@book{bishop2006pattern,
  title={Pattern recognition and machine learning},
  author={Bishop, Christopher M and Nasrabadi, Nasser M},
  volume={4},
  year={2006},
  pages={137--138},
  publisher={Springer}
}

@article{breiman2001random,
  title={Random forests},
  author={Breiman, Leo},
  journal={Machine learning},
  volume={45},
  number={1},
  pages={5--32},
  year={2001},
  publisher={Springer}
}

@article{freund1997decision,
  title={A decision-theoretic generalization of on-line learning and an application to boosting},
  author={Freund, Yoav and Schapire, Robert E},
  journal={Journal of computer and system sciences},
  volume={55},
  number={1},
  pages={119--139},
  year={1997},
  publisher={Elsevier}
}

@inproceedings{song2020denoising,
  title={Denoising Diffusion Implicit Models},
  author={Song, Jiaming and Meng, Chenlin and Ermon, Stefano},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

@article{houlsby2011bayesian,
  title={Bayesian active learning for classification and preference learning},
  author={Houlsby, Neil and Husz{\'a}r, Ferenc and Ghahramani, Zoubin and Lengyel, M{\'a}t{\'e}},
  journal={arXiv preprint arXiv:1112.5745},
  year={2011}
}

@article{lakshminarayanan2017simple,
  title={Simple and scalable predictive uncertainty estimation using deep ensembles},
  author={Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@inproceedings{chen2016xgboost,
  title={Xgboost: A scalable tree boosting system},
  author={Chen, Tianqi and Guestrin, Carlos},
  booktitle={Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining},
  pages={785--794},
  year={2016}
}

@article{hullermeier2021aleatoric,
  title={Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods},
  author={H{\"u}llermeier, Eyke and Waegeman, Willem},
  journal={Machine Learning},
  volume={110},
  number={3},
  pages={457--506},
  year={2021},
  publisher={Springer}
}

@article{settles2009active,
  title={Active learning literature survey},
  author={Settles, Burr},
  year={2009},
  publisher={University of Wisconsin-Madison Department of Computer Sciences},
  journal={Synthesis Lectures on Artificial Intelligence and Machine Learning}
}

@article{mackay1992information,
  title={Information-based objective functions for active data selection},
  author={MacKay, David JC},
  journal={Neural computation},
  volume={4},
  number={4},
  pages={590--604},
  year={1992},
  publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…}
}

@book{thomas2006elements,
  title={Elements of information theory},
  author={Cover, Thomas M and Thomas, Joy A},
  year={2006},
  pages={243--260},
  publisher={Wiley-Interscience}
}

@inproceedings{depeweg2018decomposition,
  title={Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning},
  author={Depeweg, Stefan and Hernandez-Lobato, Jose-Miguel and Doshi-Velez, Finale and Udluft, Steffen},
  booktitle={International Conference on Machine Learning},
  pages={1184--1193},
  year={2018},
  organization={PMLR}
}

@article{rubinstein2009deal,
  title={How to deal with the curse of dimensionality of likelihood ratios in Monte Carlo simulation},
  author={Rubinstein, Reuven Y and Glynn, Peter W},
  journal={Stochastic Models},
  volume={25},
  number={4},
  pages={547--568},
  year={2009},
  publisher={Taylor \& Francis}
}

@article{berry2023normalizing, 
  title={Normalizing Flow Ensembles for Rich Aleatoric and Epistemic Uncertainty Modeling}, 
  volume={37}, 
  number={6}, 
  journal={Proceedings of the AAAI Conference on Artificial Intelligence}, 
  author={Berry, Lucas and Meger, David}, 
  year={2023},
  pages={6806-6814} 
}

@article{berry2023escaping,
      title={Escaping the Sample Trap: Fast and Accurate Epistemic Uncertainty Estimation with Pairwise-Distance Estimators}, 
      author={Lucas Berry and David Meger},
      journal={arXiv preprint arXiv:2308.13498},
      year={2023}
}

@inproceedings{rombach2022high,
  title={High-resolution image synthesis with latent diffusion models},
  author={Rombach, Robin and Blattmann, Andreas and Lorenz, Dominik and Esser, Patrick and Ommer, Bj{\"o}rn},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={10684--10695},
  year={2022}
}

@article{sharma2021bayesian,
  title={Bayesian neural networks at scale: a performance analysis and pruning study},
  author={Sharma, Himanshu and Jennings, Elise},
  journal={The Journal of Supercomputing},
  volume={77},
  pages={3811--3839},
  year={2021},
  publisher={Springer}
}

@article{krizhevsky2009learning,
  title={Learning multiple layers of features from tiny images},
  author={Krizhevsky, Alex and Hinton, Geoffrey and others},
  year={2009},
  publisher={Toronto, ON, Canada}
}


@article{russakovsky2015imagenet,
  title={Imagenet large scale visual recognition challenge},
  author={Russakovsky, Olga and Deng, Jia and Su, Hao and Krause, Jonathan and Satheesh, Sanjeev and Ma, Sean and Huang, Zhiheng and Karpathy, Andrej and Khosla, Aditya and Bernstein, Michael and others},
  journal={International journal of computer vision},
  volume={115},
  pages={211--252},
  year={2015},
  publisher={Springer}
}


@article{kolchinsky2017estimating,
  title={Estimating mixture entropy with pairwise distances},
  author={Kolchinsky, Artemy and Tracey, Brendan D},
  journal={Entropy},
  volume={19},
  number={7},
  pages={361},
  year={2017},
  publisher={MDPI}
}

@article{nielsen2011chernoff,
  title={Chernoff information of exponential families},
  author={Nielsen, Frank},
  journal={arXiv preprint arXiv:1102.2684},
  year={2011}
}

@article{tabak2013family,
  title={A family of nonparametric density estimation algorithms},
  author={Tabak, Esteban G and Turner, Cristina V},
  journal={Communications on Pure and Applied Mathematics},
  volume={66},
  number={2},
  pages={145--164},
  year={2013},
  publisher={Wiley Online Library}
}

@article{tabak2010density,
  title={Density estimation by dual ascent of the log-likelihood},
  author={Tabak, Esteban G and Vanden-Eijnden, Eric},
  journal={Communications in Mathematical Sciences},
  volume={8},
  number={1},
  pages={217--233},
  year={2010},
  publisher={International Press of Boston}
}

@article{winkler2019learning,
  title={Learning likelihoods with conditional normalizing flows},
  author={Winkler, Christina and Worrall, Daniel and Hoogeboom, Emiel and Welling, Max},
  journal={arXiv preprint arXiv:1912.00042},
  year={2019}
}

@InProceedings{nf-rezende15,
  title = 	 {Variational Inference with Normalizing Flows},
  author = 	 {Rezende, Danilo and Mohamed, Shakir},
  booktitle = 	 {Proceedings of the 32nd International Conference on Machine Learning},
  pages = 	 {1530--1538},
  year = 	 {2015},
  volume = 	 {37},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Lille, France},
  month = 	 {07--09 Jul},
  pdf = 	 {http://proceedings.mlr.press/v37/rezende15.pdf},
}

@article{ardizzone2019guided,
  title={Guided image generation with conditional invertible neural networks},
  author={Ardizzone, Lynton and L{\"u}th, Carsten and Kruse, Jakob and Rother, Carsten and K{\"o}the, Ullrich},
  journal={arXiv preprint arXiv:1907.02392},
  year={2019}
}

@article{papamakarios2021normalizing,
  title={Normalizing Flows for Probabilistic Modeling and Inference.},
  author={Papamakarios, George and Nalisnick, Eric T and Rezende, Danilo Jimenez and Mohamed, Shakir and Lakshminarayanan, Balaji},
  journal={J. Mach. Learn. Res.},
  volume={22},
  number={57},
  pages={1--64},
  year={2021}
}

@article{postels2020hidden,
  title={The hidden uncertainty in a neural networks activations},
  author={Postels, Janis and Blum, Hermann and Str{\"u}mpler, Yannick and Cadena, Cesar and Siegwart, Roland and Van Gool, Luc and Tombari, Federico},
  journal={arXiv preprint arXiv:2012.03082},
  year={2020}
}

@article{choi2018waic,
  title={Waic, but why? generative ensembles for robust anomaly detection},
  author={Choi, Hyunsun and Jang, Eric and Alemi, Alexander A},
  journal={arXiv preprint arXiv:1810.01392},
  year={2018}
}

@article{brockman2016openai,
  title={Openai gym},
  author={Brockman, Greg and Cheung, Vicki and Pettersson, Ludwig and Schneider, Jonas and Schulman, John and Tang, Jie and Zaremba, Wojciech},
  journal={arXiv preprint arXiv:1606.01540},
  year={2016}
}

@misc{nflows,
  author       = {Conor Durkan and
                  Artur Bekasov and
                  Iain Murray and
                  George Papamakarios},
  title        = {{nflows}: normalizing flows in {PyTorch}},
  month        = {Nov},
  year         = {2020},
  publisher    = {Zenodo},
  version      = {v0.14},
  doi          = {10.5281/zenodo.4296287},
  howpublished="\url{https://doi.org/10.5281/zenodo.4296287}",
  note="Accessed: 2021-09-01"
}

@inproceedings{todorov2012mujoco,
  title={Mujoco: A physics engine for model-based control},
  author={Todorov, Emanuel and Erez, Tom and Tassa, Yuval},
  booktitle={2012 IEEE/RSJ international conference on intelligent robots and systems},
  pages={5026--5033},
  year={2012},
  organization={IEEE}
}

@inproceedings{csf_durkan,
 author = {Durkan, Conor and Bekasov, Artur and Murray, Iain and Papamakarios, George},
 title = {Cubic-Spline Flows},
 booktitle = {Workshop on Invertible Neural Networks and Normalizing Flows, International Conference on Machine Learning},
 year = {2019}
}

@inproceedings{gal2017deep,
  title={Deep bayesian active learning with image data},
  author={Gal, Yarin and Islam, Riashat and Ghahramani, Zoubin},
  booktitle={International Conference on Machine Learning},
  pages={1183--1192},
  year={2017},
  organization={PMLR}
}

@article{kirsch2019batchbald,
  title={Batchbald: Efficient and diverse batch acquisition for deep bayesian active learning},
  author={Kirsch, Andreas and Van Amersfoort, Joost and Gal, Yarin},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@article{kendall2017uncertainties,
  title={What uncertainties do we need in bayesian deep learning for computer vision?},
  author={Kendall, Alex and Gal, Yarin},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@inproceedings{chua2018deep,
 author = {Chua, Kurtland and Calandra, Roberto and McAllister, Rowan and Levine, Sergey},
 booktitle = {Advances in Neural Information Processing Systems},
 pages = {},
 title = {Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models},
 volume = {31},
 year = {2018}
}

@incollection{jebara2003bhattacharyya,
  title={Bhattacharyya and expected likelihood kernels},
  author={Jebara, Tony and Kondor, Risi},
  booktitle={Learning theory and kernel machines},
  pages={57--71},
  year={2003},
  publisher={Springer}
}

@article{jebara2004probability,
  title={Probability product kernels},
  author={Jebara, Tony and Kondor, Risi and Howard, Andrew},
  journal={The Journal of Machine Learning Research},
  volume={5},
  pages={819--844},
  year={2004},
  publisher={JMLR. org}
}


@article{kulak2021active,
  title={Active learning of Bayesian probabilistic movement primitives},
  author={Kulak, Thibaut and Girgin, Hakan and Odobez, Jean-Marc and Calinon, Sylvain},
  journal={IEEE Robotics and Automation Letters},
  volume={6},
  number={2},
  pages={2163--2170},
  year={2021},
  publisher={IEEE}
}


@article{kulak2021combining,
  title={Combining Social and Intrinsically-Motivated Learning for Multi-Task Robot Skill Acquisition},
  author={Kulak, Thibaut and Calinon, Sylvain},
  journal={IEEE Transactions on Cognitive and Developmental Systems},
  year={2021},
  publisher={IEEE}
}

@article{kurutach2018model,
  title={Model-ensemble trust-region policy optimization},
  author={Kurutach, Thanard and Clavera, Ignasi and Duan, Yan and Tamar, Aviv and Abbeel, Pieter},
  journal={arXiv preprint arXiv:1802.10592},
  year={2018}
}

@article{hora1996aleatory,
  title={Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management},
  author={Hora, Stephen C},
  journal={Reliability Engineering \& System Safety},
  volume={54},
  number={2-3},
  pages={217--223},
  year={1996},
  publisher={Elsevier}
}

@article{der2009aleatory,
  title={Aleatory or epistemic? Does it matter?},
  author={Der Kiureghian, Armen and Ditlevsen, Ove},
  journal={Structural safety},
  volume={31},
  number={2},
  pages={105--112},
  year={2009},
  publisher={Elsevier}
}

@article{mengersen1996rates,
  title={Rates of convergence of the Hastings and Metropolis algorithms},
  author={Mengersen, Kerrie L and Tweedie, Richard L},
  journal={The annals of Statistics},
  volume={24},
  number={1},
  pages={101--121},
  year={1996},
  publisher={Institute of Mathematical Statistics}
}

@inproceedings{gal2016dropout,
  title={Dropout as a bayesian approximation: Representing model uncertainty in deep learning},
  author={Gal, Yarin and Ghahramani, Zoubin},
  booktitle={international conference on machine learning},
  pages={1050--1059},
  year={2016},
  organization={PMLR}
}

@inproceedings{haarnoja2018soft,
  title={Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor},
  author={Haarnoja, Tuomas and Zhou, Aurick and Abbeel, Pieter and Levine, Sergey},
  booktitle={International conference on machine learning},
  pages={1861--1870},
  year={2018},
  organization={PMLR}
}


@book{rokach2010pattern,
  title={Pattern classification using ensemble methods},
  author={Rokach, Lior},
  volume={75},
  year={2010},
  publisher={World Scientific}
}

@article{haussler1997mutual,
  title={Mutual information, metric entropy and cumulative relative entropy risk},
  author={Haussler, David and Opper, Manfred},
  journal={The Annals of Statistics},
  volume={25},
  number={6},
  pages={2451--2492},
  year={1997},
  publisher={Institute of Mathematical Statistics}
}

@inproceedings{hershey2007approximating,
  title={Approximating the Kullback Leibler divergence between Gaussian mixture models},
  author={Hershey, John R and Olsen, Peder A},
  booktitle={2007 IEEE International Conference on Acoustics, Speech and Signal Processing-ICASSP'07},
  volume={4},
  pages={IV--317},
  year={2007},
  organization={IEEE}
}

@inproceedings{Paisley2010TwoUB,
  title={Two Useful Bounds for Variational Inference},
  author={John William Paisley},
  year={2010}
}

@inproceedings{huber2008entropy,
  title={On entropy approximation for Gaussian mixture random vectors},
  author={Huber, Marco F and Bailey, Tim and Durrant-Whyte, Hugh and Hanebeck, Uwe D},
  booktitle={2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems},
  pages={181--188},
  year={2008},
  organization={IEEE}
}

@article{osband2016deep,
  title={Deep exploration via bootstrapped DQN},
  author={Osband, Ian and Blundell, Charles and Pritzel, Alexander and Van Roy, Benjamin},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}

@article{harakeh2021estimating,
  title={Estimating and evaluating regression predictive uncertainty in deep object detectors},
  author={Harakeh, Ali and Waslander, Steven L},
  journal={arXiv preprint arXiv:2101.05036},
  year={2021}
}

@article{kingma2018glow,
  title={Glow: Generative flow with invertible 1x1 convolutions},
  author={Kingma, Durk P and Dhariwal, Prafulla},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}

@inproceedings{van2020uncertainty,
  title={Uncertainty estimation using a single deep deterministic neural network},
  author={Van Amersfoort, Joost and Smith, Lewis and Teh, Yee Whye and Gal, Yarin},
  booktitle={International conference on machine learning},
  pages={9690--9700},
  year={2020},
  organization={PMLR}
}

@article{charpentier2020posterior,
  title={Posterior network: Uncertainty estimation without ood samples via density-based pseudo-counts},
  author={Charpentier, Bertrand and Z{\"u}gner, Daniel and G{\"u}nnemann, Stephan},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={1356--1367},
  year={2020}
}

@article{charpentier2021natural,
  title={Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions},
  author={Charpentier, Bertrand and Borchert, Oliver and Z{\"u}gner, Daniel and Geisler, Simon and G{\"u}nnemann, Stephan},
  journal={arXiv preprint arXiv:2105.04471},
  year={2021}
}

@article{saharia2022photorealistic,
  title={Photorealistic text-to-image diffusion models with deep language understanding},
  author={Saharia, Chitwan and Chan, William and Saxena, Saurabh and Li, Lala and Whang, Jay and Denton, Emily L and Ghasemipour, Kamyar and Gontijo Lopes, Raphael and Karagol Ayan, Burcu and Salimans, Tim and others},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={36479--36494},
  year={2022}
}

@inproceedings{sohl2015deep,
  title={Deep unsupervised learning using nonequilibrium thermodynamics},
  author={Sohl-Dickstein, Jascha and Weiss, Eric and Maheswaranathan, Niru and Ganguli, Surya},
  booktitle={International Conference on Machine Learning},
  pages={2256--2265},
  year={2015},
  organization={PMLR}
}

@inproceedings{ramesh2021zero,
  title={Zero-shot text-to-image generation},
  author={Ramesh, Aditya and Pavlov, Mikhail and Goh, Gabriel and Gray, Scott and Voss, Chelsea and Radford, Alec and Chen, Mark and Sutskever, Ilya},
  booktitle={International Conference on Machine Learning},
  pages={8821--8831},
  year={2021},
  organization={PMLR}
}


@article{ho2020denoising,
  title={Denoising diffusion probabilistic models},
  author={Ho, Jonathan and Jain, Ajay and Abbeel, Pieter},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={6840--6851},
  year={2020}
}

@techreport{salay2018analysis,
  title={An Analysis of ISO 26262: Machine Learning and Safety in Automotive Software},
  author={Salay, Rick and Queiroz, Rodrigo and Czarnecki, Krzysztof},
  year={2018},
  institution={SAE Technical Paper}
}

@article{kingma2013auto,
  title={Auto-encoding variational bayes},
  author={Kingma, Diederik P and Welling, Max},
  journal={arXiv preprint arXiv:1312.6114},
  year={2013}
}

@article{hu2021lora,
  title={Lora: Low-rank adaptation of large language models},
  author={Hu, Edward J and Shen, Yelong and Wallis, Phillip and Allen-Zhu, Zeyuan and Li, Yuanzhi and Wang, Shean and Wang, Lu and Chen, Weizhu},
  journal={arXiv preprint arXiv:2106.09685},
  year={2021}
}

@inproceedings{postels2019sampling,
  title={Sampling-free epistemic uncertainty estimation using approximated variance propagation},
  author={Postels, Janis and Ferroni, Francesco and Coskun, Huseyin and Navab, Nassir and Tombari, Federico},
  booktitle={Proceedings of the IEEE/CVF International Conference on Computer Vision},
  pages={2931--2940},
  year={2019}
}

@article{balaji2022ediffi,
  title={ediffi: Text-to-image diffusion models with an ensemble of expert denoisers},
  author={Balaji, Yogesh and Nah, Seungjun and Huang, Xun and Vahdat, Arash and Song, Jiaming and Kreis, Karsten and Aittala, Miika and Aila, Timo and Laine, Samuli and Catanzaro, Bryan and others},
  journal={arXiv preprint arXiv:2211.01324},
  year={2022}
}

@incollection{fellbaum2010wordnet,
  title={WordNet},
  author={Fellbaum, Christiane},
  booktitle={Theory and applications of ontology: computer applications},
  pages={231--243},
  year={2010},
  publisher={Springer}
}

@article{dhariwal2021diffusion,
  title={Diffusion models beat gans on image synthesis},
  author={Dhariwal, Prafulla and Nichol, Alexander},
  journal={Advances in neural information processing systems},
  volume={34},
  pages={8780--8794},
  year={2021}
}

@article{kazerouni2022diffusion,
  title={Diffusion models for medical image analysis: A comprehensive survey},
  author={Kazerouni, Amirhossein and Aghdam, Ehsan Khodapanah and Heidari, Moein and Azad, Reza and Fayyaz, Mohsen and Hacihaliloglu, Ilker and Merhof, Dorit},
  journal={arXiv preprint arXiv:2211.07804},
  year={2022}
}

@article{guibas2017synthetic,
  title={Synthetic medical images from dual generative adversarial networks},
  author={Guibas, John T and Virdi, Tejpal S and Li, Peter S},
  journal={arXiv preprint arXiv:1709.01872},
  year={2017}
}


@article{hu2023gaia,
  title={Gaia-1: A generative world model for autonomous driving},
  author={Hu, Anthony and Russell, Lloyd and Yeo, Hudson and Murez, Zak and Fedoseev, George and Kendall, Alex and Shotton, Jamie and Corrado, Gianluca},
  journal={arXiv preprint arXiv:2309.17080},
  year={2023}
}

@article{brock2018large,
  title={Large scale GAN training for high fidelity natural image synthesis},
  author={Brock, Andrew and Donahue, Jeff and Simonyan, Karen},
  journal={arXiv preprint arXiv:1809.11096},
  year={2018}
}