@inproceedings{agrawal2019kernel,
  title={The Kernel interaction trick: Fast Bayesian discovery of pairwise interactions in high dimensions},
  author={Agrawal, Raj and Trippe, Brian and Huggins, Jonathan and Broderick, Tamara},
  booktitle={International Conference on Machine Learning},
  pages={141--150},
  year={2019},
  organization={PMLR}
}

@article{rajagopal2020predicting,
  title={Predicting Generalization in Deep Learning via Local Measures of Distortion},
  author={Rajagopal, Abhejit and Madala, Vamshi C and Chandrasekaran, Shivkumar and Larson, Peder EZ},
  journal={arXiv preprint arXiv:2012.06969},
  year={2020}
}
@article{natekar2020representation,
  title={Representation Based Complexity Measures for Predicting Generalization in Deep Learning},
  author={Natekar, Parth and Sharma, Manik},
  journal={arXiv preprint arXiv:2012.02775},
  year={2020}
}
@article{zhang2016understanding,
  title={Understanding deep learning requires rethinking generalization},
  author={Zhang, Chiyuan and Bengio, Samy and Hardt, Moritz and Recht, Benjamin and Vinyals, Oriol},
  journal={arXiv preprint arXiv:1611.03530},
  year={2016}
}
@book{rajagopal2019high,
  title={High-Dimensional Polynomial Approximation with Applications in Imaging and Recognition},
  author={Rajagopal, Abhejit},
  year={2019},
  publisher={University of California, Santa Barbara}
}
@article{poggio2017and,
  title={Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review},
  author={Poggio, Tomaso and Mhaskar, Hrushikesh and Rosasco, Lorenzo and Miranda, Brando and Liao, Qianli},
  journal={International Journal of Automation and Computing},
  volume={14},
  number={5},
  pages={503--519},
  year={2017},
  publisher={Springer}
}
@article{davies1979cluster,
  title={A cluster separation measure},
  author={Davies, David L and Bouldin, Donald W},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  year={1979},
  publisher={IEEE}
}

@misc{gal2016dropout,
      title={Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning}, 
      author={Yarin Gal and Zoubin Ghahramani},
      year={2016},
      eprint={1506.02142},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@INPROCEEDINGS{8917207,
  author={C. {Hubschneider} and R. {Hutmacher} and J. M. {Zöllner}},
  booktitle={2019 IEEE Intelligent Transportation Systems Conference (ITSC)}, 
  title={Calibrating Uncertainty Models for Steering Angle Estimation}, 
  year={2019},
  volume={},
  number={},
  pages={1511-1518},
  doi={10.1109/ITSC.2019.8917207}}
  
 @misc{ren2019likelihood,
      title={Likelihood Ratios for Out-of-Distribution Detection}, 
      author={Jie Ren and Peter J. Liu and Emily Fertig and Jasper Snoek and Ryan Poplin and Mark A. DePristo and Joshua V. Dillon and Balaji Lakshminarayanan},
      year={2019},
      eprint={1906.02845},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@InProceedings{pmlr-v121-linmans20a, title = {Efficient Out-of-Distribution Detection in Digital Pathology Using Multi-Head Convolutional Neural Networks}, author = {Linmans, Jasper and {van der Laak}, Jeroen and Litjens, Geert}, booktitle = {Proceedings of the Third Conference on Medical Imaging with Deep Learning}, pages = {465--478}, year = {2020}, editor = {Tal Arbel and Ismail Ben Ayed and Marleen de Bruijne and Maxime Descoteaux and Herve Lombaert and Christopher Pal}, volume = {121}, series = {Proceedings of Machine Learning Research}, address = {Montreal, QC, Canada}, month = {06--08 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v121/linmans20a/linmans20a.pdf}, url = {http://proceedings.mlr.press/v121/linmans20a.html}, abstract = {Successful clinical implementation of deep learning in medical imaging depends, in part, on the reliability of the predictions. Specifically, the system should be accurate for classes seen during training while providing calibrated estimates of uncertainty for abnormalities and unseen classes. To efficiently estimate predictive uncertainty, we propose the use of multi-head CNNs (M-heads). We compare its performance to related and more prevalent approaches, such as deep ensembles, on the task of out-of-distribution (OOD) detection. To this end, we evaluate models trained to discriminate normal lymph node tissue from breast cancer metastases, on lymph nodes containing lymphoma. We show the ability to discriminate between in-distribution lymph node tissue and lymphoma by evaluating the AUROC based on the uncertainty signal. Here, the best performing multi-head CNN (91.7) outperforms both Monte Carlo dropout (88.3) and deep ensembles (86.8). Furthermore, we show that the meta-loss function of M-heads improves OOD detection in terms of AUROC.} }

@InProceedings{pmlr-v121-ding20a, title = {Uncertainty-Aware Training of Neural Networks for Selective Medical Image Segmentation}, author = {Ding, Yukun and Liu, Jinglan and Xu, Xiaowei and Huang, Meiping and Zhuang, Jian and Xiong, Jinjun and Shi, Yiyu}, booktitle = {Proceedings of the Third Conference on Medical Imaging with Deep Learning}, pages = {156--173}, year = {2020}, editor = {Tal Arbel and Ismail Ben Ayed and Marleen de Bruijne and Maxime Descoteaux and Herve Lombaert and Christopher Pal}, volume = {121}, series = {Proceedings of Machine Learning Research}, address = {Montreal, QC, Canada}, month = {06--08 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v121/ding20a/ding20a.pdf}, url = {http://proceedings.mlr.press/v121/ding20a.html}, abstract = {State-of-the-art deep learning based methods have achieved remarkable performance on medical image segmentation. Their applications in the clinical setting are, however, limited due to the lack of trustworthiness and reliability. Selective image segmentation has been proposed to address this issue by letting a DNN model process instances with high confidence while referring difficult ones with high uncertainty to experienced radiologists. As such, the model performance is only affected by the predictions on the high confidence subset rather than the whole dataset. Existing selective segmentation methods, however, ignore this unique property of selective segmentation and train their DNN models by optimizing accuracy on the entire dataset. Motivated by such a discrepancy, we present a novel method in this paper that considers such uncertainty in the training process to maximize the accuracy on the confident subset rather than the accuracy on the whole dataset. Experimental results using the whole heart and great vessel segmentation and gland segmentation show that such a training scheme can significantly improve the performance of selective segmentation.} }


@misc{szegedy2014intriguing,
      title={Intriguing properties of neural networks}, 
      author={Christian Szegedy and Wojciech Zaremba and Ilya Sutskever and Joan Bruna and Dumitru Erhan and Ian Goodfellow and Rob Fergus},
      year={2014},
      eprint={1312.6199},
      archivePrefix={arXiv},
      primaryClass={cs.CV}
}

@InProceedings{pmlr-v121-peng20b, title = {Mutual information deep regularization for semi-supervised segmentation}, author = {Peng, Jizong and Pedersoli, Marco and Desrosiers, Christian}, booktitle = {Proceedings of the Third Conference on Medical Imaging with Deep Learning}, pages = {601--613}, year = {2020}, editor = {Tal Arbel and Ismail Ben Ayed and Marleen de Bruijne and Maxime Descoteaux and Herve Lombaert and Christopher Pal}, volume = {121}, series = {Proceedings of Machine Learning Research}, address = {Montreal, QC, Canada}, month = {06--08 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v121/peng20b/peng20b.pdf}, url = {http://proceedings.mlr.press/v121/peng20b.html}, abstract = {The scarcity of labeled data often limits the application of deep learning to medical image segmentation. Semi-supervised learning helps overcome this limitation by leveraging unlabeled images to guide the learning process. In this paper, we propose using a clustering loss based on mutual information that explicitly enforces prediction consistency between nearby pixels in unlabeled images, and for random perturbation of these images, while imposing the network to predict the correct labels for annotated images. Since mutual information does not require a strict ordering of clusters in two different cluster assignments, we propose to incorporate another consistency regularization loss which forces the alignment of class probabilities at each pixel of perturbed unlabeled images. We evaluate the method on three challenging publicly-available medical datasets for image segmentation. Experimental results show our method to outperform recently-proposed approaches for semi-supervised and yield a performance comparable to fully-supervised training.} }

@INPROCEEDINGS{8437571,
  author={A. {Pensia} and V. {Jog} and P. {Loh}},
  booktitle={2018 IEEE International Symposium on Information Theory (ISIT)}, 
  title={Generalization Error Bounds for Noisy, Iterative Algorithms}, 
  year={2018},
  volume={},
  number={},
  pages={546-550},
  doi={10.1109/ISIT.2018.8437571}}
  
  
@misc{negrea2020informationtheoretic,
      title={Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates}, 
      author={Jeffrey Negrea and Mahdi Haghifam and Gintare Karolina Dziugaite and Ashish Khisti and Daniel M. Roy},
      year={2020},
      eprint={1911.02151},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@misc{jiang2019fantastic,
      title={Fantastic Generalization Measures and Where to Find Them}, 
      author={Yiding Jiang and Behnam Neyshabur and Hossein Mobahi and Dilip Krishnan and Samy Bengio},
      year={2019},
      eprint={1912.02178},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{dziugaite2017computing,
      title={Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data}, 
      author={Gintare Karolina Dziugaite and Daniel M. Roy},
      year={2017},
      eprint={1703.11008},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@inproceedings{NIPS2017_10ce03a1,
 author = {Neyshabur, Behnam and Bhojanapalli, Srinadh and Mcallester, David and Srebro, Nati},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {I. Guyon and U. V. Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Exploring Generalization in Deep Learning},
 url = {https://proceedings.neurips.cc/paper/2017/file/10ce03a1ed01077e3e289f3e53c72813-Paper.pdf},
 volume = {30},
 year = {2017}
}

@misc{neyshabur2018understanding,
      title={Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks}, 
      author={Behnam Neyshabur and Zhiyuan Li and Srinadh Bhojanapalli and Yann LeCun and Nathan Srebro},
      year={2018},
      eprint={1805.12076},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{keskar2017largebatch,
      title={On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima}, 
      author={Nitish Shirish Keskar and Dheevatsa Mudigere and Jorge Nocedal and Mikhail Smelyanskiy and Ping Tak Peter Tang},
      year={2017},
      eprint={1609.04836},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{zhang2018mixup,
      title={mixup: Beyond Empirical Risk Minimization}, 
      author={Hongyi Zhang and Moustapha Cisse and Yann N. Dauphin and David Lopez-Paz},
      year={2018},
      eprint={1710.09412},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{jiang2020neurips,
      title={NeurIPS 2020 Competition: Predicting Generalization in Deep Learning}, 
      author={Yiding Jiang and Pierre Foret and Scott Yak and Daniel M. Roy and Hossein Mobahi and Gintare Karolina Dziugaite and Samy Bengio and Suriya Gunasekar and Isabelle Guyon and Behnam Neyshabur},
      year={2020},
      eprint={2012.07976},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{milletari2016vnet,
      title={V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation}, 
      author={Fausto Milletari and Nassir Navab and Seyed-Ahmad Ahmadi},
      year={2016},
      eprint={1606.04797},
      archivePrefix={arXiv},
      primaryClass={cs.CV}
}

@InProceedings{Simonyan15,
  author       = "Karen Simonyan and Andrew Zisserman",
  title        = "Very Deep Convolutional Networks for Large-Scale Image Recognition",
  booktitle    = "International Conference on Learning Representations",
  year         = "2015",
}

@misc{lin2014network,
      title={Network In Network}, 
      author={Min Lin and Qiang Chen and Shuicheng Yan},
      year={2014},
      eprint={1312.4400},
      archivePrefix={arXiv},
      primaryClass={cs.NE}
}

@article{liao2018surprising,
  title={A surprising linear relationship predicts test performance in deep networks},
  author={Liao, Qianli and Miranda, Brando and Banburski, Andrzej and Hidary, Jack and Poggio, Tomaso},
  journal={arXiv preprint arXiv:1807.09659},
  year={2018}
}

@ARTICLE{db_cluster,
  author={D. L. {Davies} and D. W. {Bouldin}},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
  title={A Cluster Separation Measure}, 
  year={1979},
  volume={PAMI-1},
  number={2},
  pages={224-227},
  doi={10.1109/TPAMI.1979.4766909}}
  
  @article{unterthiner2020predicting,
  title={Predicting neural network accuracy from weights},
  author={Unterthiner, Thomas and Keysers, Daniel and Gelly, Sylvain and Bousquet, Olivier and Tolstikhin, Ilya},
  journal={arXiv preprint arXiv:2002.11448},
  year={2020}
}

@article{novak2018sensitivity,
  title={Sensitivity and generalization in neural networks: an empirical study},
  author={Novak, Roman and Bahri, Yasaman and Abolafia, Daniel A and Pennington, Jeffrey and Sohl-Dickstein, Jascha},
  journal={arXiv preprint arXiv:1802.08760},
  year={2018}
}