Bayesian Learning for Neural Networks
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Methods that quantify uncertainty can be broadly classified into Bayesian approaches and Frequentist approaches.
“These methods can be broadly classified into two categories: Bayesian approaches [40,90,106] and Frequentist, approaches [14,70,113]”
From Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty (2021) · cites this paper as [90]
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“Such a covariance function implements automatic relevance automatic relevance determination determination (ARD) [Neal, 1996], since the inverse of the length-scale determines how relevant an input is: if the length-scale has a very large value, the 1This contrasts the use of the word in the SVM literature, where “trai…”
InfluentialDropout as a bayesian approximation: Representing model uncertainty in deep learning
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“n deep reinforcement learning [14]. 2Related Research It has long been known that infinitely wide (single hidden layer) MLPs with distributions placed over their weights converge to Gaussian processes [15, 16]. This known relation is through a limit argument that does not allow the transfer of properties from the Gauss…”
BackgroundBayesian calibration of computer models
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“In this regard, Monte Carlo (MC) [28] is an effective method.”
BackgroundMethodAn introduction to MCMC for machine learning.
Andrieu, C., de Freitas, N., Doucet, A., & Jordan, M. I. (2003) · Machine Learning · doi:10.1023/a:1020281327116 · Cited by 2,451 · see citing works
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Self-citationProbabilistic machine learning and artificial intelligence
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Riemann manifold langevin and hamiltonian monte carlo methods
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Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error
Faber, F. A., Hutchison, L., Huang, B., Gilmer, J., Schoenholz, S. S., Dahl, G. E., Vinyals, O., Kearnes, S., Riley, P. F., & von Lilienfeld, O. A. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00577 · Cited by 651 · see citing works
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Multiple sparse priors for the M/EEG inverse problem.
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Learning and selective attention
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Leveraging uncertainty information from deep neural networks for disease detection
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Bayesian approach for neural networks—review and case studies
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A review of deep learning applications for genomic selection
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“puts of large dimensions, since to efficiently learn the pattern of the data, more hidden layers and neurons need to be taken into account in the DL models; however, there is evidence that these problems can be solved under a Bayesian approach and some research is going in this direction to implement DL models under a…”
A small number of abnormal brain connections predicts adult autism spectrum disorder
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Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty
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“The work by [77] on Bayesian learning for neural networks also showed how domain-knowledge could help build a prior probability distribution over neural network parameters.”
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Leveraging Uncertainty in Machine Learning Accelerates Biological Discovery and Design
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“We train an MLP regressor with the same architecture described above (two hidden layers with 200 neurons per layer and ReLU non linearities) but with a unit-variance Gaussian prior on each weight and bias entry (Neal, 2012).”
BackgroundMethodInfluentialLearning for Personalized Medicine: A Comprehensive Review From a Deep Learning Perspective
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Deep Kernel for Genomic and Near Infrared Predictions in Multi-environment Breeding Trials
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Predictive automatic relevance determination by expectation propagation
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- Authors
- Neal, R. M.
- Affiliations
- University of Toronto (CA)
- Corresponding author
- Neal, Radford M.
- Venue
- Lecture Notes in Statistics
- Publisher
- Springer New York
- Published
- 1996
- ISSN
- 0930-0325 (ISSN-L)
- OpenAlex
- W1567512734
- Cited by
- 4,276
- References
- 0
- Citations by year
- 2026: 98 · 2025: 219 · 2024: 241 · 2023: 264 · 2022: 303 · 2021: 388 · 2020: 349 · 2019: 279 · 2018: 181 · 2017: 132 · 2016: 101 · 2015: 111 · 2014: 115 · 2013: 118 · 2012: 136
- FWCI
- 18.82
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Lecture notes in statistics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- Bayesian neural networks, overfitting, Markov chain Monte Carlo, limited training data, regression analysis, classification, Bayesian inference
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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.
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