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Hands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users
Open accessAbstract
Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides deep learning practitioners with an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian neural networks,i.e., stochastic artificial neural networks trained using Bayesian methods.
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“BNNs can be designed in different ways regarding the selection of stochastic components, distribution approximation, and inference approaches [74].”
From Explainable AI in medical imaging: An overview for clinical practitioners – Beyond saliency-based XAI approaches (2023) · cites this paper as [74]
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Cites
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
Gradient-based learning applied to document recognition
Lecun, Y., Bottou, L., Bengio, Y., & Haffner, P. (1998) · Proceedings of the IEEE · doi:10.1109/5.726791 · Cited by 58,805
A Mathematical Theory of Communication
Shannon, C. E. (1948) · The MIT Press eBooks · doi:10.1002/j.1538-7305.1948.tb00917.x · Cited by 50,387
(2014) · Cited by 33,419
Pan, S. J., & Yang, Q. (2010) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2009.191 · Cited by 23,387
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
Breiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
Distilling the Knowledge in a Neural Network
Hinton, G., Vinyals, O., & Dean, J. (2015) · arXiv · doi:10.48550/arxiv.1503.02531 · Cited by 14,204
Layer NormalizationPreprint
Ba, J., Kiros, J., & Hinton, G. E. (2016) · arXiv.org · doi:10.48550/arxiv.1607.06450 · Cited by 13,762
(2012) · Cited by 9,062
Intriguing properties of neural networks
Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., & Fergus, R. (2013) · arXiv · doi:10.48550/arxiv.1312.6199 · Cited by 8,143
Stan : A Probabilistic Programming Language
Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A. (2017) · Journal of Statistical Software · doi:10.18637/jss.v076.i01 · Cited by 7,754 · cited 1×
“The documentation of the probabilistic programming language Stan [49] provides examples on how to choose σ knowing the expected scale of the considered parameters [50].”
BackgroundDropout as a bayesian approximation: Representing model uncertainty in deep learning
Gal, Y., & Ghahramani, Z. (2015) · arXiv · doi:10.48550/arxiv.1506.02142 · Cited by 6,471
Strictly Proper Scoring Rules, Prediction, and Estimation
Gneiting, T., & Raftery, A. E. (2007) · Journal of the American Statistical Association · doi:10.1198/016214506000001437 · Cited by 5,793
Variational Inference: A Review for Statisticians
Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1285773 · Cited by 4,498
Understanding the Metropolis-Hastings Algorithm
Chib, S., & Greenberg, E. (1995) · The American Statistician · doi:10.1080/00031305.1995.10476177 · Cited by 4,212
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,929
Multi-column deep neural networks for image classification
Ciresan, D. C., Meier, U., & Schmidhuber, J. (2012) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2012.6248110 · Cited by 3,880
Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2016) · arXiv · doi:10.48550/arxiv.1612.01474 · Cited by 3,666
(2006) · Cited by 3,624
On calibration of modern neural networks
Guo, C., Pleiss, G., Sun, Y., & Weinberger, K. Q. (2017) · arXiv · doi:10.48550/arxiv.1706.04599 · Cited by 3,435
What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?
Kendall, A., & Gal, Y. (2017) · arXiv · doi:10.48550/arxiv.1703.04977 · Cited by 3,088
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte CarloPreprint
Homan, M. D., & Gelman, A. (2014) · arXiv (Cornell University) · Cited by 3,078
A practical Bayesian framework for backpropagation networks
MacKay, D. J. C. (1992) · Neural Computation · doi:10.1162/neco.1992.4.3.448 · Cited by 2,917
FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence
Sohn, K., Berthelot, D., Li, C.-L., Zhang, Z., Carlini, N., Cubuk, E. D., Kurakin, A., Zhang, H., & Raffel, C. (2020) · arXiv · doi:10.48550/arxiv.2001.07685 · Cited by 2,892
Understanding deep learning requires rethinking generalization
Zhang, C., Bengio, S., Hardt, M., Recht, B., & Vinyals, O. (2016) · arXiv · doi:10.48550/arxiv.1611.03530 · Cited by 2,838
The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte CarloPreprint
Hoffman, M. D., & Gelman, A. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1111.4246 · Cited by 2,815
Casella, G., & George, E. I. (1992) · The American Statistician · doi:10.1080/00031305.1992.10475878 · Cited by 2,728
An Introduction to Variational Autoencoders
Kingma, D. P., & Welling, M. (2019) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000056 · Cited by 2,609
MCMC Using Hamiltonian Dynamics
Neal, R. M. (2011) · Handbook of Markov Chain Monte Carlo · doi:10.1201/b10905-6 · Cited by 2,574
Ensemble Methods: Foundations and Algorithms
Zhou, Z.-H. (2012) · doi:10.1201/b12207 · Cited by 2,534
Aleatory or epistemic? Does it matter?
Kiureghian, A. D., & Ditlevsen, O. (2009) · Structural Safety · doi:10.1016/j.strusafe.2008.06.020 · Cited by 2,454
Understanding deep learning (still) requires rethinking generalization
Zhang, C., Bengio, S., Hardt, M., Recht, B., & Vinyals, O. (2021) · Communications of the ACM · doi:10.1145/3446776 · Cited by 2,400
Variational Inference: A Review for Statisticians
Blei, D. M., Kucukelbir, A., & McAuliffe, J. (2023) · Figshare · doi:10.6084/m9.figshare.5203696.v2 · Cited by 2,088
Ensemble Methods: Foundations and Algorithms
Zhou, Z. (2012) · Cited by 2,051
Variational Inference: A Review for Statisticians
Blei, D. M., Kucukelbir, A., & McAuliffe, J. (2017) · Figshare · doi:10.6084/m9.figshare.5203696 · Cited by 2,048
Self-Supervised Visual Feature Learning With Deep Neural Networks: A Survey
Jing, L., & Tian, Y. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.2992393 · Cited by 2,036
Stochastic Variational InferencePreprint
Hoffman, M. D., Blei, D. M., Wang, C., & Paisley, J. W. (2012) · arXiv (Cornell University) · doi:10.5555/2567709.2502622 · Cited by 1,991
A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks
Hendrycks, D., & Gimpel, K. (2016) · arXiv · doi:10.48550/arxiv.1610.02136 · Cited by 1,968
Classification in the Presence of Label Noise: A Survey
Frenay, B., & Verleysen, M. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2292894 · Cited by 1,777
The Lack of A Priori Distinctions Between Learning Algorithms
Wolpert, D. H. (1996) · Neural Computation · doi:10.1162/neco.1996.8.7.1341 · Cited by 1,652
Pre-trained models for natural language processing: A survey
Qiu, X., Sun, T., Xu, Y., Shao, Y., Dai, N., & Huang, X. (2020) · Science China Technological Sciences · doi:10.1007/s11431-020-1647-3 · Cited by 1,591
Deep Learning Applications in Medical Image Analysis
Ker, J., Wang, L., Rao, J. P., & Lim, C. C. T. (2017) · IEEE Access · doi:10.1109/access.2017.2788044 · Cited by 1,574
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
Hastings, W. K. (1970) · Biometrika · doi:10.2307/2334940 · Cited by 1,526
Pouyanfar, S., Sadiq, S. B., Yan, Y., Tian, H., Tao, Y., Reyes, M. P., Shyu, M., Chen, S., & Iyengar, S. S. (2018) · ACM Computing Surveys · doi:10.1145/3234150 · Cited by 1,510
Bayesian Learning via Stochastic Gradient Langevin Dynamics
Welling, M., & Teh, Y. W. (2012) · Cited by 1,500
Morgan, M. C. (2025) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.17575540 · Cited by 1,375
Weight Uncertainty in Neural Network
Blundell, C., Cornebise, J., Kavukcuoglu, K., & Wierstra, D. (2015) · International Conference on Machine Learning · Cited by 1,335
Huber, M. (2011) · Chapman & Hall/CRC eBooks · doi:10.1201/b10905-10 · Cited by 1,269
Understanding the Metropolis-Hastings Algorithm
Chib, S., & Greenberg, E. (1995) · The American Statistician · doi:10.2307/2684568 · Cited by 1,245
GALTON, F. (1907) · Nature · doi:10.1038/075450a0 · Cited by 1,080
Practical Variational Inference for Neural Networks
Graves, A. (2011) · Cited by 1,079
Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift
Ovadia, Y., Fertig, E., Ren, J., Nado, Z., Sculley, D., Nowozin, S., Dillon, J. V., Lakshminarayanan, B., & Snoek, J. (2019) · arXiv · doi:10.48550/arxiv.1906.02530 · Cited by 989
Deep Bayesian Active Learning with Image Data
Gal, Y., Islam, R., & Ghahramani, Z. (2017) · arXiv · doi:10.48550/arxiv.1703.02910 · Cited by 900
Meta-Learning in Neural Networks: A Survey
Hospedales, T. M., Antoniou, A., Micaelli, P., & Storkey, A. J. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3079209 · Cited by 886
Casella, G., & George, E. I. (1992) · The American Statistician · doi:10.2307/2685208 · Cited by 864
Pyro: Deep Universal Probabilistic ProgrammingPreprint
Bingham, E., Chen, J. P., Jankowiak, M., Obermeyer, F. H., Pradhan, N., Karaletsos, T., Singh, R., Szerlip, P., Horsfall, P., & Goodman, N. D. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.09538 · Cited by 853
On Loss Functions for Deep Neural Networks in Classification
Janocha, K., & Czarnecki, W. M. (2017) · Schedae Informaticae · doi:10.4467/20838476si.16.004.6185 · Cited by 794
Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational InferencePreprint
Gal, Y., & Ghahramani, Z. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.02158 · Cited by 777
S4L: Self-Supervised Semi-Supervised Learning
Zhai, X., Oliver, A., Kolesnikov, A., & Beyer, L. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00156 · Cited by 768
Natarajan, N., Dhillon, I. S., Ravikumar, P., & Tewari, A. (2013) · Cited by 740
Computational Intelligence and Financial Markets: A Survey and Future Directions
Cavalcante, R. C., Brasileiro, R. C., Souza, V. L. F., Nobrega, J. P., & Oliveira, A. L. I. (2016) · Expert Systems with Applications · doi:10.1016/j.eswa.2016.02.006 · Cited by 610
Probabilistic Backpropagation for Scalable Learning of Bayesian Neural NetworksPreprint
Hernández-Lobato, J. M., & Adams, R. P. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1502.05336 · Cited by 563
Operations for Learning with Graphical Models
Buntine, W. (1994) · Journal of Artificial Intelligence Research · doi:10.1613/jair.62 · Cited by 531
Self-citationBayesian Neural Networks for Internet Traffic Classification
Auld, T., Moore, A. W., & Gull, S. F. (2007) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2006.883010 · Cited by 494
Stochastic Gradient Descent as Approximate Bayesian InferencePreprint
Mandt, S., Hoffman, M. D., & Blei, D. M. (2017) · arXiv (Cornell University) · doi:10.5555/3122009.3208015 · Cited by 480
Image-Based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era
Han, X.-F., Laga, H., & Bennamoun, M. (2019) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2019.2954885 · Cited by 459
Self-citationAccurate Uncertainties for Deep Learning Using Calibrated RegressionPreprint
Kuleshov, V., Fenner, N., & Ermon, S. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1807.00263 · Cited by 455
A Simple Baseline for Bayesian Uncertainty in Deep Learning
Maddox, W., Garipov, T., Izmailov, P., Vetrov, D., & Wilson, A. G. (2019) · arXiv · doi:10.48550/arxiv.1902.02476 · Cited by 429
Bayesian Deep Learning and a Probabilistic Perspective of GeneralizationPreprint
Wilson, A. G., & Izmailov, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.08791 · Cited by 428
Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU NetworksPreprint
Kristiadi, A., Hein, M., & Hennig, P. (2020) · International Conference on Machine Learning · doi:10.48550/arxiv.2002.10118 · Cited by 393
Bayesian approach for neural networks—review and case studies
Lampinen, J., & Vehtari, A. (2001) · Neural Networks · doi:10.1016/s0893-6080(00)00098-8 · Cited by 392
Recasting Gradient-Based Meta-Learning as Hierarchical BayesPreprint
Grant, E., Finn, C., Levine, S., Darrell, T., & Griffiths, T. L. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1801.08930 · Cited by 388
A Survey on Deep Learning Techniques for Stereo-Based Depth Estimation
Laga, H., Jospin, L. V., Boussaïd, F., & Bennamoun, M. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.3032602 · Cited by 340
Self-citationQi, G.-J., & Luo, J. (2022) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.3031898 · Cited by 315
Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-BatchesPreprint
Wen, Y., Vicol, P. A., Ba, J. L., Tran, D., & Grosse, R. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1803.04386 · Cited by 295
Towards Bayesian Deep Learning: A Framework and Some Existing Methods
Wang, H., & Yeung, D. (2016) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2016.2606428 · Cited by 285
Propagation Algorithms for Variational Bayesian Learning
Ghahramani, Z., & Beal, M. J. (2000) · Cited by 283
Bayesian dark knowledgePreprint
Balan, A. K., Rathod, V., Murphy, K. P., & Welling, M. (2015) · Neural Information Processing Systems · doi:10.48550/arxiv.1506.04416 · Cited by 276
Neural Network-Based Uncertainty Quantification: A Survey of Methodologies and Applications
Kabir, H. M. D., Khosravi, A., Hosen, M. A., & Nahavandi, S. (2018) · IEEE Access · doi:10.1109/access.2018.2836917 · Cited by 271
A Survey on Bayesian Deep Learning
Wang, H., & Yeung, D.-Y. (2021) · ACM Computing Surveys · doi:10.1145/3409383 · Cited by 247
Chapelle, O., Weston, J., Bottou, L., & Vapnik, V. N. (2000) · Cited by 244
Uncertainty in Neural Networks: Approximately Bayesian EnsemblingPreprint
Pearce, T., Leibfried, F., Brintrup, A., et al. (2018) · International Conference on Artificial Intelligence and Statistics · doi:10.48550/arxiv.1810.05546 · Cited by 239
A baseline for detecting misclassified and out-of-distribution examples in neural networksPreprint
Hendrycks, D. (2025) · arXiv (Cornell University) · doi:10.57702/9gs720u1 · Cited by 236
Stochastic Gradient VB and the Variational Auto-EncoderPreprint
Kingma, D. P., & Welling, M. (2013) · arXiv (Cornell University) · Cited by 234
Measuring Calibration in Deep Learning
Nixon, J., Dusenberry, M., Jerfel, G., Nguyen, T., Liu, J., Zhang, L., & Tran, D. (2019) · arXiv · doi:10.48550/arxiv.1904.01685 · Cited by 209
Bayesian neural networks for flight trajectory prediction and safety assessment
Zhang, X., & Mahadevan, S. (2020) · Decision Support Systems · doi:10.1016/j.dss.2020.113246 · Cited by 204
Yu, S., Krishnapuram, B., Rosales, R., & Rao, R. B. (2011) · doi:10.5555/1953048.2078190 · Cited by 193
Deep learning for self-driving cars
Rao, Q., & Frtunikj, J. (2018) · doi:10.1145/3194085.3194087 · Cited by 192
(2018) · UCL Discovery (University College London) · Cited by 183
Online Structured Laplace Approximations For Overcoming Catastrophic ForgettingPreprint
Ritter, H., Botev, A., & Barber, D. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1805.07810 · Cited by 178
Unsupervised Data AugmentationPreprint
Xie, Q., Dai, Z., Hovy, E. H., Luong, M.-T., & Le, Q. V. (2019) · arXiv (Cornell University) · Cited by 166
Practical Deep Learning with Bayesian PrinciplesPreprint
Osawa, K., Swaroop, S., Jain, A., Eschenhagen, R., Turner, R. E., Yokota, R., & Khan, M. E. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.02506 · Cited by 165
What Are Bayesian Neural Network Posteriors Really Like?Preprint
Izmailov, P., Vikram, S., Hoffman, M. D., & Wilson, A. G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2104.14421 · Cited by 165
Bayesian Methods for Neural Networks and Related Models
Titterington, D. M. (2004) · Statistical Science · doi:10.1214/088342304000000099 · Cited by 162 · cited 1×
“Bayesian neural networks (BNNs) [8, 9, 10] are stochastic neural networks trained using a Bayesian approach.”
MethodBayesian neural networks: An introduction and survey
Goan, E., & Fookes, C. (2020) · QUT ePrints (Queensland University of Technology) · Cited by 162
Deep Probabilistic ProgrammingPreprint
Tran, D., Hoffman, M. D., Saurous, R. A., Brevdo, E., Murphy, K., & Blei, D. M. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1701.03757 · Cited by 155
Dropout Inference in Bayesian Neural Networks with Alpha-divergences
Li, Y., & Gal, Y. (2017) · Oxford University Research Archive (ORA) (University of Oxford) · doi:10.48550/arxiv.1703.02914 · Cited by 145
Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in AdamPreprint
Khan, M. E., Nielsen, D., Tangkaratt, V., Wu, L., Gal, Y., & Srivastava, A. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1806.04854 · Cited by 129
On Markov chain Monte Carlo methods for tall dataPreprint
Bardenet, R., Doucet, A., & Holmes, C. C. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1505.02827 · Cited by 123
Uncertainty in Neural Networks: Approximately Bayesian EnsemblingPreprint
Pearce, T., Leibfried, F., Brintrup, A. M., Zaki, M., & Neely, A. (2018) · arXiv (Cornell University) · doi:10.13140/rg.2.2.12913.43364 · Cited by 122
Deep Learning: A Bayesian Perspective
Polson, N. G., & Sokolov, V. (2017) · Bayesian Analysis · doi:10.1214/17-ba1082 · Cited by 120
How to become a Bayesian in eight easy steps: An annotated reading list
Etz, A. J., Gronau, Q. F., Dablander, F., Edelsbrunner, P. A., & Baribault, B. (2017) · Psychonomic Bulletin & Review · doi:10.3758/s13423-017-1317-5 · Cited by 120
A Bayesian Approach to On-line Learning
Opper, M. (1999) · Cambridge University Press eBooks · doi:10.1017/cbo9780511569920.017 · Cited by 107
Bayesian Generative Active Deep LearningPreprint
Tran, T. B., Do, T.-T., Reid, I. D., & Carneiro, G. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.11643 · Cited by 98
Estimating uncertainty of streamflow simulation using Bayesian neural networks
Zhang, X., Liang, F., Srinivasan, R., & Liew, M. W. V. (2009) · Water Resources Research · doi:10.1029/2008wr007030 · Cited by 95
Structural health monitoring of a cable-stayed bridge with Bayesian neural networks
Arangio, S., & Bontempi, F. (2014) · Structure and Infrastructure Engineering · doi:10.1080/15732479.2014.951867 · Cited by 92
Bateni, S. M., Jeng, D., & Melville, B. W. (2006) · Advances in Engineering Software · doi:10.1016/j.advengsoft.2006.08.004 · Cited by 88
Aminian, F., & Aminian, M. (2001) · Journal of Electronic Testing · doi:10.1023/a:1011141724916 · Cited by 72
An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval
Cobb, A. D., Himes, M. D., Soboczenski, F., Zorzan, S., O’Beirne, M. D., Baydin, A. G., Gal, Y., Domagal-Goldman, S. D., Arney, G., Angerhausen, D., et al. (2019) · The Astronomical Journal · doi:10.3847/1538-3881/ab2390 · Cited by 68
An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric RetrievalPreprint
Cobb, A. D., Himes, M. D., Soboczenski, F., Zorzan, S., O’Beirne, M. D., Güneş Baydin, A., Gal, Y., Domagal-Goldman, S. D., Arney, G., & Angerhausen, D. (2019) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 62
Minimal-uncertainty prediction of general drug-likeness based on Bayesian neural networks
Beker, W., Wołos, A., Szymkuć, S., & Grzybowski, B. A. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-0209-y · Cited by 59
PyMC3: Python probabilistic programming framework
Salvatier, J., Wieckiâ, T. V., & Fonnesbeck, C. (2016) · Astrophysics Source Code Library · Cited by 44
Naive semi-supervised deep learning using pseudo-label
Li, Z., Ko, B., & Choi, H. (2018) · Peer-to-Peer Networking and Applications · doi:10.1007/s12083-018-0702-9 · Cited by 43
Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Models
Khan, M. E., & Nielsen, D. (2018) · International Symposium on Information Theory and its Applications · doi:10.23919/isita.2018.8664326 · Cited by 41
Adversarial Distillation of Bayesian Neural Network PosteriorsPreprint
Wang, K.-C. J., Vicol, P. A., Lucas, J., Gu, L., Grosse, R., & Zemel, R. S. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1806.10317 · Cited by 39
Mitigating belief projection in explainable artificial intelligence via Bayesian teaching
Yang, S. C., Vong, W. K., Sojitra, R. B., Folke, T., & Shafto, P. (2021) · Scientific Reports · doi:10.1038/s41598-021-89267-4 · Cited by 37
On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty EstimationPreprint
Brosse, N., Riquelme, C., Martin, A. O., Gelly, S., & Moulines, É. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.08049 · Cited by 35
Prior choice affects ability of Bayesian neural networks to identify unknownsPreprint
Silvestro, D., & Andermann, T. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.04987 · Cited by 34
Compact approximations to Bayesian predictive distributions
Snelson, E., & Ghahramani, Z. (2005) · International Conference on Machine Learning · doi:10.1145/1102351.1102457 · Cited by 28
Depeweg, S., Hernández-Lobato, J. M., Doshi-Velez, F., & Udluft, S. (2017) · arXiv.org · doi:10.48550/arxiv.1710.07283 · Cited by 27
On the Validity of Bayesian Neural Networks for Uncertainty EstimationPreprint
Mitros, J., & Namee, B. M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.01530 · Cited by 27
Qi, G.-J., & Luo, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.11260 · Cited by 27
The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learning
Zeng, J., Lesnikowski, A., & Alvarez, J. M. (2018) · arXiv · doi:10.48550/arxiv.1811.12535 · Cited by 26
Variational Bayesian dropout: pitfalls and fixesPreprint
Hron, J., Matthews, A., & Ghahramani, Z. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1807.01969 · Cited by 23
Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate ShiftPreprint
Chan, A. J., Alaa, A. M., Qian, Z., & van der Schaar, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.14988 · Cited by 22
Bayesian Inference over the Stiefel Manifold via the Givens Representation
Pourzanjani, A., Jiang, R., Mitchell, B., Atzberger, P. J., & Petzold, L. R. (2020) · Bayesian Analysis · doi:10.1214/20-ba1202 · Cited by 22
Towards calibrated and scalable uncertainty representations for neural networksPreprint
Seedat, N., & Kanan, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.00104 · Cited by 21
Why distillation helps: a statistical perspectivePreprint
Menon, A. K., Rawat, A. S., Reddi, S. J., Kim, S., & Kumar, S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.10419 · Cited by 14
MultiMix: A Robust Data Augmentation Strategy for Cross-Lingual NLP.Preprint
Bari, M., Mohiuddin, M. T., & Joty, S. (2020) · arXiv (Cornell University) · Cited by 11
Semi-supervised Online Bayesian Network Learner for Handwritten Characters Recognition
Kunwar, R., Pal, U., & Blumenstein, M. (2014) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2014.535 · Cited by 9
Bayesian Inference over the Stiefel Manifold via the Givens RepresentationPreprint
Pourzanjani, A., Jiang, R., Mitchell, B., et al. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1710.09443 · Cited by 7
On Information RegularizationPreprint
Corduneanu, A., & Jaakkola, T. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1212.2466 · Cited by 1
Research works printed but not linked: 5
- depeweg, 0, Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning, Proc 35th Int Conf Mach Learn, 80, 1184
- robert, 2007, The Bayesian Choice From Decision-Theoretic Foundations to Computational Implementation
- gelman, 2020, Prior choice recommendations
- lee, 0, Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks, Proc Workshop Challenges Representation Learn ICML, 3
- goodfellow, 2016, Deep Learning
Cited by
Sorted by citations
A review of uncertainty quantification in deep learning: Techniques, applications and challenges
Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., Fieguth, P., Cao, X., Khosravi, A., Acharya, U. R., et al. (2021) · Information Fusion · doi:10.1016/j.inffus.2021.05.008 · Cited by 3,111
“BNNs/BDL are robust to overfitting problem and can be trained on both small and big datasets [27].”
MethodUncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
Psaros, A. F., Meng, X., Zou, Z., Guo, L., & Karniadakis, G. E. (2023) · Journal of Computational Physics · doi:10.1016/j.jcp.2022.111902 · Cited by 464
Improving the open cluster census
Hunt, E. L., & Reffert, S. (2023) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202346285 · Cited by 355
Cheng, S. L., Quilodrán-Casas, C., Ouala, S., Farchi, A., Liu, C., Tandeo, P., Fablet, R., Lucor, D., Iooss, B., Brajard, J., et al. (2023) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2023.123537 · Cited by 351
Ma, Y., Zhang, Z., Kang, Y., & Özdoğan, M. (2021) · Remote Sensing of Environment · doi:10.1016/j.rse.2021.112408 · Cited by 304
Metadata
- Authors
- Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., & Bennamoun, M.
- Affiliations
- The University of Western Australia (AU)
- Murdoch University (AU)
- University of Western Australia, Australia
- Venue
- IEEE Computational Intelligence Magazine
- Published
- 2022-05
- Volume
- 17
- Issue
- 2
- Pages
- 29-48
- ISSN
- 1556-603X (ISSN-L)
- 1556-6048
- OpenAlex
- W3043426275
- Cited by
- 879
- References
- 141
- Citations by year
- 2026: 171 · 2025: 217 · 2024: 192 · 2023: 170 · 2022: 80
- FWCI
- 54.00
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Computational Intelligence Magazine (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- UWA Profiles and Research Repository (UWA) (submittedVersion, other-oa)
- Murdoch University Research Portal (submittedVersion)
- arXiv (Cornell University)
- Funders
- Australian Research Council (DP150100294, DP150104251, DP210101682)
- Air Force Research Laboratory (FA8750-19-2-0501)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Adversarial Robustness in Machine Learning
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- Bayesian neural networks, uncertainty quantification, forecast uncertainty, black-box models, Bayesian inference, deep learning, stochastic neural networks
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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