The DOI matches its Crossref record; 50 of the 52 references it cites were found in a registry or an index.
Probable networks and plausible predictions — a review of practical Bayesian methods for supervised neural networks
Abstract
Bayesian probability theory provides a unifying framework for data modelling. In this framework the overall aims are to find models that are well-matched to the data, and to use these models to make optimal predictions. Neural network learning is interpreted as an inference of the most probable parameters for the model, given the training data. The search in model space (i.e., the space of architectures, noise models, preprocessings, regularizers and weight decay constants) can then also be treated as an inference problem, in which we infer the relative probability of alternative models, given the data. This review describes practical techniques based on Gaussian approximations for implementation of these powerful methods for controlling, comparing and using adaptive networks.
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“This reflects the fact that this form of model selection implements automatic relevance determination (MacKay 1995), by virtue of optimising the model evidence with respect to model hyperparameters; in this instance, the shrinkage priors prescribed by an adjacency matrix.”
From Network discovery with DCM (2011) · cites this paper as MacKay 1995
Citations
Cites
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
Parallel Distributed Processing: Explorations in the Microstructure of Cognition: Foundations
Rumelhart, D. E., McClelland, J. L., & AU (1986) · doi:10.7551/mitpress/5236.001.0001 · Cited by 15,686
Jeffreys, H., Moran, P. A. P., & Chatfield, C. (1922) · Nature · doi:10.1038/109132a0 · Cited by 7,877
Statistical Decision Theory and Bayesian Analysis
Berger, J. O. (1985) · Springer Series in Statistics · doi:10.1007/978-1-4757-4286-2 · Cited by 7,722
Mackay, D. (1992) · Neural Computation · doi:10.1162/neco.1992.4.3.415 · Cited by 4,440
Bayesian Learning for Neural Networks
Neal, R. M. (1996) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-0745-0 · Cited by 4,276
Bayesian Inference in Statistical Analysis.
Kadane, J. B., Box, G. E. P., & Tiao, G. C. (1975) · Journal of the American Statistical Association · doi:10.2307/2285412 · Cited by 3,853
(1989) · Cited by 3,214
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
Stastical Decision Theory and Bayesian Analysis.
Ghosh, M., & Berger, J. O. (1988) · Journal of the American Statistical Association · doi:10.2307/2288950 · Cited by 2,901
Research works printed but not linked: 11
- Breiman L, 1992, Technical Report 367
- Buntine W, 1991, Complex Systems, 5, 603
- Guyon I, 1992, Advances in Neural Information Processing Systems 4, 471
- Hinton G E, 1986, Parallel Distributed Processing, 282
- Jeffreys H, 1939, Theory of Probability
- LeCun Y, 1990, Advances in Neural Information Processing Systems 2, 598
- MacKay D J C, 1994, ASHRAE Trans. Vol 100, part 2
- MacKay D J C, 1995, Nucl. Instrum. Methods Phys. Res. A
- Moody J E, 1992, Advances in Neural Information Processing Systems 4, 847
- Thodberg H H, 1993, Technical Report 1132 E
- Wolpert D H, 1993, Advances in Neural Information Processing Systems 5, 539
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Hyok, C. J. H. J., Choe, G.-C., Nam, C.-M., Choe, M.-C., & Kim, R.-H. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6960904
Kekovic, G., Bozovic, R. R., Ketin, S., Mikić, V., Ilić, M., & Vesin, B. (2026) · Computer Science and Information Systems · doi:10.2298/csis251101031k
Zhao, Y. S., He, X., Shi, K., Xiang, Z., & Jing, H. (2026) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2026.103993
Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning
Mei, J., Zheng, T., Cheng, L., Gong, S., & Huang, X. (2026) · Journal of Guidance Control and Dynamics · doi:10.2514/1.g009696 · Cited by 1
Physicochemical rule-embedded generative modeling for constrained peptide therapeutics
Wang, Y., Cao, D., Fu, X., Zeng, X., & Yao, X. (2026) · npj Drug Discovery. · doi:10.1038/s44386-026-00090-1
Bolt Load Retention Response and Creep of AS41 Mg-Alloy
Anopuo, O. (2010) · tub.dok (Hamburg University of Technology) · doi:10.15480/882.822
Kundu, C., Pande, B. P., Tamta, P., Dhami, H. S., Akbar, S., & Bajwa, I. S. (2014) · International Journal of Computational Linguistics Research
(2013) · Cited by 2,056
(2003) · Cited by 1,680
Weight Uncertainty in Neural Networks
Blundell, C., Cornebise, J., Kavukcuoglu, K., & Wierstra, D. (2015) · arXiv · doi:10.48550/arxiv.1505.05424 · Cited by 1,342
Bayesian Recurrent Neural Networks
Fortunato, M., Blundell, C., & Vinyals, O. (2017) · arXiv · doi:10.48550/arxiv.1704.02798 · Cited by 145
Being Bayesian about Categorical Probability
Joo, T., Chung, U., & Seo, M.-G. (2020) · arXiv · doi:10.48550/arxiv.2002.07965 · Cited by 37
Metadata
- Authors
- Mackay, D. J. C.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Mackay, David J C
- ORCID
- Mackay, David J C
- Venue
- Network Computation in Neural Systems
- Publisher
- Informa UK Limited
- Published
- 1995-01
- Volume
- 6
- Issue
- 3
- Pages
- 469-505
- ISSN
- 0954-898X (ISSN-L)
- 1361-6536
- OpenAlex
- W2139701068
- Cited by
- 915
- References
- 52
- Citations by year
- 2026: 14 · 2025: 33 · 2024: 28 · 2023: 40 · 2022: 50 · 2021: 39 · 2020: 58 · 2019: 40 · 2018: 36 · 2017: 27 · 2016: 17 · 2015: 36 · 2014: 24 · 2013: 29 · 2012: 39
- FWCI
- 13.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Network Computation in Neural Systems (publishedVersion)
- Cambridge University Engineering Department Publications Database (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- Bayesian neural networks, supervised learning, Gaussian approximation, model selection, model space search, parameter inference, adaptive networks, noise models, regularization, weight decay
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