On Hyper-Parameter Estimation In Empirical Bayes: A Revisit of The MacKay Algorithm

Chune Li Beihang University, Yongyi Mao, Richong Zhang Beihang University, Jinpeng Huai Beihang University
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:742-751, 2016.

Abstract

An iterative procedure introduced in MacKay’s evidence framework is often used for estimating the hyper-parameter in empirical Bayes. Despite its effectiveness, the procedure has stayed primarily as a heuristic to date. This paper formally investigates the mathematical nature of this procedure and justifies it as a well-principled algorithm framework. This framework, which we call the MacKay algorithm, is shown to be closely related to the EM algorithm under certain Gaussian assumption.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-university16p, title = {On Hyper-Parameter Estimation In Empirical {B}ayes: A Revisit of The MacKay Algorithm}, author = {University, Chune Li Beihang and Mao, Yongyi and University, Richong Zhang Beihang and University, Jinpeng Huai Beihang}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {742--751}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/university16p/university16p.pdf}, url = {https://proceedings.mlr.press/r14/university16p.html}, abstract = {An iterative procedure introduced in MacKay’s evidence framework is often used for estimating the hyper-parameter in empirical Bayes. Despite its effectiveness, the procedure has stayed primarily as a heuristic to date. This paper formally investigates the mathematical nature of this procedure and justifies it as a well-principled algorithm framework. This framework, which we call the MacKay algorithm, is shown to be closely related to the EM algorithm under certain Gaussian assumption.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On Hyper-Parameter Estimation In Empirical Bayes: A Revisit of The MacKay Algorithm %A Chune Li Beihang University %A Yongyi Mao %A Richong Zhang Beihang University %A Jinpeng Huai Beihang University %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-university16p %I PMLR %P 742--751 %U https://proceedings.mlr.press/r14/university16p.html %V R14 %X An iterative procedure introduced in MacKay’s evidence framework is often used for estimating the hyper-parameter in empirical Bayes. Despite its effectiveness, the procedure has stayed primarily as a heuristic to date. This paper formally investigates the mathematical nature of this procedure and justifies it as a well-principled algorithm framework. This framework, which we call the MacKay algorithm, is shown to be closely related to the EM algorithm under certain Gaussian assumption. %Z Reissued by PMLR on 04 October 2026.
APA
University, C.L.B., Mao, Y., University, R.Z.B. & University, J.H.B.. (2016). On Hyper-Parameter Estimation In Empirical Bayes: A Revisit of The MacKay Algorithm. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:742-751 Available from https://proceedings.mlr.press/r14/university16p.html. Reissued by PMLR on 04 October 2026.

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