@article{geirhos_shortcut_2020,
        title = {Shortcut learning in deep neural networks},
        volume = {2},
        issn = {2522-5839},
        url = {https://doi.org/10.1038/s42256-020-00257-z},
        doi = {10.1038/s42256-020-00257-z},
        number = {11},
        journal = {Nature Machine Intelligence},
        author = {Geirhos, Robert and Jacobsen, Jörn-Henrik and Michaelis, Claudio and Zemel, Richard and Brendel, Wieland and Bethge, Matthias and Wichmann, Felix A.},
        month = nov,
        year = {2020},
        pages = {665--673},
}

@article{acharya_axial_2007,
  title={Axial signs and magnetic resonance imaging correlates in Parkinson's disease},
  author={Acharya, Hernish J and Bouchard, Thomas P and Emery, Derek J and Camicioli, Richard M},
  journal={Canadian journal of neurological sciences},
  volume={34},
  number={1},
  pages={56--61},
  year={2007},
  publisher={Cambridge University Press}
}

@article{das2022c,
  title={The C-BIG Repository: an institution-level open science platform},
  author={Das, Samir and Abou-Haidar, Rida and Rabalais, Henri and Sun, Sonia Denise Lai Wing and Rosli, Zaliqa and Chatpar, Krishna and Boivin, Marie-No{\"e}lle and Tabatabaei, Mahdieh and Rogers, Christine and Legault, Melanie and others},
  journal={Neuroinformatics},
  volume={20},
  number={1},
  pages={139--153},
  year={2022},
  publisher={Springer}
}

@article{badea_exploring_2017,
  title={Exploring the reproducibility of functional connectivity alterations in Parkinson’s disease},
  author={Badea, Liviu and Onu, Mihaela and Wu, Tao and Roceanu, Adina and Bajenaru, Ovidiu},
  journal={PLoS One},
  volume={12},
  number={11},
  pages={e0188196},
  year={2017},
  publisher={Public Library of Science San Francisco, CA USA}
}

@misc{noritaka_ds000245_r100_2018,
  author = {Noritaka Yoneyama and Hirohisa Watanabe and Kazuya Kawabata and Epifanio Bagarinao and Kazuhiro Hara and Takashi Tsuboi and Yasuhiro Tanaka and Reiko Ohdake and Kazunori Imai and Rei Ogura and Yasutaka Kato and Michihito Masuda and Tatsuya Hattori and Mizuki Ito and Satoshi Maesawa and Daisuke Mori and Masahisa Katsuno and Gen Sobue},
  title = {OpenNeuro Japan dataset},
  howpublished = {\url{https://openneuro.org/datasets/ds000245/versions/00001}},
  year = {2018}
}

@article{lang_network_2019,
  title={Network basis of the dysexecutive and posterior cortical cognitive profiles in Parkinson's disease},
  author={Lang, Stefan and Hanganu, Alexandru and Gan, Liu Shi and Kibreab, Mekale and Auclair-Ouellet, No{\'e}mie and Alrazi, Tazrina and Ramezani, Mehrafarin and Cheetham, Jenelle and Hammer, Tracy and Kathol, Iris and others},
  journal={Movement Disorders},
  volume={34},
  number={6},
  pages={893--902},
  year={2019},
  publisher={Wiley Online Library}
}

@article{brown2023detecting,
  title={Detecting shortcut learning for fair medical AI using shortcut testing},
  author={Brown, Alexander and Tomasev, Nenad and Freyberg, Jan and Liu, Yuan and Karthikesalingam, Alan and Schrouff, Jessica},
  journal={Nature communications},
  volume={14},
  number={1},
  pages={4314},
  year={2023},
  publisher={Nature Publishing Group UK London}
}

@ARTICLE{Souza,
  author={Souza, Raissa and Winder, Anthony and Stanley, Emma A. M. and Vigneshwaran, Vibujithan and Camacho, Milton and Camicioli, Richard and Monchi, Oury and Wilms, Matthias and Forkert, Nils D.},
  journal={IEEE Journal of Biomedical and Health Informatics}, 
  title={Identifying Biases in a Multicenter MRI Database for Parkinson's Disease Classification: Is the Disease Classifier a Secret Site Classifier?}, 
  year={2024},
  volume={28},
  number={4},
  pages={2047-2054},
  keywords={Diseases;Magnetic resonance imaging;Biological system modeling;Training;Deep learning;Brain modeling;Databases;Biases;deep learning;shortcut learning},
  doi={10.1109/JBHI.2024.3352513}}

@article{glocker2023algorithmic,
  title={Algorithmic encoding of protected characteristics in chest X-ray disease detection models},
  author={Glocker, Ben and Jones, Charles and Bernhardt, M{\'e}lanie and Winzeck, Stefan},
  journal={EBioMedicine},
  volume={89},
  year={2023},
  publisher={Elsevier}
}

@article{stanley_where_2025,
        title = {Where, why, and how is bias learned in medical image analysis models?},
        volume = {111},
        issn = {2352-3964},
        shorttitle = {Where, why, and how is bias learned in medical image analysis models?},
        url = {https://www.thelancet.com/journals/ebiom/article/PIIS2352-3964(24)00537-1/fulltext},
        doi = {10.1016/j.ebiom.2024.105501},
        language = {English},
        urldate = {2025-01-10},
        journal = {eBioMedicine},
        author = {Stanley, Emma A. M. and Souza, Raissa and Wilms, Matthias and Forkert, Nils D.},
        month = jan,
        year = {2025},
        pmid = {39671751},
        note = {Publisher: Elsevier},
        keywords = {Algorithmic bias, Artificial intelligence, Synthetic data},
}

@article{talai2021utility,
  title={Utility of multi-modal MRI for differentiating of Parkinson's disease and progressive supranuclear palsy using machine learning},
  author={Talai, Aron S and Sedlacik, Jan and Boelmans, Kai and Forkert, Nils D},
  journal={Frontiers in Neurology},
  volume={12},
  pages={648548},
  year={2021},
  publisher={Frontiers Media SA}
}

@article{orlhac2022guide,
  title={A guide to ComBat harmonization of imaging biomarkers in multicenter studies},
  author={Orlhac, Fanny and Eertink, Jakoba J and Cottereau, Anne-S{\'e}gol{\`e}ne and Zijlstra, Jos{\'e}e M and Thieblemont, Catherine and Meignan, Michel and Boellaard, Ronald and Buvat, Ir{\`e}ne},
  journal={Journal of Nuclear Medicine},
  volume={63},
  number={2},
  pages={172--179},
  year={2022},
  publisher={Soc Nuclear Med}
}

@article{HU2023120125,
title = {Image harmonization: A review of statistical and deep learning methods for removing batch effects and evaluation metrics for effective harmonization},
journal = {NeuroImage},
volume = {274},
pages = {120125},
year = {2023},
issn = {1053-8119},
doi = {https://doi.org/10.1016/j.neuroimage.2023.120125},
url = {https://www.sciencedirect.com/science/article/pii/S1053811923002719},
author = {Fengling Hu and Andrew A. Chen and Hannah Horng and Vishnu Bashyam and Christos Davatzikos and Aaron Alexander-Bloch and Mingyao Li and Haochang Shou and Theodore D. Satterthwaite and Meichen Yu and Russell T. Shinohara}
}

@misc{kusner2018counterfactualfairness,
      title={Counterfactual Fairness}, 
      author={Matt J. Kusner and Joshua R. Loftus and Chris Russell and Ricardo Silva},
      year={2018},
      eprint={1703.06856},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/1703.06856}, 
}

@misc{cornacchia2023counterfactualreasoningbiasevaluation,
      title={Counterfactual Reasoning for Bias Evaluation and Detection in a Fairness under Unawareness setting}, 
      author={Giandomenico Cornacchia and Vito Walter Anelli and Fedelucio Narducci and Azzurra Ragone and Eugenio Di Sciascio},
      year={2023},
      eprint={2302.08204},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2302.08204}, 
}

@article{PENG2021101871,
title = {Accurate brain age prediction with lightweight deep neural networks},
journal = {Medical Image Analysis},
volume = {68},
pages = {101871},
year = {2021},
issn = {1361-8415},
doi = {https://doi.org/10.1016/j.media.2020.101871},
url = {https://www.sciencedirect.com/science/article/pii/S1361841520302358},
author = {Han Peng and Weikang Gong and Christian F. Beckmann and Andrea Vedaldi and Stephen M. Smith},
keywords = {Neuroimaging, Brain age prediction, Predictive analysis, Convolutional neuralnetworks}
}

@misc{vigneshwaran2024macawcausalgenerativemodel,
      title={MACAW: A Causal Generative Model for Medical Imaging}, 
      author={Vibujithan Vigneshwaran and Erik Ohara and Matthias Wilms and Nils Forkert},
      year={2024},
      eprint={2412.02900},
      archivePrefix={arXiv},
      primaryClass={eess.IV},
      url={https://arxiv.org/abs/2412.02900}, 
}

@article{Kobyzev_2021,
   title={Normalizing Flows: An Introduction and Review of Current Methods},
   volume={43},
   ISSN={1939-3539},
   url={http://dx.doi.org/10.1109/TPAMI.2020.2992934},
   DOI={10.1109/tpami.2020.2992934},
   number={11},
   journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
   publisher={Institute of Electrical and Electronics Engineers (IEEE)},
   author={Kobyzev, Ivan and Prince, Simon J.D. and Brubaker, Marcus A.},
   year={2021},
   month=nov, pages={3964–3979} }

@article{camacho2023explainable,
  title={Explainable classification of Parkinson’s disease using deep learning trained on a large multi-center database of T1-weighted MRI datasets},
  author={Camacho, Milton and Wilms, Matthias and Mouches, Pauline and Almgren, Hannes and Souza, Raissa and Camicioli, Richard and Ismail, Zahinoor and Monchi, Oury and Forkert, Nils D},
  journal={NeuroImage: Clinical},
  volume={38},
  pages={103405},
  year={2023},
  publisher={Elsevier}
}

@article{castro2020causality,
  title={Causality matters in medical imaging},
  author={Castro, Daniel C and Walker, Ian and Glocker, Ben},
  journal={Nature Communications},
  volume={11},
  number={1},
  pages={3673},
  year={2020},
  publisher={Nature Publishing Group UK London}
}

@article{tustison_n4itk_2010,
	title = {{N4ITK}: {Improved} {N3} {Bias} {Correction}},
	volume = {29},
	issn = {0278-0062},
	shorttitle = {{N4ITK}},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3071855/},
	doi = {10.1109/TMI.2010.2046908},
	number = {6},
	urldate = {2023-01-10},
	journal = {IEEE transactions on medical imaging},
	author = {Tustison, Nicholas J. and Avants, Brian B. and Cook, Philip A. and Zheng, Yuanjie and Egan, Alexander and Yushkevich, Paul A. and Gee, James C.},
	month = jun,
	year = {2010},
	pmid = {20378467},
	pmcid = {PMC3071855},
	pages = {1310--1320},
}

@article{isensee_automated_2019,
	title = {Automated brain extraction of multisequence {MRI} using artificial neural networks},
	volume = {40},
	issn = {1097-0193},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/hbm.24750},
	doi = {10.1002/hbm.24750},
	language = {en},
	number = {17},
	urldate = {2023-01-10},
	journal = {Human Brain Mapping},
	author = {Isensee, Fabian and Schell, Marianne and Pflueger, Irada and Brugnara, Gianluca and Bonekamp, David and Neuberger, Ulf and Wick, Antje and Schlemmer, Heinz-Peter and Heiland, Sabine and Wick, Wolfgang and Bendszus, Martin and Maier-Hein, Klaus H. and Kickingereder, Philipp},
	year = {2019},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hbm.24750},
	keywords = {artificial neural networks, brain extraction, deep learning, magnetic resonance imaging, neuroimaging, skull stripping},
	pages = {4952--4964},}


@article{castro_causality_2020,
	title = {Causality matters in medical imaging},
	volume = {11},
	copyright = {2020 The Author(s)},
	issn = {2041-1723},
	url = {https://www.nature.com/articles/s41467-020-17478-w},
	doi = {10.1038/s41467-020-17478-w},
	abstract = {Causal reasoning can shed new light on the major challenges in machine learning for medical imaging: scarcity of high-quality annotated data and mismatch between the development dataset and the target environment. A causal perspective on these issues allows decisions about data collection, annotation, preprocessing, and learning strategies to be made and scrutinized more transparently, while providing a detailed categorisation of potential biases and mitigation techniques. Along with worked clinical examples, we highlight the importance of establishing the causal relationship between images and their annotations, and offer step-by-step recommendations for future studies.},
	language = {en},
	number = {1},
	urldate = {2023-09-27},
	journal = {Nature Communications},
	author = {Castro, Daniel C. and Walker, Ian and Glocker, Ben},
	month = jul,
	year = {2020},
	note = {Number: 1
Publisher: Nature Publishing Group},
	keywords = {Computational models, Data processing, Machine learning, Medical research, Predictive medicine},
	pages = {3673},
}
@article{souza2024harmonytm,
  title={HarmonyTM: multi-center data harmonization applied to distributed learning for Parkinson’s disease classification},
  author={Souza, Raissa and Stanley, Emma AM and Gulve, Vedant and Moore, Jasmine and Kang, Chris and Camicioli, Richard and Monchi, Oury and Ismail, Zahinoor and Wilms, Matthias and Forkert, Nils D},
  journal={Journal of Medical Imaging},
  url={https://doi.org/10.1117/1.JMI.11.5.054502},
  volume={11},
  number={5},
  pages={054502--054502},
  year={2024},
  publisher={Society of Photo-Optical Instrumentation Engineers}
}

@article{emma,
    author = {Stanley, Emma A M and Souza, Raissa and Winder, Anthony J and Gulve, Vedant and Amador, Kimberly and Wilms, Matthias and Forkert, Nils D},
    title = {Towards objective and systematic evaluation of bias in artificial intelligence for medical imaging},
    journal = {Journal of the American Medical Informatics Association},
    volume = {31},
    number = {11},
    pages = {2613-2621},
    year = {2024},
    month = {06},
    issn = {1527-974X},
    doi = {10.1093/jamia/ocae165},
    url = {https://doi.org/10.1093/jamia/ocae165},
    eprint = {https://academic.oup.com/jamia/article-pdf/31/11/2613/59813548/ocae165.pdf},
}

@inproceedings{vigneshwaran2024improved,
  title={Improved multi-site Parkinson’s disease classification using neuroimaging data with counterfactual inference},
  author={Vigneshwaran, Vibujithan and Wilms, Matthias and Camacho, Milton Ivan Camacho and Souza, Raissa and Forkert, Nils},
  booktitle={Medical Imaging with Deep Learning},
  pages={1304--1317},
  year={2024},
  organization={PMLR}
}

@article{souza2023image,
  title={Image-encoded biological and non-biological variables may be used as shortcuts in deep learning models trained on multisite neuroimaging data},
  author={Souza, Raissa and Wilms, Matthias and Camacho, Milton and Pike, G Bruce and Camicioli, Richard and Monchi, Oury and Forkert, Nils D},
  journal={Journal of the American Medical Informatics Association},
  volume={30},
  number={12},
  pages={1925--1933},
  year={2023},
  publisher={Oxford University Press}
}

@article{boelmans2012brain,
  title={Brain iron deposition fingerprints in Parkinson's disease and progressive supranuclear palsy},
  author={Boelmans, Kai and Holst, Brigitte and Hackius, Marc and Finsterbusch, J{\"u}rgen and Gerloff, Christian and Fiehler, Jens and M{\"u}nchau, Alexander},
  journal={Movement Disorders},
  volume={27},
  number={3},
  pages={421--427},
  year={2012},
  publisher={Wiley Online Library}
}

@article{xiao2017dataset,
  title={A dataset of multi-contrast population-averaged brain MRI atlases of a Parkinson's disease cohort},
  author={Xiao, Yiming and Fonov, Vladimir and Chakravarty, M Mallar and Beriault, Silvain and Al Subaie, Fahd and Sadikot, Abbas and Pike, G Bruce and Bertrand, Gilles and Collins, D Louis},
  journal={Data in brief},
  volume={12},
  pages={370--379},
  year={2017},
  publisher={Elsevier}
}

@article{petersen2023path,
  title={The path toward equal performance in medical machine learning},
  author={Petersen, Eike and Holm, Sune and Ganz, Melanie and Feragen, Aasa},
  journal={Patterns},
  volume={4},
  number={7},
  year={2023},
  publisher={Elsevier}
}

@article{wang2024drop,
  title={Drop the shortcuts: image augmentation improves fairness and decreases AI detection of race and other demographics from medical images},
  author={Wang, Ryan and Kuo, Po-Chih and Chen, Li-Ching and Seastedt, Kenneth Patrick and Gichoya, Judy Wawira and Celi, Leo Anthony},
  journal={EBioMedicine},
  volume={102},
  year={2024},
  publisher={Elsevier}
}

@inproceedings{rane2024deeprepviz,
  title={DeepRepViz: Identifying Potential Confounders in Deep Learning Model Predictions},
  author={Rane, Roshan Prakash and Kim, JiHoon and Umesha, Arjun and Stark, Didem and Schulz, Marc-Andr{\'e} and Ritter, Kerstin},
  booktitle={International Conference on Medical Image Computing and Computer-Assisted Intervention},
  pages={186--196},
  year={2024},
  organization={Springer}
}

@article{sagawa2019distributionally,
  title={Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization},
  author={Sagawa, Shiori and Koh, Pang Wei and Hashimoto, Tatsunori B and Liang, Percy},
  journal={arXiv preprint arXiv:1911.08731},
  year={2019}
}
@article{salahuddin_transparency_2022,
	title = {Transparency of deep neural networks for medical image analysis: {A} review of interpretability methods},
	volume = {140},
	issn = {0010-4825},
	shorttitle = {Transparency of deep neural networks for medical image analysis},
	url = {https://www.sciencedirect.com/science/article/pii/S0010482521009057},
	doi = {10.1016/j.compbiomed.2021.105111},
	urldate = {2023-10-10},
	journal = {Computers in Biology and Medicine},
	author = {Salahuddin, Zohaib and Woodruff, Henry C. and Chatterjee, Avishek and Lambin, Philippe},
	month = jan,
	year = {2022},
	keywords = {Deep neural networks, Explainability, Explainable artificial intelligence, Interpretability, Medical imaging},
	pages = {105111},
}

@article{babic_beware_2021,
	title = {Beware explanations from {AI} in health care},
	volume = {373},
	url = {https://www.science.org/doi/10.1126/science.abg1834},
	doi = {10.1126/science.abg1834},
	number = {6552},
	urldate = {2023-10-10},
	journal = {Science},
	author = {Babic, Boris and Gerke, Sara and Evgeniou, Theodoros and Cohen, I. Glenn},
	month = jul,
	year = {2021},
	note = {Publisher: American Association for the Advancement of Science},
	pages = {284--286},
}

@incollection{scholkopf_causality_2022,
	address = {New York, NY, USA},
	edition = {1},
	title = {Causality for {Machine} {Learning}},
	volume = {36},
	isbn = {978-1-4503-9586-1},
	url = {https://doi.org/10.1145/3501714.3501755},
	urldate = {2024-01-02},
	booktitle = {Probabilistic and {Causal} {Inference}: {The} {Works} of {Judea} {Pearl}},
	publisher = {Association for Computing Machinery},
	author = {Schölkopf, Bernhard},
	month = mar,
	year = {2022},
	pages = {765--804},
}

@article{sanchez_causal_2022,
	title = {Causal machine learning for healthcare and precision medicine},
	volume = {9},
	url = {https://royalsocietypublishing.org/doi/10.1098/rsos.220638},
	doi = {10.1098/rsos.220638},
	number = {8},
	urldate = {2023-06-21},
	journal = {Royal Society Open Science},
	author = {Sanchez, Pedro and Voisey, Jeremy P. and Xia, Tian and Watson, Hannah I. and O’Neil, Alison Q. and Tsaftaris, Sotirios A.},
	month = aug,
	year = {2022},
	note = {Publisher: Royal Society},
	keywords = {causal machine learning, causal representation learning, precision medicine},
	pages = {220638},
}

@techreport{pearl_causal_2012,
	address = {Fort Belvoir, VA},
	title = {The {Causal} {Foundations} of {Structural} {Equation} {Modeling}:},
	shorttitle = {The {Causal} {Foundations} of {Structural} {Equation} {Modeling}},
	url = {http://www.dtic.mil/docs/citations/ADA557445},
	language = {en},
	urldate = {2023-01-06},
	institution = {Defense Technical Information Center},
	author = {Pearl, Judea},
	month = feb,
	year = {2012},
	doi = {10.21236/ADA557445},
}

@inproceedings{pawlowski_deep_2020,
	title = {Deep {Structural} {Causal} {Models} for {Tractable} {Counterfactual} {Inference}},
	volume = {33},
	url = {https://proceedings.neurips.cc/paper/2020/hash/0987b8b338d6c90bbedd8631bc499221-Abstract.html},
	urldate = {2024-01-02},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	publisher = {Curran Associates, Inc.},
	author = {Pawlowski, Nick and Coelho de Castro, Daniel and Glocker, Ben},
	year = {2020},
	pages = {857--869},
}

@misc{melistas_benchmarking_2024,
	title = {Benchmarking {Counterfactual} {Image} {Generation}},
	url = {http://arxiv.org/abs/2403.20287},
	doi = {10.48550/arXiv.2403.20287},
	urldate = {2024-06-08},
	publisher = {arXiv},
	author = {Melistas, Thomas and Spyrou, Nikos and Gkouti, Nefeli and Sanchez, Pedro and Vlontzos, Athanasios and Papanastasiou, Giorgos and Tsaftaris, Sotirios A.},
	month = mar,
	year = {2024},
	note = {arXiv:2403.20287 [cs]},
	keywords = {Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning},
}

@inproceedings{ribeiro_high_2023,
	title = {High {Fidelity} {Image} {Counterfactuals} with {Probabilistic} {Causal} {Models}},
	url = {https://proceedings.mlr.press/v202/de-sousa-ribeiro23a.html},
	abstract = {We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals.},
	language = {en},
	urldate = {2024-05-08},
	booktitle = {Proceedings of the 40th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Ribeiro, Fabio De Sousa and Xia, Tian and Monteiro, Miguel and Pawlowski, Nick and Glocker, Ben},
	month = jul,
	year = {2023},
	note = {ISSN: 2640-3498},
	pages = {7390--7425},
}

@article{wilms_invertible_2022,
	title = {Invertible {Modeling} of {Bidirectional} {Relationships} in {Neuroimaging} {With} {Normalizing} {Flows}: {Application} to {Brain} {Aging}},
	volume = {41},
	issn = {1558-254X},
	shorttitle = {Invertible {Modeling} of {Bidirectional} {Relationships} in {Neuroimaging} {With} {Normalizing} {Flows}},
	doi = {10.1109/TMI.2022.3161947},
	abstract = {Many machine learning tasks in neuroimaging aim at modeling complex relationships between a brain’s morphology as seen in structural MR images and clinical scores and variables of interest. A frequently modeled process is healthy brain aging for which many image-based brain age estimation or age-conditioned brain morphology template generation approaches exist. While age estimation is a regression task, template generation is related to generative modeling. Both tasks can be seen as inverse directions of the same relationship between brain morphology and age. However, this view is rarely exploited and most existing approaches train separate models for each direction. In this paper, we propose a novel bidirectional approach that unifies score regression and generative morphology modeling and we use it to build a bidirectional brain aging model. We achieve this by defining an invertible normalizing flow architecture that learns a probability distribution of 3D brain morphology conditioned on age. The use of full 3D brain data is achieved by deriving a manifold-constrained formulation that models morphology variations within a low-dimensional subspace of diffeomorphic transformations. This modeling idea is evaluated on a database of MR scans of more than 5000 subjects. The evaluation results show that our bidirectional brain aging model (1) accurately estimates brain age, (2) is able to visually explain its decisions through attribution maps and counterfactuals, (3) generates realistic age-specific brain morphology templates, (4) supports the analysis of morphological variations, and (5) can be utilized for subject-specific brain aging simulation.},
	number = {9},
	journal = {IEEE Transactions on Medical Imaging},
	author = {Wilms, Matthias and Bannister, Jordan J. and Mouches, Pauline and MacDonald, M. Ethan and Rajashekar, Deepthi and Langner, Sönke and Forkert, Nils D.},
	month = sep,
	year = {2022},
	note = {Conference Name: IEEE Transactions on Medical Imaging},
	keywords = {Aging, Bidirectional modeling, Brain modeling, Data models, Morphology, Predictive models, Solid modeling, Three-dimensional displays, brain aging, conditional templates, normalizing flows},
	pages = {2331--2347},
}

@article{bannister_deep_2022,
	title = {A {Deep} {Invertible} 3-{D} {Facial} {Shape} {Model} for {Interpretable} {Genetic} {Syndrome} {Diagnosis}},
	volume = {26},
	issn = {2168-2208},
	doi = {10.1109/JBHI.2022.3164848},
	abstract = {One of the primary difficulties in treating patients with genetic syndromes is diagnosing their condition. Many syndromes are associated with characteristic facial features that can be imaged and utilized by computer-assisted diagnosis systems. In this work, we develop a novel 3D facial surface modeling approach with the objective of maximizing diagnostic model interpretability within a flexible deep learning framework. Therefore, an invertible normalizing flow architecture is introduced to enable both inferential and generative tasks in a unified and efficient manner. The proposed model can be used (1) to infer syndrome diagnosis and other demographic variables given a 3D facial surface scan and (2) to explain model inferences to non-technical users via multiple interpretability mechanisms. The model was trained and evaluated on more than 4700 facial surface scans from subjects with 47 different syndromes. For the challenging task of predicting syndrome diagnosis given a new 3D facial surface scan, age, and sex of a subject, the model achieves a competitive overall top-1 accuracy of 71\%, and a mean sensitivity of 43\% across all syndrome classes. We believe that invertible models such as the one presented in this work can achieve competitive inferential performance while greatly increasing model interpretability in the domain of medical diagnosis.},
	language = {eng},
	number = {7},
	journal = {IEEE journal of biomedical and health informatics},
	author = {Bannister, Jordan J. and Wilms, Matthias and Aponte, J. David and Katz, David C. and Klein, Ophir D. and Bernier, Francois P. J. and Spritz, Richard A. and Hallgrimsson, Benedikt and Forkert, Nils D.},
	month = jul,
	year = {2022},
	pmid = {35380975},
	pmcid = {PMC9429803},
	keywords = {Diagnosis, Computer-Assisted, Face, Humans},
	pages = {3229--3239},
}

@book{peters_elements_2017,
	address = {Cambridge, Massachuestts},
	series = {Adaptive computation and machine learning series},
	title = {Elements of causal inference: foundations and learning algorithms},
	isbn = {978-0-262-03731-0},
	shorttitle = {Elements of causal inference},
	publisher = {The MIT Press},
	author = {Peters, Jonas and Janzing, Dominik and Schölkopf, Bernhard},
	year = {2017},
	keywords = {Causation, Computer algorithms, Inference, Logic, Symbolic and mathematical, Machine learning},
}

@article{glymour_review_2019,
	title = {Review of {Causal} {Discovery} {Methods} {Based} on {Graphical} {Models}},
	volume = {10},
	issn = {1664-8021},
	url = {https://www.frontiersin.org/articles/10.3389/fgene.2019.00524},
	abstract = {A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. It is then necessary to discover causal relations by analyzing statistical properties of purely observational data, which is known as causal discovery or causal structure search. This paper aims to give a introduction to and a brief review of the computational methods for causal discovery that were developed in the past three decades, including constraint-based and score-based methods and those based on functional causal models, supplemented by some illustrations and applications.},
	urldate = {2023-07-17},
	journal = {Frontiers in Genetics},
	author = {Glymour, Clark and Zhang, Kun and Spirtes, Peter},
	year = {2019},
}

@article{kobyzev_normalizing_2021,
	title = {Normalizing {Flows}: {An} {Introduction} and {Review} of {Current} {Methods}},
	volume = {43},
	issn = {1939-3539},
	shorttitle = {Normalizing {Flows}},
	doi = {10.1109/TPAMI.2020.2992934},
	number = {11},
	urldate = {2024-01-02},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	author = {Kobyzev, Ivan and Prince, Simon J.D. and Brubaker, Marcus A.},
	month = nov,
	year = {2021},
	note = {Conference Name: IEEE Transactions on Pattern Analysis and Machine Intelligence},
	pages = {3964--3979},
}

@inproceedings{wehenkel_graphical_2021,
	title = {Graphical {Normalizing} {Flows}},
	url = {https://proceedings.mlr.press/v130/wehenkel21a.html},
	abstract = {Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible functions from scalars to vectors. In this work, we revisit these transformations as probabilistic graphical models, showing they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we propose the graphical normalizing flow, a new invertible transformation with either a prescribed or a learnable graphical structure. This model provides a promising way to inject domain knowledge into normalizing flows while preserving both the interpretability of Bayesian networks and the representation capacity of normalizing flows. We show that graphical conditioners discover relevant graph structure when we cannot hypothesize it. In addition, we analyze the effect of \${\textbackslash}ell\_1\$-penalization on the recovered structure and on the quality of the resulting density estimation. Finally, we show that graphical conditioners lead to competitive white box density estimators. Our implementation is available at .},
	language = {en},
	urldate = {2024-01-02},
	booktitle = {Proceedings of {The} 24th {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Wehenkel, Antoine and Louppe, Gilles},
	month = mar,
	year = {2021},
	note = {ISSN: 2640-3498},
	pages = {37--45},
}

@article{monteiro2023measuring,
  title={Measuring axiomatic soundness of counterfactual image models},
  author={Monteiro, Miguel and Ribeiro, Fabio De Sousa and Pawlowski, Nick and Castro, Daniel C and Glocker, Ben},
  journal={arXiv preprint arXiv:2303.01274},
  year={2023}
}

@inproceedings{khemakhem_causal_2021,
	title = {Causal {Autoregressive} {Flows}},
	url = {https://proceedings.mlr.press/v130/khemakhem21a.html},
	abstract = {Two apparently unrelated fields — normalizing flows and causality — have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of autoregressive normalizing flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks, ranging from causal discovery to making interventional and counterfactual predictions. First, we show that causal models derived from both affine and additive autoregressive flows with fixed orderings over variables are identifiable, i.e. the true direction of causal influence can be recovered. This provides a generalization of the additive noise model well-known in causal discovery. Second, we derive a bivariate measure of causal direction based on likelihood ratios, leveraging the fact that flow models can estimate normalized log-densities of data. Third, we demonstrate that flows naturally allow for direct evaluation of both interventional and counterfactual queries, the latter case being possible due to the invertible nature of flows. Finally, throughout a series of experiments on synthetic and real data, the proposed method is shown to outperform current approaches for causal discovery as well as making accurate interventional and counterfactual predictions.},
	language = {en},
	urldate = {2024-01-02},
	booktitle = {Proceedings of {The} 24th {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Khemakhem, Ilyes and Monti, Ricardo and Leech, Robert and Hyvarinen, Aapo},
	month = mar,
	year = {2021},
	note = {ISSN: 2640-3498},
	pages = {3520--3528},
}

@inproceedings{germain_made_2015,
	title = {{MADE}: {Masked} {Autoencoder} for {Distribution} {Estimation}},
	shorttitle = {{MADE}},
	url = {https://proceedings.mlr.press/v37/germain15.html},
	abstract = {There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder’s parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.},
	language = {en},
	urldate = {2024-01-02},
	booktitle = {Proceedings of the 32nd {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Germain, Mathieu and Gregor, Karol and Murray, Iain and Larochelle, Hugo},
	month = jun,
	year = {2015},
	note = {ISSN: 1938-7228},
	pages = {881--889},
}

@inproceedings{papamakarios_masked_2017,
	title = {Masked {Autoregressive} {Flow} for {Density} {Estimation}},
	volume = {30},
	url = {https://papers.nips.cc/paper_files/paper/2017/hash/6c1da886822c67822bcf3679d04369fa-Abstract.html},
	abstract = {Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.},
	urldate = {2024-01-02},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	publisher = {Curran Associates, Inc.},
	author = {Papamakarios, George and Pavlakou, Theo and Murray, Iain},
	year = {2017},
}

@misc{szegedy_rethinking_2015,
	title = {Rethinking the {Inception} {Architecture} for {Computer} {Vision}},
	url = {http://arxiv.org/abs/1512.00567},
	doi = {10.48550/arXiv.1512.00567},
	abstract = {Convolutional networks are at the core of most state-of-the-art computer vision solutions for a wide variety of tasks. Since 2014 very deep convolutional networks started to become mainstream, yielding substantial gains in various benchmarks. Although increased model size and computational cost tend to translate to immediate quality gains for most tasks (as long as enough labeled data is provided for training), computational efficiency and low parameter count are still enabling factors for various use cases such as mobile vision and big-data scenarios. Here we explore ways to scale up networks in ways that aim at utilizing the added computation as efficiently as possible by suitably factorized convolutions and aggressive regularization. We benchmark our methods on the ILSVRC 2012 classification challenge validation set demonstrate substantial gains over the state of the art: 21.2\% top-1 and 5.6\% top-5 error for single frame evaluation using a network with a computational cost of 5 billion multiply-adds per inference and with using less than 25 million parameters. With an ensemble of 4 models and multi-crop evaluation, we report 3.5\% top-5 error on the validation set (3.6\% error on the test set) and 17.3\% top-1 error on the validation set.},
	urldate = {2024-06-08},
	publisher = {arXiv},
	author = {Szegedy, Christian and Vanhoucke, Vincent and Ioffe, Sergey and Shlens, Jonathon and Wojna, Zbigniew},
	month = dec,
	year = {2015},
	note = {arXiv:1512.00567 [cs]
version: 3},
	keywords = {Computer Science - Computer Vision and Pattern Recognition},
}

@article{miller_multimodal_2016,
	title = {Multimodal population brain imaging in the {UK} {Biobank} prospective epidemiological study},
	volume = {19},
	copyright = {2016 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {1546-1726},
	url = {https://www.nature.com/articles/nn.4393},
	doi = {10.1038/nn.4393},
	abstract = {The UK Biobank combines detailed phenotyping and genotyping with tracking of long-term health outcomes in a large cohort. This study describes the recently launched brain-imaging component that will ultimately scan 100,000 individuals. Results from the first 5,000 subjects are reported, including thousands of associations, population modes and hypothesis-driven results.},
	language = {en},
	number = {11},
	urldate = {2022-12-16},
	journal = {Nature Neuroscience},
	author = {Miller, Karla L. and Alfaro-Almagro, Fidel and Bangerter, Neal K. and Thomas, David L. and Yacoub, Essa and Xu, Junqian and Bartsch, Andreas J. and Jbabdi, Saad and Sotiropoulos, Stamatios N. and Andersson, Jesper L. R. and Griffanti, Ludovica and Douaud, Gwenaëlle and Okell, Thomas W. and Weale, Peter and Dragonu, Iulius and Garratt, Steve and Hudson, Sarah and Collins, Rory and Jenkinson, Mark and Matthews, Paul M. and Smith, Stephen M.},
	month = nov,
	year = {2016},
	note = {Number: 11
Publisher: Nature Publishing Group},
	keywords = {Cognitive ageing, Neurological disorders, Predictive markers},
	pages = {1523--1536},
}

@article{rohlfing_sri24_2010,
	title = {The {SRI24} multichannel atlas of normal adult human brain structure},
	volume = {31},
	issn = {1097-0193},
	doi = {10.1002/hbm.20906},
	abstract = {This article describes the SRI24 atlas, a new standard reference system of normal human brain anatomy, that was created using template-free population registration of high-resolution magnetic resonance images acquired at 3T in a group of 24 normal control subjects. The atlas comprises anatomical channels (T1, T2, and proton density weighted), diffusion-related channels (fractional anisotropy, mean diffusivity, longitudinal diffusivity, mean diffusion-weighted image), tissue channels (CSF probability, gray matter probability, white matter probability, tissue labels), and two cortical parcellation maps. The SRI24 atlas enables multichannel atlas-to-subject image registration. It is uniquely versatile in that it is equally suited for the two fundamentally different atlas applications: label propagation and spatial normalization. Label propagation, herein demonstrated using diffusion tensor image fiber tracking, is enabled by the increased sharpness of the SRI24 atlas compared with other available atlases. Spatial normalization, herein demonstrated using data from a young-old group comparison study, is enabled by its unbiased average population shape property. For both propagation and normalization, we also report the results of quantitative comparisons with seven other published atlases: Colin27, MNI152, ICBM452 (warp5 and air12), and LPBA40 (SPM5, FLIRT, AIR). Our results suggest that the SRI24 atlas, although based on 3T MR data, allows equally accurate spatial normalization of data acquired at 1.5T as the comparison atlases, all of which are based on 1.5T data. Furthermore, the SRI24 atlas is as suitable for label propagation as the comparison atlases and detailed enough to allow delineation of anatomical structures for this purpose directly in the atlas.},
	language = {eng},
	number = {5},
	journal = {Human Brain Mapping},
	author = {Rohlfing, Torsten and Zahr, Natalie M. and Sullivan, Edith V. and Pfefferbaum, Adolf},
	month = may,
	year = {2010},
	pmid = {20017133},
	pmcid = {PMC2915788},
	keywords = {Access to Information, Adult, Aged, Aged, 80 and over, Aging, Algorithms, Atlases as Topic, Brain, Diffusion Magnetic Resonance Imaging, Female, Humans, Image Processing, Computer-Assisted, Imaging, Three-Dimensional, Internet, Magnetic Resonance Imaging, Male, Neural Pathways, Probability, Young Adult},
	pages = {798--819},
}

@article{avants_reproducible_2011,
	title = {A reproducible evaluation of {ANTs} similarity metric performance in brain image registration},
	volume = {54},
	issn = {1095-9572},
	doi = {10.1016/j.neuroimage.2010.09.025},
	abstract = {The United States National Institutes of Health (NIH) commit significant support to open-source data and software resources in order to foment reproducibility in the biomedical imaging sciences. Here, we report and evaluate a recent product of this commitment: Advanced Neuroimaging Tools (ANTs), which is approaching its 2.0 release. The ANTs open source software library consists of a suite of state-of-the-art image registration, segmentation and template building tools for quantitative morphometric analysis. In this work, we use ANTs to quantify, for the first time, the impact of similarity metrics on the affine and deformable components of a template-based normalization study. We detail the ANTs implementation of three similarity metrics: squared intensity difference, a new and faster cross-correlation, and voxel-wise mutual information. We then use two-fold cross-validation to compare their performance on openly available, manually labeled, T1-weighted MRI brain image data of 40 subjects (UCLA's LPBA40 dataset). We report evaluation results on cortical and whole brain labels for both the affine and deformable components of the registration. Results indicate that the best ANTs methods are competitive with existing brain extraction results (Jaccard=0.958) and cortical labeling approaches. Mutual information affine mapping combined with cross-correlation diffeomorphic mapping gave the best cortical labeling results (Jaccard=0.669±0.022). Furthermore, our two-fold cross-validation allows us to quantify the similarity of templates derived from different subgroups. Our open code, data and evaluation scripts set performance benchmark parameters for this state-of-the-art toolkit. This is the first study to use a consistent transformation framework to provide a reproducible evaluation of the isolated effect of the similarity metric on optimal template construction and brain labeling.},
	language = {eng},
	number = {3},
	journal = {NeuroImage},
	author = {Avants, Brian B. and Tustison, Nicholas J. and Song, Gang and Cook, Philip A. and Klein, Arno and Gee, James C.},
	month = feb,
	year = {2011},
	pmid = {20851191},
	pmcid = {PMC3065962},
	keywords = {Algorithms, Brain, Databases, Factual, Diagnostic Imaging, Head, Humans, Image Processing, Computer-Assisted, Linear Models, Models, Anatomic, Models, Neurological, Population, Reproducibility of Results, Software},
	pages = {2033--2044},
}

@article{lotze_novel_2019,
	title = {Novel findings from 2,838 {Adult} {Brains} on {Sex} {Differences} in {Gray} {Matter} {Brain} {Volume}},
	volume = {9},
	copyright = {2019 The Author(s)},
	issn = {2045-2322},
	url = {https://www.nature.com/articles/s41598-018-38239-2},
	doi = {10.1038/s41598-018-38239-2},
	abstract = {There is still disagreement among studies with respect to the magnitude, location, and direction of sex differences of local gray matter volume (GMV) in the human brain. Here, we applied a state-of-the-art technique examining GMV in a well-powered sample (n = 2,838) validating effects in two independent general-population cohorts, age range 21–90 years, measured using the same MRI scanner. More GMV in women than in men was prominent in medial and lateral prefrontal areas, the superior temporal sulcus, the posterior insula, and orbitofrontal cortex. In contrast, more GMV in men than in women was detected in subcortical temporal structures, such as the amygdala, hippocampus, temporal pole, fusiform gyrus, visual primary cortex, and motor areas (premotor cortex, putamen, anterior cerebellum). The findings in this large-scale study may clarify previous inconsistencies and contribute to the understanding of sex-specific differences in cognition and behavior.},
	language = {en},
	number = {1},
	urldate = {2023-12-19},
	journal = {Scientific Reports},
	author = {Lotze, Martin and Domin, Martin and Gerlach, Florian H. and Gaser, Christian and Lueders, Eileen and Schmidt, Carsten O. and Neumann, Nicola},
	month = feb,
	year = {2019},
	note = {Number: 1
Publisher: Nature Publishing Group},
	keywords = {Cognitive neuroscience, Sexual dimorphism},
	pages = {1671},
}

@article{beck_cardiometabolic_2021,
	title = {Cardiometabolic risk factors associated with brain age and accelerate brain ageing},
	volume = {43},
	issn = {1065-9471},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8720200/},
	doi = {10.1002/hbm.25680},
	abstract = {The structure and integrity of the ageing brain is interchangeably linked to physical health, and cardiometabolic risk factors (CMRs) are associated with dementia and other brain disorders. In this mixed cross‐sectional and longitudinal study (interval mean = 19.7 months), including 790 healthy individuals (mean age = 46.7 years, 53\% women), we investigated CMRs and health indicators including anthropometric measures, lifestyle factors, and blood biomarkers in relation to brain structure using MRI‐based morphometry and diffusion tensor imaging (DTI). We performed tissue specific brain age prediction using machine learning and performed Bayesian multilevel modeling to assess changes in each CMR over time, their respective association with brain age gap (BAG), and their interaction effects with time and age on the tissue‐specific BAGs. The results showed credible associations between DTI‐based BAG and blood levels of phosphate and mean cell volume (MCV), and between T1‐based BAG and systolic blood pressure, smoking, pulse, and C‐reactive protein (CRP), indicating older‐appearing brains in people with higher cardiometabolic risk (smoking, higher blood pressure and pulse, low‐grade inflammation). Longitudinal evidence supported interactions between both BAGs and waist‐to‐hip ratio (WHR), and between DTI‐based BAG and systolic blood pressure and smoking, indicating accelerated ageing in people with higher cardiometabolic risk (smoking, higher blood pressure, and WHR). The results demonstrate that cardiometabolic risk factors are associated with brain ageing. While randomized controlled trials are needed to establish causality, our results indicate that public health initiatives and treatment strategies targeting modifiable cardiometabolic risk factors may also improve risk trajectories and delay brain ageing., The structure and integrity of the ageing brain is interchangeably linked to physical health, and cardiometabolic risk factors (CMRs). We investigated CMRs and health indicators including anthropometric measures, lifestyle factors, and blood biomarkers in relation to brain structure using MRI‐based morphometry and diffusion tensor imaging (DTI). Tissue‐specific brain age prediction using machine learning revealed older‐appearing brains and accelerated ageing in people with higher cardiometabolic risk.},
	number = {2},
	urldate = {2023-07-04},
	journal = {Human Brain Mapping},
	author = {Beck, Dani and de Lange, Ann‐Marie G. and Pedersen, Mads L. and Alnæs, Dag and Maximov, Ivan I. and Voldsbekk, Irene and Richard, Geneviève and Sanders, Anne‐Marthe and Ulrichsen, Kristine M. and Dørum, Erlend S. and Kolskår, Knut K. and Høgestøl, Einar A. and Steen, Nils Eiel and Djurovic, Srdjan and Andreassen, Ole A. and Nordvik, Jan E. and Kaufmann, Tobias and Westlye, Lars T.},
	month = oct,
	year = {2021},
	pmid = {34626047},
	pmcid = {PMC8720200},
	pages = {700--720},
}

@article{peng_accurate_2021,
	title = {Accurate brain age prediction with lightweight deep neural networks},
	volume = {68},
	issn = {1361-8415},
	url = {https://www.sciencedirect.com/science/article/pii/S1361841520302358},
	doi = {10.1016/j.media.2020.101871},
	abstract = {Deep learning has huge potential for accurate disease prediction with neuroimaging data, but the prediction performance is often limited by training-dataset size and computing memory requirements. To address this, we propose a deep convolutional neural network model, Simple Fully Convolutional Network (SFCN), for accurate prediction of brain age using T1-weighted structural MRI data. Compared with other popular deep network architectures, SFCN has fewer parameters, so is more compatible with small dataset size and 3D volume data. The network architecture was combined with several techniques for boosting performance, including data augmentation, pre-training, model regularization, model ensemble and prediction bias correction. We compared our overall SFCN approach with several widely-used machine learning models. It achieved state-of-the-art performance in UK Biobank data (N = 14,503), with mean absolute error (MAE) = 2.14y in brain age prediction and 99.5\% in sex classification. SFCN also won (both parts of) the 2019 Predictive Analysis Challenge for brain age prediction, involving 79 competing teams (N = 2,638, MAE = 2.90y). We describe here the details of our approach, and its optimisation and validation. Our approach can easily be generalised to other tasks using different image modalities, and is released on GitHub.},
	urldate = {2023-09-14},
	journal = {Medical Image Analysis},
	author = {Peng, Han and Gong, Weikang and Beckmann, Christian F. and Vedaldi, Andrea and Smith, Stephen M.},
	month = feb,
	year = {2021},
	keywords = {Brain age prediction, Convolutional neuralnetworks, Neuroimaging, Predictive analysis},
	pages = {101871},
}

@inproceedings{ribeiro_high_2023,
	title = {High {Fidelity} {Image} {Counterfactuals} with {Probabilistic} {Causal} {Models}},
	url = {https://proceedings.mlr.press/v202/de-sousa-ribeiro23a.html},
	abstract = {We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals.},
	language = {en},
	urldate = {2024-05-08},
	booktitle = {Proceedings of the 40th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Ribeiro, Fabio De Sousa and Xia, Tian and Monteiro, Miguel and Pawlowski, Nick and Glocker, Ben},
	month = jul,
	year = {2023},
	note = {ISSN: 2640-3498},
	pages = {7390--7425},
}

@misc{nemirovsky_countergan_2021,
	title = {{CounteRGAN}: {Generating} {Realistic} {Counterfactuals} with {Residual} {Generative} {Adversarial} {Nets}},
	shorttitle = {{CounteRGAN}},
	url = {http://arxiv.org/abs/2009.05199},
	abstract = {The prevalence of machine learning models in various industries has led to growing demands for model interpretability and for the ability to provide meaningful recourse to users. For example, patients hoping to improve their diagnoses or loan applicants seeking to increase their chances of approval. Counterfactuals can help in this regard by identifying input perturbations that would result in more desirable prediction outcomes. Meaningful counterfactuals should be able to achieve the desired outcome, but also be realistic, actionable, and efficient to compute. Current approaches achieve desired outcomes with moderate actionability but are severely limited in terms of realism and latency. To tackle these limitations, we apply Generative Adversarial Nets (GANs) toward counterfactual search. We also introduce a novel Residual GAN (RGAN) that helps to improve counterfactual realism and actionability compared to regular GANs. The proposed CounteRGAN method utilizes an RGAN and a target classifier to produce counterfactuals capable of providing meaningful recourse. Evaluations on two popular datasets highlight how the CounteRGAN is able to overcome the limitations of existing methods, including latency improvements of {\textgreater}50x to {\textgreater}90,000x, making meaningful recourse available in real-time and applicable to a wide range of domains.},
	urldate = {2024-02-29},
	publisher = {arXiv},
	author = {Nemirovsky, Daniel and Thiebaut, Nicolas and Xu, Ye and Gupta, Abhishek},
	month = may,
	year = {2021},
	note = {arXiv:2009.05199 [cs, stat]},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Statistics - Machine Learning},
}

@inproceedings{sanchez_what_2022,
	address = {Cham},
	series = {Lecture {Notes} in {Computer} {Science}},
	title = {What is {Healthy}? {Generative} {Counterfactual} {Diffusion} for {Lesion} {Localization}},
	isbn = {978-3-031-18576-2},
	shorttitle = {What is {Healthy}?},
	doi = {10.1007/978-3-031-18576-2_4},
	abstract = {Reducing the requirement for densely annotated masks in medical image segmentation is important due to cost constraints. In this paper, we consider the problem of inferring pixel-level predictions of brain lesions by only using image-level labels for training. By leveraging recent advances in generative diffusion probabilistic models (DPM), we synthesize counterfactuals of “How would a patient appear if X pathology was not present?”. The difference image between the observed patient state and the healthy counterfactual can be used for inferring the location of pathology. We generate counterfactuals that correspond to the minimal change of the input such that it is transformed to healthy domain. This requires training with healthy and unhealthy data in DPMs. We improve on previous counterfactual DPMs by manipulating the generation process with implicit guidance along with attention conditioning instead of using classifiers (Code is available at https://github.com/vios-s/Diff-SCM).},
	language = {en},
	booktitle = {Deep {Generative} {Models}},
	publisher = {Springer Nature Switzerland},
	author = {Sanchez, Pedro and Kascenas, Antanas and Liu, Xiao and O’Neil, Alison Q. and Tsaftaris, Sotirios A.},
	editor = {Mukhopadhyay, Anirban and Oksuz, Ilkay and Engelhardt, Sandy and Zhu, Dajiang and Yuan, Yixuan},
	year = {2022},
	keywords = {Counterfactuals, Diffusion probabilistic models, Generative models},
	pages = {34--44},
}


@misc{komanduri_identifiable_2024,
	title = {From {Identifiable} {Causal} {Representations} to {Controllable} {Counterfactual} {Generation}: {A} {Survey} on {Causal} {Generative} {Modeling}},
	shorttitle = {From {Identifiable} {Causal} {Representations} to {Controllable} {Counterfactual} {Generation}},
	url = {http://arxiv.org/abs/2310.11011},
	abstract = {Deep generative models have shown tremendous capability in data density estimation and data generation from finite samples. While these models have shown impressive performance by learning correlations among features in the data, some fundamental shortcomings are their lack of explainability, tendency to induce spurious correlations, and poor out-ofdistribution extrapolation. To remedy such challenges, recent work has proposed a shift toward causal generative models. Causal models offer several beneficial properties to deep generative models, such as distribution shift robustness, fairness, and interpretability. Structural causal models (SCMs) describe data-generating processes and model complex causal relationships and mechanisms among variables in a system. Thus, SCMs can naturally be combined with deep generative models. We provide a technical survey on causal generative modeling categorized into causal representation learning and controllable counterfactual generation methods. We focus on fundamental theory, methodology, drawbacks, datasets, and metrics. Then, we cover applications of causal generative models in fairness, privacy, out-of-distribution generalization, precision medicine, and biological sciences. Lastly, we discuss open problems and fruitful research directions for future work in the field.},
	language = {en},
	urldate = {2024-10-23},
	publisher = {arXiv},
	author = {Komanduri, Aneesh and Wu, Xintao and Wu, Yongkai and Chen, Feng},
	month = may,
	year = {2024},
	note = {arXiv:2310.11011 [cs]},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, Computer Science - Artificial Intelligence},
	file = {Komanduri et al. - 2024 - From Identifiable Causal Representations to Contro.pdf:/home/vibujithan/Zotero/storage/S94LZELG/Komanduri et al. - 2024 - From Identifiable Causal Representations to Contro.pdf:application/pdf},
}

@article{winder2024challenges,
  title={Challenges and Potential of Artificial Intelligence in Neuroradiology},
  author={Winder, Anthony J and Stanley, Emma AM and Fiehler, Jens and Forkert, Nils D},
  journal={Clinical Neuroradiology},
  pages={1--13},
  year={2024},
  publisher={Springer}
}

@inproceedings{ohara2024macaw,
  title={MACAW 3D: A masked causal normalizing flow method for counterfactual 3D brain image generation},
  author={Ohara, Erik Y and Vamosi, Finn and Patil, Harsh and Vigneshwaran, Vibujithan and Wilms, Matthias and Forkert, Nils D},
  booktitle={Medical Imaging 2024: Imaging Informatics for Healthcare, Research, and Applications},
  volume={12931},
  pages={110--115},
  year={2024},
  organization={SPIE}
}

@article{xia2022neural,
  title={Neural causal models for counterfactual identification and estimation},
  author={Xia, Kevin and Pan, Yushu and Bareinboim, Elias},
  journal={arXiv preprint arXiv:2210.00035},
  year={2022}
}