The DOI matches its Crossref record; 102 of the 103 references it cites were found in a registry or an index.
Bayesian Methods for Neural Networks and Related Models
Abstract
Models such as feed-forward neural networks and certain other structures investigated in the computer science literature are not amenable to closed-form Bayesian analysis. The paper reviews the various approaches taken to overcome this difficulty, involving the use of Gaussian approximations, Markov chain Monte Carlo simulation routines and a class of non-Gaussian but “deterministic” approximations called variational approximations.
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“Bayesian Neural Networks (BNNs) [68,71,72] are stochastic ANNs trained using Bayesian inference.”
From Explainable AI in medical imaging: An overview for clinical practitioners – Beyond saliency-based XAI approaches (2023) · cites this paper as [72]
Citations
Cites
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
Neural networks for pattern recognition
Bishop, C. (1994) · Choice Reviews Online · doi:10.5860/choice.31-5500 · Cited by 18,537
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
Pattern Recognition and Neural Networks
Ripley, B. D. (1996) · Cambridge University Press eBooks · doi:10.1017/cbo9780511812651 · Cited by 6,500
Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination
Green, P. J. (1995) · Biometrika · doi:10.1093/biomet/82.4.711 · Cited by 5,941
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
Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91197-x · Cited by 3,920
An Introduction to Variational Methods for Graphical Models
Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999) · Machine Learning · doi:10.1023/a:1007665907178 · Cited by 3,791
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
Research works printed but not linked: 3
- Choudrey, R. and Roberts, S. J. (2001). Variational Bayesian independent component analysis with flexible sources. Technical Report PARG-01-03, Dept. Engineering Science, Univ. Oxford.
- MacKay, D. J. C. (1997). Ensemble learning for hidden Markov models. Technical report, Cavendish Lab., Univ. Cambridge.
- Ripley, B. D. (1995). Choosing network complexity. In Probabilistic Reasoning and Bayesian Belief Networks (A. Gammerman, ed.) 97--108. Waller, Henley-on-Thames, UK.
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Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Bioinformatics and Computational Biology Solutions Using R and Bioconductor
Gentleman, R. C., Carey, V. J., Huber, W. K., Irizarry, R. A., & Dudoit, S. (2005) · Statistics in the health sciences · doi:10.1007/0-387-29362-0 · Cited by 3,470
“A review of Bayesian inference methods with neural network models is given in Titterington (2004).”
MethodHands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users
Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., & Bennamoun, M. (2022) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2022.3155327 · Cited by 879
“Bayesian neural networks (BNNs) [8, 9, 10] are stochastic neural networks trained using a Bayesian approach.”
MethodConfronting the Challenge of Modeling Cloud and Precipitation Microphysics
Morrison, H., van Lier‐Walqui, M., Fridlind, A. M., Grabowski, W. W., Harrington, J. Y., Hoose, C., Korolev, A. V., Kumjian, M. R., Milbrandt, J. A., Pawłowska, H., et al. (2020) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2019ms001689 · Cited by 672
Jordan, M. I. (2004) · Statistical Science · doi:10.1214/088342304000000026 · Cited by 440
“…were formulated in terms of the minimization of a Kullback–Leibler (KL) divergence , and the space over which the optimization was performed was a set of " simplified " probability distributions , generally obtained by removing edges from a graphical model (see Titterington, 2004, this volume ).”
Metadata
- Authors
- Titterington, D. M.
- Corresponding author
- Titterington, D. M.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 2004-02-01
- Volume
- 19
- Issue
- 1
- Pages
- 128-139
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W2019449965
- Cited by
- 162
- References
- 103
- Citations by year
- 2026: 2 · 2025: 9 · 2024: 20 · 2023: 16 · 2022: 17 · 2021: 9 · 2020: 9 · 2019: 7 · 2018: 6 · 2017: 7 · 2016: 10 · 2015: 9 · 2014: 8 · 2013: 3 · 2012: 1
- FWCI
- 3.05
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- Bayesian neural networks, feedforward neural networks, Gaussian approximation, Markov chain Monte Carlo, variational approximation, computational intractability
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