralgraphmodelling,
  title={Neural graphical modelling in continuous-time: consistency guarantees and algorithms},
  author={Bellot, Alexis and Branson, Kim and van der Schaar, Mihaela},
  booktitle={International Conference on Learning Representations},
  year={2022}
}

@inproceedings{lowe2022amortized,
  title={{Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data}},
  author={L{\"o}we, Sindy and Madras, David and Zemel, Richard and Welling, Max},
  booktitle={Conference on Causal Learning and Reasoning},
  pages={509--525},
  year={2022},
  organization={PMLR}
}


%%%%%%%%%%%% Irregular time-series %%%%%%%%%%
% has been accepted to ICLR 2023
% summary graph for irregular time series
% Time-series data some times do not have the same measurement frequency (e.g. different sensor specifications) or random missing values (e.g. transmission loss)
% Methods CUTS \cite{cheng2023cuts}, CUTS+ \cite{cheng2024cuts+}. 
@inproceedings{cheng2023cuts,
  title={{CUTS: Neural Causal Discovery from Irregular Time-Series Data}},
  author={Cheng, Yuxiao and Yang, Runzhao and Xiao, Tingxiong and Li, Zongren and Suo, Jinli and He, Kunlun and Dai, Qionghai},
  booktitle={The Eleventh International Conference on Learning Representations},
  year={2023}
}

@inproceedings{cheng2024cuts+,
  title={{CUTS+: High-dimensional Causal Discovery from Irregular Time-series}},
  author={Cheng, Yuxiao and Li, Lianglong and Xiao, Tingxiong and Li, Zongren and Suo, Jinli and He, Kunlun and Dai, Qionghai},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={38},
  pages={11525--11533},
  year={2024}
}

% Subsampled data are those that their sampling frequency is smaller than the causal effect frequency (causal dependencies changes happen faster than the measurements). 
% has only lag up to 1 
@inproceedings{gong2015subsampledNGEM,
  title={{Discovering Temporal Causal Relations from Subsampled Data
}},
  author={Gong, Mingming and Zhang, Kun and Schoelkopf, Bernhard and Tao, Dacheng and Geiger, Philipp},
  booktitle={International Conference on Machine Learning},
  pages={1898--1906},
  year={2015},
  organization={PMLR}
}

% summary graph
% Neurips was in 2023
@article{liu2023subsampledproxy,
  title={{Causal Discovery from Subsampled Time Series with Proxy Variables
}},
  author={Liu, Mingzhou and Sun, Xinwei and Hu, Lingjing and Wang, Yizhou},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2023}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%% Vector autoregression
@misc{sims1980comparison,
  title={{Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered}},
  author={Sims, Christopher A},
  year={1980},
  publisher={National Bureau of Economic Research Cambridge, Mass., USA}
}

@book{lutkepohl2005new,
  title={{New Introduction to Multiple Time Series Analysis}},
  author={L{\"u}tkepohl, Helmut},
  year={2005},
  publisher={Springer Science \& Business Media}
}

@incollection{kilian2013SVAR,
  title={{Structural Vector Autoregressions}},
  author={Kilian, Lutz},
  booktitle={Handbook of research methods and applications in empirical macroeconomics},
  pages={515--554},
  year={2013},
  publisher={Edward Elgar Publishing}
}

@book{saikkonen2001stability,
  title={{Stability results for nonlinear vector autoregressions with an application to a nonlinear error correction model}},
  author={Saikkonen, Pentti},
  year={2001},
  publisher={Humboldt-Universit{\"a}t zu Berlin, Wirtschaftswissenschaftliche Fakult{\"a}t}
}

@article{lv2021linearconvergence,
  title={{Linear Convergence of Gradient Methods for Estimating Structured Transition Matrices in High-dimensional Vector Autoregressive Models}},
  author={Lv, Xiao and Cui, Wei and Liu, Yulong},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={16751--16763},
  year={2021}
}

%%%%%%%%%%%%% Applications VAR 
@inproceedings{varlingam2023linkagesfinance,
  title={{Linkages among the Foreign Exchange, Stock, and Bond Markets in Japan and the United States}},
  author={Jiang, Yi and Shimizu, Shohei},
  booktitle={Causal Analysis Workshop Series},
  pages={1--19},
  year={2023},
  organization={PMLR}
}

%%%% Fourier Analysis DAGs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% theory of causal fourier analysis with examples of Fourier sparse functions on DAGs

@article{bastiJournalpaper,
  author={Seifert, Bastian and Wendler, Chris and Püschel, Markus},
  journal={IEEE Trans.~Signal Process.}, 
  title={{Causal Fourier Analysis on Directed Acyclic Graphs and Posets}}, 
  year={2023},
  volume={71},
  number={},
  pages={3805-3820},
  doi={10.1109/TSP.2023.3324988}
}
  

% workshop paper on learning fourier sparse functions on DAGs 
@inproceedings{bastiSparseFunctionsOnDAGs,
  title={{Learning Fourier-Sparse Functions on DAGs}},
  author={Seifert, Bastian and Wendler, Chris and P{\"u}schel, Markus},
  booktitle={ICLR2022 Workshop on the Elements of Reasoning: Objects, Structure and Causality},
  year={2022}
}

%%%% Fourier Sparsity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% applying sparsity for compression of images and sensor measurements
@inproceedings{sandryhailaGFTsignalCompression,
  title={{Discrete signal processing on graphs: Graph Fourier transform}},
  author={Sandryhaila, Aliaksei and Moura, Jos{\'e} MF},
  booktitle={2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
  pages={6167--6170},
  year={2013},
  organization={IEEE}
}

% Fourier sparse learning theory
% contains arguments about compressive sensing
@inproceedings{stobbe2012learning,
  title={{Learning Fourier Sparse Set Functions}},
  author={Stobbe, Peter and Krause, Andreas},
  booktitle={Artificial Intelligence and Statistics},
  pages={1125--1133},
  year={2012},
  organization={PMLR}
}

% andisheh's efficient fourier sparse learning
@article{andishehEfficientSparse,
  title={{Efficiently Learning Fourier Sparse Set Functions}},
  author={Amrollahi, Andisheh and Zandieh, Amir and Kapralov, Michael and Krause, Andreas},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  year={2019}
}


% Chris learning Fourier-sparse set functions on non-orthogonal domains.
@article{wendler2021NonOrthogonal,
  title={{Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases}},
  author={Wendler, Chris and Amrollahi, Andisheh and Seifert, Bastian and Krause, Andreas and P{\"u}schel, Markus},
  journal={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  number={12},
  pages={10283--10292},
  year={2021}
}


@ARTICLE{DPSSAmplingTheory,
  author={{Chen, Siheng and Varma, Rohan and Sandryhaila, Aliaksei and Kovačević, Jelena}},
  journal={IEEE Transactions on Signal Processing}, 
  title={Discrete Signal Processing on Graphs: Sampling Theory}, 
  year={2015},
  volume={63},
  number={24},
  pages={6510-6523},
  doi={10.1109/TSP.2015.2469645}}
  

% sparse FFT with applications from MIT team.
@inproceedings{SFFT2012,
  title={{Simple and practical algorithm for sparse Fourier transform}},
  author={Hassanieh, Haitham and Indyk, Piotr and Katabi, Dina and Price, Eric},
  booktitle={Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms},
  pages={1183--1194},
  year={2012},
  organization={SIAM}
}

@inproceedings{SFFT2014,
  title={{Sample-optimal sparse Fourier transform in any constant dimension}},
  author={Indyk, Piotr and Kapralov, Michael},
  booktitle={FOCS},
  year={2014}
}

@article{JPEG,
author = {Wallace, Gregory K.},
title = {{The JPEG Still Picture Compression Standard}},
year = {1991},
issue_date = {April 1991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {34},
number = {4},
issn = {0001-0782},
url = {https://doi.org/10.1145/103085.103089},
doi = {10.1145/103085.103089},
journal = {Commun. ACM},
month = {apr},
pages = {30–44},
numpages = {15}
}

@inproceedings{spectrumsensing,
  title={{GHz-wide sensing and decoding using the sparse Fourier transform}},
  author={Hassanieh, Haitham and Shi, Lixin and Abari, Omid and Hamed, Ezzeldin and Katabi, Dina},
  booktitle={IEEE INFOCOM 2014-IEEE Conference on Computer Communications},
  pages={2256--2264},
  year={2014},
  organization={IEEE}
}

@inproceedings{MRS,
  title={Mrs sparse-fft: Reducing acquisition time and artifacts for in vivo 2d correlation spectroscopy},
  author={Shi, Lixin and Andronesi, Ovidiu and Hassanieh, Haitham and Ghazi, Badih and Katabi, Dina and Adalsteinsson, Elfar},
  booktitle={ISMRM13, Int. Society for Magnetic Resonance in Medicine Annual Meeting and Exhibition},
  year={2013}
}

@inproceedings{GPSlocking,
  title={Faster GPS via the sparse Fourier transform},
  author={Hassanieh, Haitham and Adib, Fadel and Katabi, Dina and Indyk, Piotr},
  booktitle={Proceedings of the 18th annual international conference on Mobile computing and networking},
  pages={353--364},
  year={2012}
}

@inproceedings{cellularaudio,
  title={Hearing voices in the high frequencies: What your cell phone isn’t telling you},
  author={Monson, BB},
  booktitle={Proc 168th Acoustic Society of America (ASA) Meeting, Indianapolis, October},
  year={2014}
}

@article{algebraicSPtheory,
  title={Algebraic signal processing theory},
  author={P{\"u}schel, Markus and Moura, Jos{\'e} MF},
  journal={arXiv preprint cs/0612077},
  year={2006}
}

@article{Pueschel.Moura:2008a,
    AUTHOR = {P{\"u}schel, M. and Moura, J.~M.~F. },
    TITLE = {Algebraic Signal Processing Theory: Foundation and {1-D} Time},
    JOURNAL = {{IEEE Trans.~Signal Process.}},
    VOLUME = {56},
    NUMBER = {8},
    PAGES = {3572--3585},
    YEAR = {2008}
 }

@book{sparse-fft,
author = {Hassanieh, Haitham},
title = {The Sparse Fourier Transform: Theory and Practice},
year = {2018},
publisher = {Association for Computing Machinery and Morgan and Claypool},
volume = {19}
}

%%%% Surveys & Books %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book{horn2012matrixanalysis,
  title={Matrix analysis},
  author={Horn, Roger A. and Johnson, Charles R.},
  year={2012},
  publisher={Cambridge university press}
}

@book{probabilisticgraphicalmodels,
  title={{Probabilistic graphical models: principles and techniques}},
  author={Koller, Daphne and Friedman, Nir},
  year={2009},
  publisher={The MIT press}
}

@book{elementsCausalInference,
  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}
}

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

@article{dyalikedags,
  title={{D’ya like DAGs? A survey on structure learning and causal discovery}},
  author={Vowels, Matthew J and Camgoz, Necati Cihan and Bowden, Richard},
  journal={ACM Computing Surveys (CSUR)},
  year={2021},
  publisher={ACM New York, NY}
}

% problems SEMs
@article{drton2016algebraic,
  title={{Algebraic problems in structural equation modeling}},
  author={Drton, Mathias and others},
  journal={The 50th anniversary of Gr{\"o}bner bases},
  pages={35--86},
  year={2016}
}

@article{heinze2018causal,
  title={{Causal structure learning}},
  author={Heinze-Deml, Christina and Maathuis, Marloes H and Meinshausen, Nicolai},
  journal={Annual Review of Statistics and Its Application},
  volume={5},
  pages={371--391},
  year={2018},
  publisher={Annual Reviews}
}

%%%% DAG Learning methods %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PC algorithm
@book{spirtes2000PC,
  title={{Causation, prediction, and search}},
  author={Spirtes, Peter and Glymour, Clark N and Scheines, Richard and Heckerman, David},
  year={2000},
  publisher={MIT press}
}

% GES
@article{chickering2002ges,
  title={{Optimal structure identification with greedy search}},
  author={Chickering, David Maxwell},
  journal={Journal of machine learning research},
  volume={3},
  number={Nov},
  pages={507--554},
  year={2002}
}

% permutations - combinatorial approach
@article{raskutti2018permutations,
  title={{Learning directed acyclic graph models based on sparsest permutations}},
  author={Raskutti, Garvesh and Uhler, Caroline},
  journal={Stat},
  volume={7},
  number={1},
  pages={e183},
  year={2018},
  publisher={Wiley Online Library}
}

@inproceedings{dagpermutahedron,
  title={{DAG Learning on the Permutahedron}},
  author={Zantedeschi, Valentina and Kaddour, Jean and Franceschi, Luca and Kusner, Matt and Niculae, Vlad},
  booktitle={ICLR2022 Workshop on the Elements of Reasoning: Objects, Structure and Causality},
  year={2022}
}


@article{lorch2021dibs,
  title={{DiBS: Differentiable Bayesian structure learning}},
  author={Lorch, Lars and Rothfuss, Jonas and Sch{\"o}lkopf, Bernhard and Krause, Andreas},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={24111--24123},
  year={2021}
}


@inproceedings{differentiableDAGsampling,
  title={{Differentiable DAG Sampling}},
  author={Charpentier, Bertrand and Kibler, Simon and G{\"u}nnemann, Stephan},
  booktitle={International Conference on Learning Representations},
  year={2022}
}

% fGES scales to more vertices
@article{ramsey2017fGES,
  title={{A million variables and more: the fast greedy equivalence search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images}},
  author={Ramsey, Joseph and Glymour, Madelyn and Sanchez-Romero, Ruben and Glymour, Clark},
  journal={International journal of data science and analytics},
  volume={3},
  number={2},
  pages={121--129},
  year={2017},
  publisher={Springer}
}

@article{tsamardinos2006MMHC,
  title={{The max-min hill-climbing Bayesian network structure learning algorithm}},
  author={Tsamardinos, Ioannis and Brown, Laura E and Aliferis, Constantin F},
  journal={Machine learning},
  volume={65},
  number={1},
  pages={31--78},
  year={2006},
  publisher={Springer}
}


@article{shimizu2006lingam,
  author  = {Shohei Shimizu and Patrik O. Hoyer and Aapo Hyvärinen and Antti Kerminen},
  title   = {{A Linear Non-Gaussian Acyclic Model for Causal Discovery}},
  journal = {Journal of Machine Learning Research},
  year    = {2006},
  volume  = {7},
  number  = {72},
  pages   = {2003--2030},
  url     = {http://jmlr.org/papers/v7/shimizu06a.html}
}

@article{shimizu2011directlingam,
  title={{DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model}},
  author={Shimizu, Shohei and Inazumi, Takanori and Sogawa, Yasuhiro and Hyvarinen, Aapo and Kawahara, Yoshinobu and Washio, Takashi and Hoyer, Patrik O and Bollen, Kenneth and Hoyer, Patrik},
  journal={Journal of Machine Learning Research-JMLR},
  volume={12},
  number={Apr},
  pages={1225--1248},
  year={2011}
}

@article{akinwande2024acceleratedlingam,
  title={{AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs}},
  author={Akinwande, Victor and Kolter, J Zico},
  journal={arXiv preprint arXiv:2403.03772},
  year={2024}
}


% indicates that most synthetic experiments can be solved by sortnregress
@article{reisach2021beware,
  title={{Beware of the simulated DAG! causal discovery benchmarks may be easy to game}},
  author={Reisach, Alexander and Seiler, Christof and Weichwald, Sebastian},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={27772--27784},
  year={2021}
}


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

% Dag no curl
@inproceedings{DAGnoCurl2021,
  title={{DAGs with no curl: An efficient DAG structure learning approach}},
  author={Yu, Yue and Gao, Tian and Yin, Naiyu and Ji, Qiang},
  booktitle={International Conference on Machine Learning},
  pages={12156--12166},
  year={2021},
  organization={PMLR}
}

% DAG-GAN
@inproceedings{gao2021dagGAN,
  title={{DAG-GAN: Causal structure learning with generative adversarial nets}},
  author={Gao, Yinghua and Shen, Li and Xia, Shu-Tao},
  booktitle={International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={3320--3324},
  year={2021},
  organization={IEEE}
}

% new more effiecient acyclicity constraint - but more unstable
@inproceedings{yu2019dagGNN,
  title={{DAG-GNN: DAG structure learning with graph neural networks}},
  author={Yu, Yue and Chen, Jie and Gao, Tian and Yu, Mo},
  booktitle={International Conference on Machine Learning},
  pages={7154--7163},
  year={2019},
  organization={PMLR}
}

% DAGMA
@article{bello2022dagma,
  title={{DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization}},
  author={Bello, Kevin and Aragam, Bryon and Ravikumar, Pradeep},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={8226--8239},
  year={2022}
}

% GOLEM better than NOTEARS for linear SEMs
@article{ng2020GOLEM,
  title={{On the Role of Sparsity and DAG Constraints for
Learning Linear DAGs}},
  author={Ng, Ignavier and Ghassami, AmirEmad and Zhang, Kun},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={17943--17954},
  year={2020}
}

% NO BEARS scales to more vertices
@inproceedings{lee2019NOBEARS,
  title={{Scaling structural learning with NO-BEARS to infer causal transcriptome networks}},
  author={Lee, Hao-Chih and Danieletto, Matteo and Miotto, Riccardo and Cherng, Sarah T and Dudley, Joel T},
  booktitle={Pacific Symposium on Biocomputing},
  pages={391--402},
  year={2019},
  organization={World Scientific}
}

@article{zheng2018notears,
  title={{DAGs with NO TEARS: Continuous Optimization for Structure Learning}},
  author={Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep K and Xing, Eric P},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  year={2018}
}

% with reinforcement learning 
% explicitly mentions definition of causal discovery.
@inproceedings{zhu2020reinforcement,
  title={{Causal Discovery with Reinforcement Learning}},
  author={Zhu, Shengyu and Ng, Ignavier and Chen, Zhitang},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

@inproceedings{zheng2020notearsnonlinear,
  title={{Learning Sparse Nonparametric DAGs}},
  author={Zheng, Xun and Dan, Chen and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3414--3425},
  year={2020},
  organization={PMLR}
}


@inproceedings{cao2022skeletonNeuralDAG,
  title={{A New Skeleton-Neural DAG Learning Approach}},
  author={Cao, Yiwen and Yu, Kui and Huang, Xiaoling and Wang, Yujie},
  booktitle={Pacific-Asia Conference on Knowledge Discovery and Data Mining},
  pages={626--638},
  year={2022},
  organization={Springer}
}


@inproceedings{lachapelle2019granDAG,
  title={Gradient-Based Neural DAG Learning},
  author={Lachapelle, S{\'e}bastien and Brouillard, Philippe and Deleu, Tristan and Lacoste-Julien, Simon},
  booktitle={International Conference on Learning Representations},
  year={2019}
}


%%%% Identifiability & Theory %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% NP complete
@incollection{chickering1996npcomplete,
  title={{Learning Bayesian networks is NP-complete}},
  author={Chickering, David Maxwell},
  booktitle={Learning from data},
  pages={121--130},
  year={1996},
  publisher={Springer}
}

% NP hard
@article{chickering2004nphard,
  title={{Large-Sample Learning of Bayesian Networks is NP-Hard}},
  author={Chickering, Max and Heckerman, David and Meek, Chris},
  journal={Journal of Machine Learning Research},
  volume={5},
  pages={1287--1330},
  year={2004}
}


% faithfulness violations have measure 0
% infer some edge directions due to the acyclicity of the graph
@inproceedings{meek1995causal,
  title={{Casual Inference and Causal Explanation with Background Knowledge}},
  author={Meek, C},
  booktitle={Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence},
  pages={403--410},
  year={1995},
  organization={Morgan Kaufmann}
}

% faithfulness can exist in linear causal models and its violations are of measure 0
@inproceedings{meek1995measure0,
  title={{Strong Completeness and Faithfulness in Bayesian Networks}},
  author={Meek, C},
  booktitle={Proc. Conf. on Uncertainty in Artificial Intelligence (UAI-95)},
  pages={411--418},
  year={1995}
}

% Construction of faithfulness violations
@inproceedings{ramsey2006adjacencyFaithfullness,
  title={{Adjacency-faithfulness and conservative causal inference}},
  author={Ramsey, Joseph and Spirtes, Peter and Zhang, Jiji},
  booktitle={Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
  pages={401--408},
  year={2006}
}


% weaker faithfulness
@inproceedings{marx2021weaker,
  title={{A weaker faithfulness assumption based on triple interactions}},
  author={Marx, Alexander and Gretton, Arthur and Mooij, Joris M},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={451--460},
  year={2021},
  organization={PMLR}
}

% nonlinear ANMs identifiability
@inproceedings{zhang2009identifiability,
  title={{Causality Discovery with Additive Disturbances: An Information-Theoretical Perspective}},
  author={Zhang, Kun and Hyv{\"a}rinen, Aapo},
  booktitle={Joint European Conference on Machine Learning and Knowledge Discovery in Databases},
  pages={570--585},
  year={2009},
  organization={Springer}
}

% linear non-gaussian additive are identifiable
@inproceedings{zhang2009PNL,
  title={{On the Identifiability of the Post-Nonlinear Causal Model}},
  author={Zhang, K and Hyv{\"a}rinen, A},
  booktitle={25th Conference on Uncertainty in Artificial Intelligence (UAI 2009)},
  pages={647--655},
  year={2009},
  organization={AUAI Press}
}


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


% peters 2010
@inproceedings{peters2010identifying,
  title={{Identifying cause and effect on discrete data using additive noise models}},
  author={Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  booktitle={Proceedings of the thirteenth international conference on artificial intelligence and statistics},
  pages={597--604},
  year={2010},
  organization={JMLR Workshop and Conference Proceedings}
}

% peters 2012
@article{peters2012identifiabilityfunctional,
  title={{Identifiability of causal graphs using functional models}},
  author={Peters, Jonas and Mooij, Joris and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  journal={arXiv preprint arXiv:1202.3757},
  year={2012}
}


% non-linear identifiability additive noise
@article{hoyer2008nonlinear,
  title={{Nonlinear causal discovery with additive noise models}},
  author={Hoyer, Patrik and Janzing, Dominik and Mooij, Joris M and Peters, Jonas and Sch{\"o}lkopf, Bernhard},
  journal={Advances in neural information processing systems},
  volume={21},
  year={2008}
}

@inproceedings{mooij2009regression,
  title={{Regression by dependence minimization and its application to causal inference in additive noise models}},
  author={Mooij, Joris and Janzing, Dominik and Peters, Jonas and Sch{\"o}lkopf, Bernhard},
  booktitle={Proceedings of the 26th annual international conference on machine learning},
  pages={745--752},
  year={2009}
}

% peters 2014
@article{peters2014causal,
  title={{Causal discovery with continuous additive noise models}},
  author={Peters, Jonas and Mooij, Joris M and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  year={2014}
}

% equal or known error variances identifiability
@article{loh2014equalerror,
  title={{High-dimensional learning of linear causal networks via inverse covariance estimation}},
  author={Loh, Po-Ling and B{\"u}hlmann, Peter},
  journal={The Journal of Machine Learning Research},
  volume={15},
  number={1},
  pages={3065--3105},
  year={2014},
  publisher={JMLR. org}
}

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


% at nips
@article{honorio2017learning,
  title={{Learning identifiable Gaussian Bayesian networks in polynomial time and sample complexity}},
  author={Ghoshal, Asish and Honorio, Jean},
  journal={Advances in Neural Information Processing Systems},
  volume={30},
  year={2017}
}

% linear identifiable
@inproceedings{ghoshal2018learning,
  title={{Learning linear structural equation models in polynomial time and sample complexity}},
  author={Ghoshal, Asish and Honorio, Jean},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={1466--1475},
  year={2018},
  organization={PMLR}
}

% Chen equal variances
@article{chen2019causal,
  title={{On causal discovery with an equal-variance assumption}},
  author={Chen, Wenyu and Drton, Mathias and Wang, Y Samuel},
  journal={Biometrika},
  volume={106},
  number={4},
  pages={973--980},
  year={2019},
  publisher={Oxford University Press}
}

% identifiability with conditional variances 
@article{park2020conditional,
  title={{Identifiability of Additive Noise Models Using Conditional Variances}},
  author={Park, Gunwoong},
  journal={J. Mach. Learn. Res.},
  volume={21},
  number={75},
  pages={1--34},
  year={2020}
}

% comb perspective for causal learning
@article{causalCombpersp,
  title={{Causal Structure Learning: a Combinatorial Perspective}},
  author={Squires, Chandler and Uhler, Caroline},
  journal={arXiv preprint arXiv:2206.01152},
  year={2022}
}

%unsuitability notears
@article{kaiser2022unsuitability,
  title={{Unsuitability of NOTEARS for Causal Graph Discovery when dealing with Dimensional Quantities}},
  author={Kaiser, Marcus and Sipos, Maksim},
  journal={Neural Processing Letters},
  pages={1--9},
  year={2022},
  publisher={Springer}
}


%%%% Scalability %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Time Series & Granger Causality %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Applications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@article{max_linear_noise,
  title={{PRecursive max-linear models with propagating noise}},
  author={Buck, Johannes and Kl{\"u}ppelberg, Claudia},
  journal={Electronic Journal of Statistics},
  volume={15},
  number={2},
  pages={4770--4822},
  year={2021},
  publisher={Institute of Mathematical Statistics and Bernoulli Society}
}

@article{max_linear_bayesian_tree,
  title={{Estimating a Latent Tree for Extremes}},
  author={Tran, Ngoc Mai and Buck, Johannes and Kl{\"u}ppelberg, Claudia},
  journal={arXiv preprint arXiv:2102.06197},
  year={2021}
}

@article{stocks_max_linear,
  title={{A continuous updating weighted least squares estimator of tail dependence in high dimensions}},
  author={Einmahl, John HJ and Kiriliouk, Anna and Segers, Johan},
  journal={Extremes},
  volume={21},
  number={2},
  pages={205--233},
  year={2018},
  publisher={Springer}
}

% data on thames river and its major tributaries
@misc{river_thames_dataset,
        doi = {10.5285/cf10ea9a-a249-4074-ac0c-e0c3079e5e45},
        url = {https://doi.org/10.5285/cf10ea9a-a249-4074-ac0c-e0c3079e5e45},
     author = {Bowes, M.J.;Armstrong, L.K.;Harman, S.A.;Nicholls, D.J.E.;Wickham, H.D.;Scarlett, P.M.;Juergens, M.D.},
  publisher = {NERC Environmental Information Data Centre},
      title = {{Weekly water quality data from the River Thames and its major tributaries (2009-2017)}},
       year = {2020}
}

% Learning Paths in education - causal discovery
@article{neurips_causal_edu,
  title={{Instructions and Guide: Causal Insights for Learning Paths in Education}},
  author={Gong, Wenbo and Smith, Digory and Wang, Zichao and Barton, Craig and Woodhead, Simon and Pawlowski, Nick and Jennings, Joel and Zhang, Cheng},
  journal={arXiv preprint arXiv:2208.12610},
  year={2022}
}

@article{HaslemereDataset,
  title={{Sparking “The BBC Four Pandemic”: Leveraging citizen science and mobile phones to model the spread of disease}},
  author={Kissler, Stephen M and Klepac, Petra and Tang, Maria and Conlan, Andrew JK and Gog, Julia R},
  journal={BioRxiv},
  pages={479154},
  year={2020},
  publisher={Cold Spring Harbor Laboratory}
}

@article{cdt,
  title={Causal discovery toolbox: Uncover causal relationships in python},
  author={Kalainathan, Diviyan and Goudet, Olivier},
  journal={arXiv preprint arXiv:1903.02278},
  year={2019},
  url={https://github.com/FenTechSolutions/CausalDiscoveryToolbox}
}
%%%% Data Generation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Causal protein-signaling dataset Sachs et al. 
@article{sachs2005causal,
  title={{Causal protein-signaling networks derived from multiparameter single-cell data}},
  author={Sachs, Karen and Perez, Omar and Pe'er, Dana and Lauffenburger, Douglas A and Nolan, Garry P},
  journal={Science},
  volume={308},
  number={5721},
  pages={523--529},
  year={2005},
  publisher={American Association for the Advancement of Science}
}

% Alex marx heteroscedastic noise
@inproceedings{MarxHeteroscedasticNoise,
  title={{Inferring cause and effect in the presence of heteroscedastic noise}},
  author={Xu, Sascha and Mian, Osman A and Marx, Alexander and Vreeken, Jilles},
  booktitle={International Conference on Machine Learning},
  pages={24615--24630},
  year={2022},
  organization={PMLR}
}

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




%%%% Uncategorized %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@article{DAG_max_linear,
  title={{Max-linear models on directed acyclic graphs}},
  author={Gissibl, Nadine and Kl{\"u}ppelberg, Claudia},
  journal={Bernoulli},
  volume={24},
  number={4A},
  pages={2693--2720},
  year={2018},
  publisher={Bernoulli Society for Mathematical Statistics and Probability}
}

@article{identifiability_max_linear,
  title={{Identifiability and estimation of recursive max-linear models}},
  author={Gissibl, Nadine and Kl{\"u}ppelberg, Claudia and Lauritzen, Steffen},
  journal={Scandinavian Journal of Statistics},
  volume={48},
  number={1},
  pages={188--211},
  year={2021},
  publisher={Wiley Online Library}
}

@article{rotaMoebius,
  title={On the foundations of combinatorial theory I. Theory of M{\"o}bius functions},
  author={Rota, Gian-Carlo},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete},
  volume={2},
  number={4},
  pages={340--368},
  year={1964},
  publisher={Springer-Verlag}
}

@article{waughfrisch1933,
  title={Partial time regressions as compared with individual trends},
  author={Frisch, Ragnar and Waugh, Frederick V},
  journal={Econometrica: Journal of the Econometric Society},
  pages={387--401},
  year={1933},
  publisher={JSTOR}
}

@article{Abdali.Saunders:1985a,
	author = {S. Kamal Abdali and B. David Saunders},
	title = {Transitive closure and related semiring properties via eliminants},
	journal = {Theor. Comput. Sci.},
	year = {1985},
	volume = {40},
	pages = {257-274}
}

@article{algebraictransclos,
  title={Algebraic structures for transitive closure},
  author={Lehmann, Daniel J},
  journal={Theoretical Computer Science},
  volume={4},
  number={1},
  pages={59--76},
  year={1977},
  publisher={Elsevier}
}

%%%%%%%%%%%%%%%%%%%%% GSP 
@article{sandryhaila2013discrete,
  title={Discrete signal processing on graphs},
  author={Sandryhaila, Aliaksei and Moura, Jos{\'e} MF},
  journal={IEEE transactions on signal processing},
  volume={61},
  number={7},
  pages={1644--1656},
  year={2013},
  publisher={IEEE}
}

@inproceedings{sandryhaila2013GFT,
  title={Discrete signal processing on graphs: Graph Fourier transform},
  author={Sandryhaila, Aliaksei and Moura, Jos{\'e} MF},
  booktitle={2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
  pages={6167--6170},
  year={2013},
  organization={IEEE}
}

@article{ortega2018graph,
  title={Graph signal processing: Overview, challenges, and applications},
  author={Ortega, Antonio and Frossard, Pascal and Kova{\v{c}}evi{\'c}, Jelena and Moura, Jos{\'e} MF and Vandergheynst, Pierre},
  journal={Proceedings of the IEEE},
  volume={106},
  number={5},
  pages={808--828},
  year={2018},
  publisher={IEEE}
}

%%%%%%%%%%%%%%%%%%% Graph Learning

@inproceedings{kalofolias2017large,
  title={{Large Scale Graph Learning From Smooth Signals}},
  author={Kalofolias, Vassilis and Perraudin, Nathana{\"e}l},
  booktitle={International Conference on Learning Representations},
  year={2019}
}

@inproceedings{kalofolias2016learn,
  title={How to learn a graph from smooth signals},
  author={Kalofolias, Vassilis},
  booktitle={Artificial Intelligence and Statistics},
  pages={920--929},
  year={2016},
  organization={PMLR}
}

@article{surveyGraphLearning,
  title={Graph learning: A survey},
  author={Xia, Feng and Sun, Ke and Yu, Shuo and Aziz, Abdul and Wan, Liangtian and Pan, Shirui and Liu, Huan},
  journal={IEEE Transactions on Artificial Intelligence},
  volume={2},
  number={2},
  pages={109--127},
  year={2021},
  publisher={IEEE}
}

@article{LaplacianlearningDorinaThanou,
  title={Learning Laplacian matrix in smooth graph signal representations},
  author={Dong, Xiaowen and Thanou, Dorina and Frossard, Pascal and Vandergheynst, Pierre},
  journal={IEEE Transactions on Signal Processing},
  volume={64},
  number={23},
  pages={6160--6173},
  year={2016},
  publisher={IEEE}
}

@ARTICLE{ortegaMonotoneTopology,
  author={Pavez, Eduardo and Egilmez, Hilmi E. and Ortega, Antonio},
  journal={IEEE Transactions on Signal Processing}, 
  title={Learning Graphs With Monotone Topology Properties and Multiple Connected Components}, 
  year={2018},
  volume={66},
  number={9},
  pages={2399-2413},
  doi={10.1109/TSP.2018.2813337}}


@ARTICLE{OrtegaLaplacianStructural,
  author={Egilmez, Hilmi E. and Pavez, Eduardo and Ortega, Antonio},
  journal={IEEE Journal of Selected Topics in Signal Processing}, 
  title={Graph Learning From Data Under Laplacian and Structural Constraints}, 
  year={2017},
  volume={11},
  number={6},
  pages={825-841},
  doi={10.1109/JSTSP.2017.2726975}}
  
@INPROCEEDINGS{GMRFsOrtega,
  author={Koyakumaru, Tatsuya and Yukawa, Masahiro and Pavez, Eduardo and Ortega, Antonio},
  booktitle={ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, 
  title={A Graph Learning Algorithm Based On Gaussian Markov Random Fields And Minimax Concave Penalty}, 
  year={2021},
  volume={},
  number={},
  pages={5410-5414},
  doi={10.1109/ICASSP39728.2021.9413850}}

@article{DSPlattices,
  title={Discrete signal processing on meet/join lattices},
  author={P{\"u}schel, Markus and Seifert, Bastian and Wendler, Chris},
  journal={IEEE Transactions on Signal Processing},
  volume={69},
  pages={3571--3584},
  year={2021},
  publisher={IEEE}
}

@article{DSPsetfunctions,
  title={Discrete signal processing with set functions},
  author={P{\"u}schel, Markus and Wendler, Chris},
  journal={IEEE Transactions on Signal Processing},
  volume={69},
  pages={1039--1053},
  year={2020},
  publisher={IEEE}
}


@article{kim2012temporal,
  title={Temporal node centrality in complex networks},
  author={Kim, Hyoungshick and Anderson, Ross},
  journal={Physical Review E},
  volume={85},
  number={2},
  pages={026107},
  year={2012},
  publisher={APS}
}

@article{ramirez2013l1,
  title={{Why $\ell_1$ is a good approximation to $\ell_0$: A Geometric Explanation}},
  author={Ramirez, Carlos and Kreinovich, Vladik and Argaez, Miguel},
  journal={Journal of Uncertain Systems},
  volume={7},
  number={3},
  pages={203--207},
  year={2013}
}

@article{peters201SID,
  title={Structural intervention distance for evaluating causal graphs},
  author={Peters, Jonas and B{\"u}hlmann, Peter},
  journal={Neural computation},
  volume={27},
  number={3},
  pages={771--799},
  year={2015},
  publisher={MIT Press}
}

@incollection{Bengio+chapter2007,
author = {Bengio, Yoshua and LeCun, Yann},
booktitle = {Large Scale Kernel Machines},
publisher = {MIT Press},
title = {Scaling Learning Algorithms Towards {AI}},
year = {2007}
}

@article{Hinton06,
author = {Hinton, Geoffrey E. and Osindero, Simon and Teh, Yee Whye},
journal = {Neural Computation},
pages = {1527--1554},
title = {A Fast Learning Algorithm for Deep Belief Nets},
volume = {18},
year = {2006}
}

@book{goodfellow2016deep,
title={Deep learning},
author={Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron and Bengio, Yoshua},
volume={1},
year={2016},
publisher={MIT Press}
}

# Causal bench contest small paper
@article{misiakos2023contest,
  title={{Learning Gene Regulatory Networks under Few Root Causes assumption}},
  author={Misiakos, Panagiotis and Wendler, Chris and P{\"u}schel, Markus},
  year={2023},
  journal = {OpenReview},
  URL = {https://openreview.net/pdf?id=TOaPl9tXlmD}
}

@inproceedings{misiakos2024icassp,
  title={{Learning Signals and Graphs from Time-Series Graph Data with Few Causes}},
  author={Misiakos, Panagiotis and Mihal, Vedran and P{\"u}schel, Markus},
  booktitle={ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={9681-9685},
  year={2024}
}

@article{chevalley2022causalbench,
  title={{CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data}},
  author={Chevalley, Mathieu and Roohani, Yusuf and Mehrjou, Arash and Leskovec, Jure and Schwab, Patrick},
  journal={arXiv preprint arXiv:2210.17283},
  year={2022}
}

@article{chevalley2023contestreport,
  title={{The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data}},
  author={Chevalley, Mathieu and Sackett-Sanders, Jacob and Roohani, Yusuf and Notin, Pascal and Bakulin, Artemy and Brzezinski, Dariusz and Deng, Kaiwen and Guan, Yuanfang and Hong, Justin and Ibrahim, Michael and others},
  journal={arXiv preprint arXiv:2308.15395},
  year={2023}
}


@article{replogle2022mapping,
  title={Mapping information-rich genotype-phenotype landscapes with genome-scale Perturb-seq},
  author={Replogle, Joseph M and Saunders, Reuben A and Pogson, Angela N and Hussmann, Jeffrey A and Lenail, Alexander and Guna, Alina and Mascibroda, Lauren and Wagner, Eric J and Adelman, Karen and Lithwick-Yanai, Gila and others},
  journal={Cell},
  volume={185},
  number={14},
  pages={2559--2575},
  year={2022},
  publisher={Elsevier}
}

@article{aragam2015concave,
  title={{Concave penalized estimation of sparse Gaussian Bayesian networks}},
  author={Aragam, Bryon and Zhou, Qing},
  journal={The Journal of Machine Learning Research},
  volume={16},
  number={1},
  pages={2273--2328},
  year={2015},
  publisher={JMLR. org}
}

% Levy-Cramer theorem %%%%%%%%%%%
@article{levy1935proprietes,
  title={Propri{\'e}t{\'e}s asymptotiques des sommes de variables al{\'e}atoires encha{\^\i}n{\'e}es},
  author={L{\'e}vy, Paul},
  journal={Bull. Sci. Math},
  volume={59},
  number={84-96},
  pages={109--128},
  year={1935}
}

@article{cramer1936propriete,
  title={Sur une propri{\'e}t{\'e} de la loi de Gauss},
  author={Cram{\'e}r, H},
  journal={CR Acad. Sci. Paris},
  volume={202},
  pages={615--616},
  year={1936}
}

@article{cramer1936eigenschaft,
  title={{\"U}ber eine Eigenschaft der normalen Verteilungsfunktion},
  author={Cram{\'e}r, Harald},
  journal={Mathematische Zeitschrift},
  volume={41},
  number={1},
  pages={405--414},
  year={1936},
  publisher={Springer}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


@article{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik P and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@Article{foldedDist,
AUTHOR = {Tsagris, Michail and Beneki, Christina and Hassani, Hossein},
TITLE = {On the Folded Normal Distribution},
JOURNAL = {Mathematics},
VOLUME = {2},
YEAR = {2014},
NUMBER = {1},
PAGES = {12--28},
URL = {https://www.mdpi.com/2227-7390/2/1/12},
ISSN = {2227-7390},
ABSTRACT = {The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined.},
DOI = {10.3390/math2010012}
}





%%%%%%%%%%%%%% Laplace distribution and sparsity 
@article{eltoft2006multivariatelaplacedist,
  title={On the multivariate Laplace distribution},
  author={Eltoft, Torbj{\o}rn and Kim, Taesu and Lee, Te-Won},
  journal={IEEE Signal Processing Letters},
  volume={13},
  number={5},
  pages={300--303},
  year={2006},
  publisher={IEEE}
}

@inproceedings{guan2009sparsePCA,
  title={Sparse probabilistic principal component analysis},
  author={Guan, Yue and Dy, Jennifer},
  booktitle={Artificial Intelligence and Statistics},
  pages={185--192},
  year={2009},
  organization={PMLR}
}

@article{gazor2003speechdistribution,
  title={Speech probability distribution},
  author={Gazor, Saeed and Zhang, Wei},
  journal={IEEE Signal Processing Letters},
  volume={10},
  number={7},
  pages={204--207},
  year={2003},
  publisher={IEEE}
}

@inproceedings{jing2015sparsematrixfactLaplace,
  title={Sparse probabilistic matrix factorization by laplace distribution for collaborative filtering},
  author={Jing, Liping and Wang, Peng and Yang, Liu},
  booktitle={Twenty-Fourth International Joint Conference on Artificial Intelligence},
  year={2015}
}

@article{bai2023sparseBayesLearningAuto,
  title={Sparse Bayesian learning with automatic-weighting Laplace priors for sparse signal recovery},
  author={Bai, Zonglong and Sun, Jinwei},
  journal={Computational Statistics},
  volume={38},
  number={4},
  pages={2053--2074},
  year={2023},
  publisher={Springer}
}

@article{tibshirani1996LASSOregression,
  title={Regression shrinkage and selection via the lasso},
  author={Tibshirani, Robert},
  journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume={58},
  number={1},
  pages={267--288},
  year={1996},
  publisher={Oxford University Press}
}

@article{castillo2015bayesiansparseregression,
  title={Bayesian linear regression with sparse priors},
  author={Castillo, Isma{\"e}l and Schmidt-Hieber, Johannes and Van der Vaart, Aad},
  journal={The Annals of Statistics},
  pages={1986--2018},
  year={2015},
  publisher={JSTOR}
}

@article{park2008bayesianLasso,
  title={The bayesian lasso},
  author={Park, Trevor and Casella, George},
  journal={Journal of the american statistical association},
  volume={103},
  number={482},
  pages={681--686},
  year={2008},
  publisher={Taylor \& Francis}
}

@article{babacan2009bayesianComprSensing,
  title={Bayesian compressive sensing using Laplace priors},
  author={Babacan, S Derin and Molina, Rafael and Katsaggelos, Aggelos K},
  journal={IEEE Transactions on image processing},
  volume={19},
  number={1},
  pages={53--63},
  year={2009},
  publisher={IEEE}
}



%%%%%%%%%%%%%%%%%%%%%%%%%%% Maximum likelihood estimator consistency
@article{newey1994MLEconsistency,
  title={Large sample estimation and hypothesis testing},
  author={Newey, Whitney K and McFadden, Daniel},
  journal={Handbook of econometrics},
  volume={4},
  pages={2111--2245},
  year={1994},
  publisher={Elsevier}
}

@book{sutherland2009topologicalspaces,
  title={Introduction to metric and topological spaces},
  author={Sutherland, Wilson A},
  year={2009},
  publisher={Oxford University Press}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MLE applications %%%%%%%%%%%%%%%%%%%%%
@article{lanne2017MLE_estimation_SVAR,
  title={Identification and estimation of non-Gaussian structural vector autoregressions},
  author={Lanne, Markku and Meitz, Mika and Saikkonen, Pentti},
  journal={Journal of Econometrics},
  volume={196},
  number={2},
  pages={288--304},
  year={2017},
  publisher={Elsevier}
}

@article{maekawa2023pseudo_log_likelihood_nonGauss,
  title={Estimation of non-Gaussian SVAR models: a pseudo-log-likelihood function approach},
  author={Maekawa, Koichi and Nakanishi, Tadashi},
  journal={Journal of Statistical Computation and Simulation},
  volume={93},
  number={11},
  pages={1830--1850},
  year={2023},
  publisher={Taylor \& Francis}
}

@article{fiorentini2023pseudoMLE_SVAR,
  title={Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions},
  author={Fiorentini, Gabriele and Sentana, Enrique},
  journal={Journal of Econometrics},
  volume={235},
  number={2},
  pages={643--665},
  year={2023},
  publisher={Elsevier}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LAD applications dynamical systems %%%%%%%%%%%%%%
@article{he2024LAD_sparse_dynamical_systems,
  title={Sparse identification of dynamical systems by reweighted l1-regularized least absolute deviation regression},
  author={He, Xin and Sun, ZhongKui},
  journal={Communications in Nonlinear Science and Numerical Simulation},
  volume={131},
  pages={107813},
  year={2024},
  publisher={Elsevier}
}

@article{jiang2023RLAD_dynamical_systems,
  title={Regularized least absolute deviation-based sparse identification of dynamical systems},
  author={Jiang, Feng and Du, Lin and Yang, Fan and Deng, Zi-Chen},
  journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume={33},
  number={1},
  year={2023},
  publisher={AIP Publishing}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LAE regression %%%%%%%%%%%%%%
@article{narula1999minimumAbsErrorRegression,
  title={The minimum sum of absolute errors regression: a robust alternative to the least squares regression},
  author={Narula, Subhash C and Saldiva, Paulo HN and Andre, Carmen DS and Elian, Silvia N and Ferreira, Aurea Favero and Capelozzi, Vera},
  journal={Statistics in medicine},
  volume={18},
  number={11},
  pages={1401--1417},
  year={1999},
  publisher={Wiley Online Library}
}

@article{kumar2015regression_model_LAD,
  title={Regression model estimation using least absolute deviations, least squares deviations and minimax absolute deviations criteria},
  author={Kumar, Pranesh and Singh, Jai Narain},
  journal={IJCSEE},
  volume={3},
  number={4},
  pages={2320--4028},
  year={2015}
}


@article{pollard1991asymptoticsLAD,
  title={Asymptotics for least absolute deviation regression estimators},
  author={Pollard, David},
  journal={Econometric Theory},
  volume={7},
  number={2},
  pages={186--199},
  year={1991},
  publisher={Cambridge University Press}
}

@article{chai2019GeneralGaussianDistRegression,
  title={Using generalized Gaussian distributions to improve regression error modeling for deep learning-based speech enhancement},
  author={Chai, Li and Du, Jun and Liu, Qing-Feng and Lee, Chin-Hui},
  journal={IEEE/ACM Transactions on Audio, Speech, and Language Processing},
  volume={27},
  number={12},
  pages={1919--1931},
  year={2019},
  publisher={IEEE}
}

@inproceedings{li2004fastMLE_LAD,
  title={A fast maximum likelihood estimation approach to LAD regression},
  author={Li, Yinbo and Arce, Gonzalo R},
  booktitle={2004 IEEE International Conference on Acoustics, Speech, and Signal Processing},
  volume={2},
  pages={ii--889},
  year={2004},
  organization={IEEE}
}

@article{bassett1978asymptotic_theoryLAD,
  title={Asymptotic theory of least absolute error regression},
  author={Bassett Jr, Gilbert and Koenker, Roger},
  journal={Journal of the American Statistical Association},
  volume={73},
  number={363},
  pages={618--622},
  year={1978},
  publisher={Taylor \& Francis}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sparse vectors creation %%%%%%%%%%%%%%
@article{kalisch2007highDimDAGs,
  title={Estimating high-dimensional directed acyclic graphs with the PC-algorithm.},
  author={Kalisch, Markus and B{\"u}hlman, Peter},
  journal={Journal of Machine Learning Research},
  volume={8},
  number={3},
  year={2007}
}