Information Theory, Inference, and Learning Algorithms
Abstract
Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
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On a Bayesian reading, expected information gain is exactly the same quantity that underwrites the principles of optimal Bayesian design.
“On a Bayesian reading, the expected information gain is exactly the same quantity that underwrites the principles of optimal Bayesian design [134, 76, 163].”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [76]
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Mones, L., Bernstein, N., & Csányi, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00553 · Cited by 91 · see citing works
LeDuc, R. D., Fellers, R. T., Early, B. P., Greer, J. B., Thomas, P. M., & Kelleher, N. L. (2014) · Journal of Proteome Research · doi:10.1021/pr401277r · Cited by 85 · see citing works
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El-Sappagh, S., Alonso, J. M., Ali, F., Ali, A., Jang, J.-H., & Kwak, K.-S. (2018) · IEEE Access · doi:10.1109/access.2018.2852004 · Cited by 79 · see citing works
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Ullman, S., Harari, D., & Dorfman, N. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1207690109 · Cited by 77 · see citing works
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Kopp, B., Seer, C., Lange, F., Kluytmans, A., Kolossa, A., Fingscheidt, T., & Hoijtink, H. (2016) · Cognitive, Affective, & Behavioral Neuroscience · doi:10.3758/s13415-016-0442-3 · Cited by 60 · see citing works
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Gartner, D., Kolisch, R., Neill, D. B., & Padman, R. (2015) · INFORMS Journal on Computing · doi:10.1287/ijoc.2015.0655 · Cited by 58 · see citing works
Jiang, H., Dai, X., Gao, D. W., Zhang, J. J., Zhang, Y., & Muljadi, E. (2016) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2016.2552229 · Cited by 56 · see citing works
Hilbert, M., Ahmed, S., Cho, J., Liu, B., & Luu, J. (2018) · Communication Methods and Measures · doi:10.1080/19312458.2018.1479843 · Cited by 49 · see citing works
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Bennett, M. T. (2022) · Lecture notes in computer science · doi:10.1007/978-3-030-93758-4_5 · Cited by 31 · see citing works
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Yu, X., Xiao, B., Ni, W., & Wang, X. (2023) · IEEE Transactions on Communications · doi:10.1109/tcomm.2023.3283790 · Cited by 19 · see citing works
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Sykacek, P., Kreil, D. P., Meadows, L. A., Auburn, R. P., Fischer, B., Russell, S., & Micklem, G. (2011) · BMC Bioinformatics · doi:10.1186/1471-2105-12-73 · Cited by 13 · see citing works
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Anderson, P., Aranas, E., Assaf, Y., Behrendt, R., Black, R., Caballero, M., Cameron, P., Canakci, B., Chatzieleftheriou, A., Clarke, R., et al. (2025) · ACM Transactions on Storage · doi:10.1145/3708996 · Cited by 13 · see citing works
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Vehlow, C., Hasenauer, J., Kramer, A., Raue, A., Hug, S., Timmer, J., Radde, N., Theis, F. J., & Weiskopf, D. (2013) · BMC Bioinformatics · doi:10.1186/1471-2105-14-s19-s2 · Cited by 11 · see citing works
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Nekhaev, I., Zhuykov, I., Manukyants, S., & Maslennikov, A. (2020) · Advances in Intelligent Systems and Computing · doi:10.1007/978-3-030-63322-6_94 · Cited by 3 · see citing works
Tsanas, A. (2025) · World Forum on Internet of Things · doi:10.1109/wf-iot64238.2025.11270790
- Authors
- MacKay, D.
- Corresponding author
- Djc MacKay
- Venue
- Kybernetes
- Publisher
- Emerald
- Published
- 2004-08-01
- Volume
- 33
- Issue
- 7
- Pages
- 1217-1218
- ISSN
- 0368-492X (ISSN-L)
- OpenAlex
- W1607198972
- Cited by
- 4,937
- References
- 0
- Citations by year
- 2026: 1 · 2025: 163 · 2024: 204 · 2023: 340 · 2022: 267 · 2021: 297 · 2020: 334 · 2019: 273 · 2018: 313 · 2017: 243 · 2016: 205 · 2015: 234 · 2014: 266 · 2013: 217 · 2012: 237
- Type
- book review
- Language
- en
- Open access
- closed
- Locations
- Kybernetes (publishedVersion)
- International Linear Collider (submittedVersion)
- Cambridge University Engineering Department Publications Database (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Keywords
- information theory, statistical inference, learning algorithms, mathematical foundations of machine learning
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