@article{coifman2006diffusion,
  title={Diffusion maps},
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  year={2006},
  publisher={Elsevier}
}


@article{li2021representation,
  title={Representation Learning for Networks in Biology and Medicine: Advancements, Challenges, and Opportunities},
  author={Li, Michelle M and Huang, Kexin and Zitnik, Marinka},
  journal={arXiv preprint arXiv:2104.04883},
  year={2021}
}

@article{velickovic2019deep,
  title={Deep Graph Infomax.},
  author={Velickovic, Petar and Fedus, William and Hamilton, William L and Li{\`o}, Pietro and Bengio, Yoshua and Hjelm, R Devon},
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  pages={4},
  year={2019}
}

@inproceedings{zilke2016deepred,
  title={Deepred--rule extraction from deep neural networks},
  author={Zilke, Jan Ruben and Menc{\'\i}a, Eneldo Loza and Janssen, Frederik},
  booktitle={International Conference on Discovery Science},
  pages={457--473},
  year={2016},
  organization={Springer}
}

@article{craven1996extracting,
  title={Extracting Tree-Structured Representations of Trained Networks, Advances, Neural Information Processing Systems 8},
  author={Craven, MW and Shavlik, JW},
  year={1996},
  publisher={MIT Press Cambridge, MA}
}


@book{thrun1993extracting,
  title={Extracting provably correct rules from artificial neural networks},
  author={Thrun, Sebastian},
  year={1993},
  publisher={Citeseer}
}


@article{lipton2018mythos,
  title={The Mythos of Model Interpretability: In machine learning, the concept of interpretability is both important and slippery.},
  author={Lipton, Zachary C},
  journal={Queue},
  volume={16},
  number={3},
  pages={31--57},
  year={2018},
  publisher={ACM New York, NY, USA}
}

@article{abdar2020review,
  title={A review of uncertainty quantification in deep learning: Techniques, applications and challenges},
  author={Abdar, Moloud and Pourpanah, Farhad and Hussain, Sadiq and Rezazadegan, Dana and Liu, Li and Ghavamzadeh, Mohammad and Fieguth, Paul and Cao, Xiaochun and Khosravi, Abbas and Acharya, U Rajendra and others},
  journal={arXiv preprint arXiv:2011.06225},
  year={2020}
}


@article{kabir2018neural,
  title={Neural network-based uncertainty quantification: A survey of methodologies and applications},
  author={Kabir, HM Dipu and Khosravi, Abbas and Hosen, Mohammad Anwar and Nahavandi, Saeid},
  journal={IEEE access},
  volume={6},
  pages={36218--36234},
  year={2018},
  publisher={IEEE}
}


@article{vovk2012venn,
  title={Venn-abers predictors},
  author={Vovk, Vladimir and Petej, Ivan},
  journal={arXiv preprint arXiv:1211.0025},
  year={2012}
}

@article{vovk2015large,
  title={Large-scale probabilistic predictors with and without guarantees of validity},
  author={Vovk, Vladimir and Petej, Ivan and Fedorova, Valentina},
  journal={arXiv preprint arXiv:1511.00213},
  year={2015}
}
@article{vovk2012venn,
  title={Venn predictors and isotonic regression},
  author={Vovk, Vladimir},
  journal={CoRR abs/1211.0025},
  year={2012}
}

@book{vovk2005algorithmic,
  title={Algorithmic learning in a random world},
  author={Vovk, Vladimir and Gammerman, Alex and Shafer, Glenn},
  year={2005},
  publisher={Springer Science \& Business Media}
}


@article{pereira2020targeting,
  title={Targeting the uncertainty of predictions at patient-level using an ensemble of classifiers coupled with calibration methods, Venn-ABERS, and Conformal Predictors: A case study in AD},
  author={Pereira, Telma and Cardoso, Sandra and Guerreiro, Manuela and Madeira, Sara C and Alzheimer’s Disease Neuroimaging Initiative and others},
  journal={Journal of biomedical informatics},
  volume={101},
  pages={103350},
  year={2020},
  publisher={Elsevier}
}


@article{cortes2019concepts,
  title={Concepts and applications of conformal prediction in computational drug discovery},
  author={Cort{\'e}s-Ciriano, Isidro and Bender, Andreas},
  journal={arXiv preprint arXiv:1908.03569},
  year={2019}
}

@article{battaglia2018relational,
  title={Relational inductive biases, deep learning, and graph networks},
  author={Battaglia, Peter W and Hamrick, Jessica B and Bapst, Victor and Sanchez-Gonzalez, Alvaro and Zambaldi, Vinicius and Malinowski, Mateusz and Tacchetti, Andrea and Raposo, David and Santoro, Adam and Faulkner, Ryan and others},
  journal={arXiv preprint arXiv:1806.01261},
  year={2018}
}


@article{kipf2016semi,
  title={Semi-supervised classification with graph convolutional networks},
  author={Kipf, Thomas N and Welling, Max},
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  year={2016}
}

@article{hamilton2017inductive,
  title={Inductive representation learning on large graphs},
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  year={2017}
}


@article{law2021ultrahyperbolic,
  title={Ultrahyperbolic Neural Networks},
  author={Law, Marc},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={22058--22069},
  year={2021}
}


@article{liu2019hyperbolic,
  title={Hyperbolic graph neural networks},
  author={Liu, Qi and Nickel, Maximilian and Kiela, Douwe},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  year={2019}
}


@article{zitnik2018modeling,
  title={Modeling polypharmacy side effects with graph convolutional networks},
  author={Zitnik, Marinka and Agrawal, Monica and Leskovec, Jure},
  journal={Bioinformatics},
  volume={34},
  number={13},
  pages={i457--i466},
  year={2018},
  publisher={Oxford University Press}
}

@article{ma2019genn,
  title={GENN: predicting correlated drug-drug interactions with graph energy neural networks},
  author={Ma, Tengfei and Shang, Junyuan and Xiao, Cao and Sun, Jimeng},
  journal={arXiv preprint arXiv:1910.02107},
  year={2019}
}


@inproceedings{dai2018adversarial,
  title={Adversarial attack on graph structured data},
  author={Dai, Hanjun and Li, Hui and Tian, Tian and Huang, Xin and Wang, Lin and Zhu, Jun and Song, Le},
  booktitle={International conference on machine learning},
  pages={1115--1124},
  year={2018},
  organization={PMLR}
}


@inproceedings{ijcai2019-669,
  title     = {Adversarial Examples for Graph Data: Deep Insights into Attack and Defense},
  author    = {Wu, Huijun and Wang, Chen and Tyshetskiy, Yuriy and Docherty, Andrew and Lu, Kai and Zhu, Liming},
  booktitle = {Proceedings of the Twenty-Eighth International Joint Conference on
               Artificial Intelligence, {IJCAI-19}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},             
  pages     = {4816--4823},
  year      = {2019},
  month     = {7},
  doi       = {10.24963/ijcai.2019/669},
  url       = {https://doi.org/10.24963/ijcai.2019/669},
}


@article{stokes2020deep,
  title={A deep learning approach to antibiotic discovery},
  author={Stokes, Jonathan M and Yang, Kevin and Swanson, Kyle and Jin, Wengong and Cubillos-Ruiz, Andres and Donghia, Nina M and MacNair, Craig R and French, Shawn and Carfrae, Lindsey A and Bloom-Ackermann, Zohar and others},
  journal={Cell},
  volume={180},
  number={4},
  pages={688--702},
  year={2020},
  publisher={Elsevier}
}

@article{casas2019spatially,
  title={Spatially-aware graph neural networks for relational behavior forecasting from sensor data},
  author={Casas, Sergio and Gulino, Cole and Liao, Renjie and Urtasun, Raquel},
  journal={arXiv preprint arXiv:1910.08233},
  year={2019}
}

@article{wu2020graph,
  title={Graph neural networks in recommender systems: a survey},
  author={Wu, Shiwen and Sun, Fei and Zhang, Wentao and Cui, Bin},
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  year={2020}
}


@inproceedings{gilmer2017neural,
  title={Neural message passing for quantum chemistry},
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  pages={1263--1272},
  year={2017},
  organization={PMLR}
}


@article{hamaguchi2017knowledge,
  title={Knowledge transfer for out-of-knowledge-base entities: A graph neural network approach},
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  year={2017}
}


@techreport{cui2019high,
  title={High-order graph convolutional recurrent neural network: A deep learning framework for network-scale traffic learning and forecasting},
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  year={2019}
}

@article{duvenaud2015convolutional,
  title={Convolutional networks on graphs for learning molecular fingerprints},
  author={Duvenaud, David and Maclaurin, Dougal and Aguilera-Iparraguirre, Jorge and G{\'o}mez-Bombarelli, Rafael and Hirzel, Timothy and Aspuru-Guzik, Al{\'a}n and Adams, Ryan P},
  journal={arXiv preprint arXiv:1509.09292},
  year={2015}
}


@article{gao2020deep,
  title={Deep Learning on Knowledge Graph for Recommender System: A Survey},
  author={Gao, Yang and Li, Yi-Fan and Lin, Yu and Gao, Hang and Khan, Latifur},
  journal={arXiv preprint arXiv:2004.00387},
  year={2020}
}


@inproceedings{wang2019knowledge,
  title={Knowledge-aware graph neural networks with label smoothness regularization for recommender systems},
  author={Wang, Hongwei and Zhang, Fuzheng and Zhang, Mengdi and Leskovec, Jure and Zhao, Miao and Li, Wenjie and Wang, Zhongyuan},
  booktitle={Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  pages={968--977},
  year={2019}
}


@inproceedings{zhao2020attention,
  title={Attention-based aggregation graph networks for knowledge graph information transfer},
  author={Zhao, Ming and Jia, Weijia and Huang, Yusheng},
  booktitle={Pacific-Asia Conference on Knowledge Discovery and Data Mining},
  pages={542--554},
  year={2020},
  organization={Springer}
}

@inproceedings{sun2020knowledge,
  title={Knowledge graph alignment network with gated multi-hop neighborhood aggregation},
  author={Sun, Zequn and Wang, Chengming and Hu, Wei and Chen, Muhao and Dai, Jian and Zhang, Wei and Qu, Yuzhong},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={34},
  number={01},
  pages={222--229},
  year={2020}
}

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  title={The Human Phenotype Ontology: a tool for annotating and analyzing human hereditary disease},
  author={Robinson, Peter N and K{\"o}hler, Sebastian and Bauer, Sebastian and Seelow, Dominik and Horn, Denise and Mundlos, Stefan},
  journal={The American Journal of Human Genetics},
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  number={5},
  pages={610--615},
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  publisher={Elsevier}
}

@article{rocheteau2021predicting,
  title={Predicting Patient Outcomes with Graph Representation Learning},
  author={Rocheteau, Emma and Tong, Catherine and Veli{\v{c}}kovi{\'c}, Petar and Lane, Nicholas and Li{\`o}, Pietro},
  journal={arXiv preprint arXiv:2101.03940},
  year={2021}
}

@inproceedings{liu2020heterogeneous,
  title={Heterogeneous Similarity Graph Neural Network on Electronic Health Records},
  author={Liu, Zheng and Li, Xiaohan and Peng, Hao and He, Lifang and Philip, S Yu},
  booktitle={2020 IEEE International Conference on Big Data (Big Data)},
  pages={1196--1205},
  year={2020},
  organization={IEEE}
}

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  title={Adversarial attack and defense on graph data: A survey},
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  journal={arXiv preprint arXiv:1812.10528},
  year={2018}
}

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}

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@article{scarselli2008graph,
  title={The graph neural network model},
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}

@article{defferrard2016convolutional,
  title={Convolutional neural networks on graphs with fast localized spectral filtering},
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  year={2016}
}



@inproceedings{10.1145/3178876.3186116,
author = {Zhuang, Chenyi and Ma, Qiang},
title = {Dual Graph Convolutional Networks for Graph-Based Semi-Supervised Classification},
year = {2018},
isbn = {9781450356398},
publisher = {International World Wide Web Conferences Steering Committee},
address = {Republic and Canton of Geneva, CHE},
url = {https://doi.org/10.1145/3178876.3186116},
doi = {10.1145/3178876.3186116},
abstract = {The problem of extracting meaningful data through graph analysis spans a range of different fields, such as the internet, social networks, biological networks, and many others. The importance of being able to effectively mine and learn from such data continues to grow as more and more structured data become available. In this paper, we present a simple and scalable semi-supervised learning method for graph-structured data in which only a very small portion of the training data are labeled. To sufficiently embed the graph knowledge, our method performs graph convolution from different views of the raw data. In particular, a dual graph convolutional neural network method is devised to jointly consider the two essential assumptions of semi-supervised learning: (1) local consistency and (2) global consistency. Accordingly, two convolutional neural networks are devised to embed the local-consistency-based and global-consistency-based knowledge, respectively. Given the different data transformations from the two networks, we then introduce an unsupervised temporal loss function for the ensemble. In experiments using both unsupervised and supervised loss functions, our method outperforms state-of-the-art techniques on different datasets.},
booktitle = {Proceedings of the 2018 World Wide Web Conference},
pages = {499–508},
numpages = {10},
keywords = {semi-supervised learning, graph convolutional networks, pointwise mutual information, adjacency matrix, graph diffusion},
location = {Lyon, France},
series = {WWW '18}
}


@inproceedings{gao2018large,
  title={Large-Scale Learnable Graph Convolutional Networks},
  author={Gao, Hongyang and Wang, Zhengyang and Ji, Shuiwang},
  booktitle={Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  pages={1416--1424},
  year={2018},
  organization={ACM}
}

@article{xu2019graph,
  title={Graph wavelet neural network},
  author={Xu, Bingbing and Shen, Huawei and Cao, Qi and Qiu, Yunqi and Cheng, Xueqi},
  journal={arXiv preprint arXiv:1904.07785},
  year={2019}
}


@article{duvenaud2015convolutional,
  title={Convolutional networks on graphs for learning molecular fingerprints},
  author={Duvenaud, David and Maclaurin, Dougal and Aguilera-Iparraguirre, Jorge and G{\'o}mez-Bombarelli, Rafael and Hirzel, Timothy and Aspuru-Guzik, Al{\'a}n and Adams, Ryan P},
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  year={2015}
}

@inproceedings{atwood2016diffusion,
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  year={2016}
}

@article{frasca2020sign,
  title={Sign: Scalable inception graph neural networks},
  author={Frasca, Fabrizio and Rossi, Emanuele and Eynard, Davide and Chamberlain, Ben and Bronstein, Michael and Monti, Federico},
  journal={arXiv preprint arXiv:2004.11198},
  year={2020}
}

@article{dong2020graph,
  title={Graph signal processing for machine learning: A review and new perspectives},
  author={Dong, Xiaowen and Thanou, Dorina and Toni, Laura and Bronstein, Michael and Frossard, Pascal},
  journal={IEEE Signal processing magazine},
  volume={37},
  number={6},
  pages={117--127},
  year={2020},
  publisher={IEEE}
}

@article{gaudelet2021utilizing,
  title={Utilizing graph machine learning within drug discovery and development},
  author={Gaudelet, Thomas and Day, Ben and Jamasb, Arian R and Soman, Jyothish and Regep, Cristian and Liu, Gertrude and Hayter, Jeremy BR and Vickers, Richard and Roberts, Charles and Tang, Jian and others},
  journal={Briefings in bioinformatics},
  volume={22},
  number={6},
  pages={bbab159},
  year={2021},
  publisher={Oxford University Press}
}


@article{liu2020simplification,
  title={Simplification of Graph Convolutional Networks: A Matrix Factorization-based Perspective},
  author={Liu, Qiang and Zhang, Haoli and Liu, Zhaocheng},
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  year={2020}
}


@inproceedings{wu2019simplifying,
  title={Simplifying graph convolutional networks},
  author={Wu, Felix and Souza, Amauri and Zhang, Tianyi and Fifty, Christopher and Yu, Tao and Weinberger, Kilian},
  booktitle={International conference on machine learning},
  pages={6861--6871},
  year={2019},
  organization={PMLR}
}

@article{wang2019improving,
  title={Improving graph attention networks with large margin-based constraints},
  author={Wang, Guangtao and Ying, Rex and Huang, Jing and Leskovec, Jure},
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  year={2019}
}

@inproceedings{morris2019weisfeiler,
  title={Weisfeiler and leman go neural: Higher-order graph neural networks},
  author={Morris, Christopher and Ritzert, Martin and Fey, Matthias and Hamilton, William L and Lenssen, Jan Eric and Rattan, Gaurav and Grohe, Martin},
  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={33},
  number={01},
  pages={4602--4609},
  year={2019}
}

@article{bresson2017residual,
  title={Residual gated graph convnets},
  author={Bresson, Xavier and Laurent, Thomas},
  journal={arXiv preprint arXiv:1711.07553},
  year={2017}
}

@article{brody2021attentive,
  title={How attentive are graph attention networks?},
  author={Brody, Shaked and Alon, Uri and Yahav, Eran},
  journal={arXiv preprint arXiv:2105.14491},
  year={2021}
}


@article{bianchi2021graph,
  title={Graph neural networks with convolutional arma filters},
  author={Bianchi, Filippo Maria and Grattarola, Daniele and Livi, Lorenzo and Alippi, Cesare},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2021},
  publisher={IEEE}
}

@article{hu2019strategies,
  title={Strategies for pre-training graph neural networks},
  author={Hu, Weihua and Liu, Bowen and Gomes, Joseph and Zitnik, Marinka and Liang, Percy and Pande, Vijay and Leskovec, Jure},
  journal={arXiv preprint arXiv:1905.12265},
  year={2019}
}
@article{du2017topology,
  title={Topology adaptive graph convolutional networks},
  author={Du, Jian and Zhang, Shanghang and Wu, Guanhang and Moura, Jos{\'e} MF and Kar, Soummya},
  journal={arXiv preprint arXiv:1710.10370},
  year={2017}
}
@article{shi2020masked,
  title={Masked label prediction: Unified message passing model for semi-supervised classification},
  author={Shi, Yunsheng and Huang, Zhengjie and Feng, Shikun and Zhong, Hui and Wang, Wenjin and Sun, Yu},
  journal={arXiv preprint arXiv:2009.03509},
  year={2020}
}

@article{thekumparampil2018attention,
  title={Attention-based graph neural network for semi-supervised learning},
  author={Thekumparampil, Kiran K and Wang, Chong and Oh, Sewoong and Li, Li-Jia},
  journal={arXiv preprint arXiv:1803.03735},
  year={2018}
}

@article{li2015gated,
  title={Gated graph sequence neural networks},
  author={Li, Yujia and Tarlow, Daniel and Brockschmidt, Marc and Zemel, Richard},
  journal={arXiv preprint arXiv:1511.05493},
  year={2015}
}


@inproceedings{zilke2016deepred,
  title={Deepred--rule extraction from deep neural networks},
  author={Zilke, Jan Ruben and Menc{\'\i}a, Eneldo Loza and Janssen, Frederik},
  booktitle={International Conference on Discovery Science},
  pages={457--473},
  year={2016},
  organization={Springer}
}

@article{craven1996extracting,
  title={Extracting Tree-Structured Representations of Trained Networks, Advances, Neural Information Processing Systems 8},
  author={Craven, MW and Shavlik, JW},
  year={1996},
  publisher={MIT Press Cambridge, MA}
}


@book{thrun1993extracting,
  title={Extracting provably correct rules from artificial neural networks},
  author={Thrun, Sebastian},
  year={1993},
  publisher={Citeseer}
}


@article{lipton2018mythos,
  title={The Mythos of Model Interpretability: In machine learning, the concept of interpretability is both important and slippery.},
  author={Lipton, Zachary C},
  journal={Queue},
  volume={16},
  number={3},
  pages={31--57},
  year={2018},
  publisher={ACM New York, NY, USA}
}

@article{abdar2020review,
  title={A review of uncertainty quantification in deep learning: Techniques, applications and challenges},
  author={Abdar, Moloud and Pourpanah, Farhad and Hussain, Sadiq and Rezazadegan, Dana and Liu, Li and Ghavamzadeh, Mohammad and Fieguth, Paul and Cao, Xiaochun and Khosravi, Abbas and Acharya, U Rajendra and others},
  journal={arXiv preprint arXiv:2011.06225},
  year={2020}
}


@article{kabir2018neural,
  title={Neural network-based uncertainty quantification: A survey of methodologies and applications},
  author={Kabir, HM Dipu and Khosravi, Abbas and Hosen, Mohammad Anwar and Nahavandi, Saeid},
  journal={IEEE access},
  volume={6},
  pages={36218--36234},
  year={2018},
  publisher={IEEE}
}


@article{vovk2012venn,
  title={Venn-abers predictors},
  author={Vovk, Vladimir and Petej, Ivan},
  journal={arXiv preprint arXiv:1211.0025},
  year={2012}
}

@article{vovk2015large,
  title={Large-scale probabilistic predictors with and without guarantees of validity},
  author={Vovk, Vladimir and Petej, Ivan and Fedorova, Valentina},
  journal={arXiv preprint arXiv:1511.00213},
  year={2015}
}
@article{vovk2012venn,
  title={Venn predictors and isotonic regression},
  author={Vovk, Vladimir},
  journal={CoRR abs/1211.0025},
  year={2012}
}

@book{vovk2005algorithmic,
  title={Algorithmic learning in a random world},
  author={Vovk, Vladimir and Gammerman, Alex and Shafer, Glenn},
  year={2005},
  publisher={Springer Science \& Business Media}
}


@article{pereira2020targeting,
  title={Targeting the uncertainty of predictions at patient-level using an ensemble of classifiers coupled with calibration methods, Venn-ABERS, and Conformal Predictors: A case study in AD},
  author={Pereira, Telma and Cardoso, Sandra and Guerreiro, Manuela and Madeira, Sara C and Alzheimer’s Disease Neuroimaging Initiative and others},
  journal={Journal of biomedical informatics},
  volume={101},
  pages={103350},
  year={2020},
  publisher={Elsevier}
}


@article{cortes2019concepts,
  title={Concepts and applications of conformal prediction in computational drug discovery},
  author={Cort{\'e}s-Ciriano, Isidro and Bender, Andreas},
  journal={arXiv preprint arXiv:1908.03569},
  year={2019}
}


@article{zitnik2018modeling,
  title={Modeling polypharmacy side effects with graph convolutional networks},
  author={Zitnik, Marinka and Agrawal, Monica and Leskovec, Jure},
  journal={Bioinformatics},
  volume={34},
  number={13},
  pages={i457--i466},
  year={2018},
  publisher={Oxford University Press}
}

@inproceedings{dai2018adversarial,
  title={Adversarial attack on graph structured data},
  author={Dai, Hanjun and Li, Hui and Tian, Tian and Huang, Xin and Wang, Lin and Zhu, Jun and Song, Le},
  booktitle={International conference on machine learning},
  pages={1115--1124},
  year={2018},
  organization={PMLR}
}


@inproceedings{ijcai2019-669,
  title     = {Adversarial Examples for Graph Data: Deep Insights into Attack and Defense},
  author    = {Wu, Huijun and Wang, Chen and Tyshetskiy, Yuriy and Docherty, Andrew and Lu, Kai and Zhu, Liming},
  booktitle = {Proceedings of the Twenty-Eighth International Joint Conference on
               Artificial Intelligence, {IJCAI-19}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},             
  pages     = {4816--4823},
  year      = {2019},
  month     = {7},
  doi       = {10.24963/ijcai.2019/669},
  url       = {https://doi.org/10.24963/ijcai.2019/669},
}


@article{stokes2020deep,
  title={A deep learning approach to antibiotic discovery},
  author={Stokes, Jonathan M and Yang, Kevin and Swanson, Kyle and Jin, Wengong and Cubillos-Ruiz, Andres and Donghia, Nina M and MacNair, Craig R and French, Shawn and Carfrae, Lindsey A and Bloom-Ackermann, Zohar and others},
  journal={Cell},
  volume={180},
  number={4},
  pages={688--702},
  year={2020},
  publisher={Elsevier}
}


@article{hamaguchi2017knowledge,
  title={Knowledge transfer for out-of-knowledge-base entities: A graph neural network approach},
  author={Hamaguchi, Takuo and Oiwa, Hidekazu and Shimbo, Masashi and Matsumoto, Yuji},
  journal={arXiv preprint arXiv:1706.05674},
  year={2017}
}


@techreport{cui2019high,
  title={High-order graph convolutional recurrent neural network: A deep learning framework for network-scale traffic learning and forecasting},
  author={Cui, Zhiyong and Henrickson, Kristian and Ke, Ruimin and Dong, Xiao and Wang, Yinhai},
  year={2019}
}

@article{duvenaud2015convolutional,
  title={Convolutional networks on graphs for learning molecular fingerprints},
  author={Duvenaud, David and Maclaurin, Dougal and Aguilera-Iparraguirre, Jorge and G{\'o}mez-Bombarelli, Rafael and Hirzel, Timothy and Aspuru-Guzik, Al{\'a}n and Adams, Ryan P},
  journal={arXiv preprint arXiv:1509.09292},
  year={2015}
}


@article{gao2020deep,
  title={Deep Learning on Knowledge Graph for Recommender System: A Survey},
  author={Gao, Yang and Li, Yi-Fan and Lin, Yu and Gao, Hang and Khan, Latifur},
  journal={arXiv preprint arXiv:2004.00387},
  year={2020}
}


@inproceedings{wang2019knowledge,
  title={Knowledge-aware graph neural networks with label smoothness regularization for recommender systems},
  author={Wang, Hongwei and Zhang, Fuzheng and Zhang, Mengdi and Leskovec, Jure and Zhao, Miao and Li, Wenjie and Wang, Zhongyuan},
  booktitle={Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  pages={968--977},
  year={2019}
}


@inproceedings{zhao2020attention,
  title={Attention-based aggregation graph networks for knowledge graph information transfer},
  author={Zhao, Ming and Jia, Weijia and Huang, Yusheng},
  booktitle={Pacific-Asia Conference on Knowledge Discovery and Data Mining},
  pages={542--554},
  year={2020},
  organization={Springer}
}

@inproceedings{sun2020knowledge,
  title={Knowledge graph alignment network with gated multi-hop neighborhood aggregation},
  author={Sun, Zequn and Wang, Chengming and Hu, Wei and Chen, Muhao and Dai, Jian and Zhang, Wei and Qu, Yuzhong},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={34},
  number={01},
  pages={222--229},
  year={2020}
}

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  title={The Human Phenotype Ontology: a tool for annotating and analyzing human hereditary disease},
  author={Robinson, Peter N and K{\"o}hler, Sebastian and Bauer, Sebastian and Seelow, Dominik and Horn, Denise and Mundlos, Stefan},
  journal={The American Journal of Human Genetics},
  volume={83},
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  publisher={Elsevier}
}

@article{rocheteau2021predicting,
  title={Predicting Patient Outcomes with Graph Representation Learning},
  author={Rocheteau, Emma and Tong, Catherine and Veli{\v{c}}kovi{\'c}, Petar and Lane, Nicholas and Li{\`o}, Pietro},
  journal={arXiv preprint arXiv:2101.03940},
  year={2021}
}

@inproceedings{liu2020heterogeneous,
  title={Heterogeneous Similarity Graph Neural Network on Electronic Health Records},
  author={Liu, Zheng and Li, Xiaohan and Peng, Hao and He, Lifang and Philip, S Yu},
  booktitle={2020 IEEE International Conference on Big Data (Big Data)},
  pages={1196--1205},
  year={2020},
  organization={IEEE}
}

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  journal={arXiv preprint arXiv:1812.10528},
  year={2018}
}

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@article{scarselli2008graph,
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@inproceedings{10.1145/3178876.3186116,
author = {Zhuang, Chenyi and Ma, Qiang},
title = {Dual Graph Convolutional Networks for Graph-Based Semi-Supervised Classification},
year = {2018},
isbn = {9781450356398},
publisher = {International World Wide Web Conferences Steering Committee},
address = {Republic and Canton of Geneva, CHE},
url = {https://doi.org/10.1145/3178876.3186116},
doi = {10.1145/3178876.3186116},
abstract = {The problem of extracting meaningful data through graph analysis spans a range of different fields, such as the internet, social networks, biological networks, and many others. The importance of being able to effectively mine and learn from such data continues to grow as more and more structured data become available. In this paper, we present a simple and scalable semi-supervised learning method for graph-structured data in which only a very small portion of the training data are labeled. To sufficiently embed the graph knowledge, our method performs graph convolution from different views of the raw data. In particular, a dual graph convolutional neural network method is devised to jointly consider the two essential assumptions of semi-supervised learning: (1) local consistency and (2) global consistency. Accordingly, two convolutional neural networks are devised to embed the local-consistency-based and global-consistency-based knowledge, respectively. Given the different data transformations from the two networks, we then introduce an unsupervised temporal loss function for the ensemble. In experiments using both unsupervised and supervised loss functions, our method outperforms state-of-the-art techniques on different datasets.},
booktitle = {Proceedings of the 2018 World Wide Web Conference},
pages = {499–508},
numpages = {10},
keywords = {semi-supervised learning, graph convolutional networks, pointwise mutual information, adjacency matrix, graph diffusion},
location = {Lyon, France},
series = {WWW '18}
}


@inproceedings{gao2018large,
  title={Large-Scale Learnable Graph Convolutional Networks},
  author={Gao, Hongyang and Wang, Zhengyang and Ji, Shuiwang},
  booktitle={Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  pages={1416--1424},
  year={2018},
  organization={ACM}
}

@article{xu2019graph,
  title={Graph wavelet neural network},
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  journal={arXiv preprint arXiv:1904.07785},
  year={2019}
}


@article{duvenaud2015convolutional,
  title={Convolutional networks on graphs for learning molecular fingerprints},
  author={Duvenaud, David and Maclaurin, Dougal and Aguilera-Iparraguirre, Jorge and G{\'o}mez-Bombarelli, Rafael and Hirzel, Timothy and Aspuru-Guzik, Al{\'a}n and Adams, Ryan P},
  journal={arXiv preprint arXiv:1509.09292},
  year={2015}
}

@article{gama2018convolutional,
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  journal={IEEE Transactions on Signal Processing},
  volume={67},
  number={4},
  pages={1034--1049},
  year={2018},
  publisher={IEEE}
}


@article{gama2018diffusion,
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  author={Gama, Fernando and Ribeiro, Alejandro and Bruna, Joan},
  journal={arXiv preprint arXiv:1806.08829},
  year={2018}
}
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  year={2015}
}

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  publisher={IEEE}
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  year={2016}
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@article{liu2020simplification,
  title={Simplification of Graph Convolutional Networks: A Matrix Factorization-based Perspective},
  author={Liu, Qiang and Zhang, Haoli and Liu, Zhaocheng},
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  year={2020}
}


@article{wang2019improving,
  title={Improving graph attention networks with large margin-based constraints},
  author={Wang, Guangtao and Ying, Rex and Huang, Jing and Leskovec, Jure},
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  year={2019}
}


@article{cai2020note,
  title={A note on over-smoothing for graph neural networks},
  author={Cai, Chen and Wang, Yusu},
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  year={2020}
}

@article{oono2019graph,
  title={Graph neural networks exponentially lose expressive power for node classification},
  author={Oono, Kenta and Suzuki, Taiji},
  journal={arXiv preprint arXiv:1905.10947},
  year={2019}
}

@article{nt2019revisiting,
  title={Revisiting graph neural networks: All we have is low-pass filters},
  author={Nt, Hoang and Maehara, Takanori},
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  year={2019}
}

@article{nikolentzos2020random,
  title={Random walk graph neural networks},
  author={Nikolentzos, Giannis and Vazirgiannis, Michalis},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={16211--16222},
  year={2020}
}

@inproceedings{balcilar2020analyzing,
  title={Analyzing the expressive power of graph neural networks in a spectral perspective},
  author={Balcilar, Muhammet and Renton, Guillaume and H{\'e}roux, Pierre and Ga{\"u}z{\`e}re, Benoit and Adam, S{\'e}bastien and Honeine, Paul},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

@article{petersen2020equivalence,
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  author={Petersen, Philipp and Voigtlaender, Felix},
  journal={Proceedings of the American Mathematical Society},
  volume={148},
  number={4},
  pages={1567--1581},
  year={2020}
}


@article{poggio2017theory,
  title={Theory of deep learning III: explaining the non-overfitting puzzle},
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  year={2017}
}


@inproceedings{allen2019convergence,
  title={A convergence theory for deep learning via over-parameterization},
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  booktitle={International Conference on Machine Learning},
  pages={242--252},
  year={2019},
  organization={PMLR}
}


@article{saxe2019information,
  title={On the information bottleneck theory of deep learning},
  author={Saxe, Andrew M and Bansal, Yamini and Dapello, Joel and Advani, Madhu and Kolchinsky, Artemy and Tracey, Brendan D and Cox, David D},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  volume={2019},
  number={12},
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  year={2019},
  publisher={IOP Publishing}
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@article{bartlett2021deep,
  title={Deep learning: a statistical viewpoint},
  author={Bartlett, Peter L and Montanari, Andrea and Rakhlin, Alexander},
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  year={2021}
}

@article{zhou2020graph,
  title={Graph neural networks: A review of methods and applications},
  author={Zhou, Jie and Cui, Ganqu and Hu, Shengding and Zhang, Zhengyan and Yang, Cheng and Liu, Zhiyuan and Wang, Lifeng and Li, Changcheng and Sun, Maosong},
  journal={AI Open},
  volume={1},
  pages={57--81},
  year={2020},
  publisher={Elsevier}
}


@article{zhou2020understanding,
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  year={2020}
}

@inproceedings{li2018deeper,
  title={Deeper insights into graph convolutional networks for semi-supervised learning},
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  volume={32},
  number={1},
  year={2018}
}


@article{wu2020comprehensive,
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  author={Wu, Zonghan and Pan, Shirui and Chen, Fengwen and Long, Guodong and Zhang, Chengqi and Philip, S Yu},
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  year={2020},
  publisher={IEEE}
}


@article{velivckovic2017graph,
  title={Graph attention networks},
  author={Veli{\v{c}}kovi{\'c}, Petar and Cucurull, Guillem and Casanova, Arantxa and Romero, Adriana and Lio, Pietro and Bengio, Yoshua},
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  year={2017}
}


@article{wang2019improving,
  title={Improving graph attention networks with large margin-based constraints},
  author={Wang, Guangtao and Ying, Rex and Huang, Jing and Leskovec, Jure},
  journal={arXiv preprint arXiv:1910.11945},
  year={2019}
}

@article{wang2020unifying,
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  author={Wang, Hongwei and Leskovec, Jure},
  journal={arXiv preprint arXiv:2002.06755},
  year={2020}
}


@article{liu2020simplification,
  title={Simplification of Graph Convolutional Networks: A Matrix Factorization-based Perspective},
  author={Liu, Qiang and Zhang, Haoli and Liu, Zhaocheng},
  journal={arXiv preprint arXiv:2007.09036},
  year={2020}
}


@inproceedings{yanardag2015deep,
  title={Deep graph kernels},
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  booktitle={Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining},
  pages={1365--1374},
  year={2015}
}

@inproceedings{borgwardt2005shortest,
  title={Shortest-path kernels on graphs},
  author={Borgwardt, Karsten M and Kriegel, Hans-Peter},
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  pages={8--pp},
  year={2005},
  organization={IEEE}
}

@techreport{haussler1999convolution,
  title={Convolution kernels on discrete structures},
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  publisher={Springer}
}

@article{grinsztajn2021low,
  title={Low-rank projections of GCNs laplacian},
  author={Grinsztajn, Nathan and Preux, Philippe and Oyallon, Edouard},
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  year={2021}
}

@article{kawamoto2019mean,
  title={Mean-field theory of graph neural networks in graph partitioning},
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  volume={2019},
  number={12},
  pages={124007},
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  publisher={IOP Publishing}
}

@article{yang2021graph,
  title={Graph Neural Networks Inspired by Classical Iterative Algorithms},
  author={Yang, Yongyi and Liu, Tang and Wang, Yangkun and Zhou, Jinjing and Gan, Quan and Wei, Zhewei and Zhang, Zheng and Huang, Zengfeng and Wipf, David},
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}



@article{donnat2018tracking,
  title={Tracking network dynamics: A survey using graph distances},
  author={Donnat, Claire and Holmes, Susan},
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  volume={12},
  number={2},
  pages={971--1012},
  year={2018},
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}

@article{botvinik2020variability,
  title={Variability in the analysis of a single neuroimaging dataset by many teams},
  author={Botvinik-Nezer, Rotem and Holzmeister, Felix and Camerer, Colin F and Dreber, Anna and Huber, Juergen and Johannesson, Magnus and Kirchler, Michael and Iwanir, Roni and Mumford, Jeanette A and Adcock, R Alison and others},
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  year={2020},
  publisher={Nature Publishing Group}
}

@inproceedings{donnat2018learning,
  title={Learning structural node embeddings via diffusion wavelets},
  author={Donnat, Claire and Zitnik, Marinka and Hallac, David and Leskovec, Jure},
  booktitle={Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  pages={1320--1329},
  year={2018}
}

@article{donnat2021modeling,
  title={Modeling the heterogeneity in COVID-19's reproductive number and its impact on predictive scenarios},
  author={Donnat, Claire and Holmes, Susan},
  journal={Journal of Applied Statistics},
  pages={1--29},
  year={2021},
  publisher={Taylor \& Francis}
}

@inproceedings{donnat2020bayesian,
  title={A bayesian hierarchical network for combining heterogeneous data sources in medical diagnoses},
  author={Donnat, Claire and Miolane, Nina and Bunbury, Freddy and Kreindler, Jack},
  booktitle={Machine Learning for Health},
  pages={53--84},
  year={2020},
  organization={PMLR}
}

@article{donnat2018tracking,
  title={Tracking network dynamics: A survey of distances and similarity metrics},
  author={Donnat, Claire and Holmes, Susan},
  journal={arXiv preprint arXiv:1801.07351},
  year={2018}
}

@article{donnat2021predictive,
  title={A Predictive Modelling Framework for COVID-19 Transmission to Inform the Management of Mass Events},
  author={Donnat, Claire and Bunbury, Freddy and Kreindler, Jack and Filippidis, Filippos T and El-Osta, Austen and Esko, T{\~o}nu and Harris, Matthew},
  journal={medRxiv},
  year={2021},
  publisher={Cold Spring Harbor Laboratory Press}
}


@inproceedings{rossi2018relational,
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  booktitle={2018 IEEE International Conference on Big Data (Big Data)},
  pages={1807--1816},
  year={2018},
  organization={IEEE}
}


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  year={2019}
}

@inproceedings{donnat2019convex,
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@MISC{obama,
   author =       {Chen, Grace},
   title =        {
Why President Obama is Hailed as the Community College President},
   editor =       {Community College Review},
   month =        {April},
   year =         {2021},
   url =          {https://www.communitycollegereview.com/blog/why-president-obama-is-hailed-as-the-community-college-president/},
   note =         {[Online; posted 19-April-2021]},
 }
 
 
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 @inproceedings{sanchez2020learning,
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  year={2020},
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}

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  year={2019},
  organization={PMLR}
}

@inproceedings{koh2017understanding,
  title={Understanding black-box predictions via influence functions},
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@ARTICLE{lele2020,
  
AUTHOR={Lele, Subhash R.},   
	 
TITLE={How Should We Quantify Uncertainty in Statistical Inference?},      
	
JOURNAL={Frontiers in Ecology and Evolution},      
	
VOLUME={8},      

PAGES={35},     
	
YEAR={2020},      
	  
URL={https://www.frontiersin.org/article/10.3389/fevo.2020.00035},       
	
DOI={10.3389/fevo.2020.00035},      
	
ISSN={2296-701X},   
   
ABSTRACT={An inferential statement is any statement about the parameters, form of the underlying process or future outcomes. An inferential statement, that provides an approximation to the truth, becomes “statistical” only when there is a measure of uncertainty associated with it. The uncertainty of an inferential statement is generally quantified in terms of probability of the strength of approximation to the truth. This is what we term “inferential uncertainty.” Answer to this question has significant implications in statistical decision making where inferential uncertainty is combined with loss functions for predicted outcomes to compute the risk associated with the decision. The Classical and the Evidential paradigms use aleatory (frequency based) probability for quantifying uncertainty whereas the Bayesian approach utilizes epistemic (belief based) probability. To compute aleatory uncertainty, one needs to answer the question: which experiment is being repeated, hypothetically or otherwise? whereas computing epistemic uncertainty requires: What is the prior belief? Deciding which type of uncertainty is appropriate for scientific inference has been a contentious issue and without proper resolution because it has been commonly formulated in terms of statements about parameters, that are statistical constructs, not observables. Common to these approaches is the desire to understand the data generating mechanism. Whether one follows the Frequentist or the Bayesian approach inferential statements concerning prediction are aleatory in nature and are practically ascertainable. We consider the desirable characteristics for quantification of uncertainty as: (1) Parameterization and data transformation invariance, (2) correct predictive coverage, (3) uncertainty that depends only on the data at hand and the hypothesized data generating mechanism, and (4) diagnostics for model misspecification and guidance for correction. We examine the Classical, Bayesian and Evidential approaches in the light of these characteristics. Unfortunately, none of these inferential approaches possesses all of our desiderata although the Evidential approach seems to come closest. Choosing an inferential approach, thus, involves choosing between either specifying the hypothetical experiment that will be repeated or equivalently a sampling distribution of the estimator or a prior distribution on the model space or an evidence function.}
}

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