Bayesian Inference of Log Determinants

J Fitzsimons, K Cutajar, M Filippone, M Osborne, S Roberts
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:131-140, 2017.

Abstract

The log determinant of a kernel matrix ap- pears in a variety of machine learning prob- lems, ranging from determinantal point pro- cesses and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often in- tractable when the size of the kernel matrix ex- ceeds a few thousands. In the spirit of proba- bilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we com- bine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain proba- bilistic estimates for the log determinant and its associated uncertainty within a given com- putational budget. Beyond its novelty and the- oretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budget- constrained evidence.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-fitzsimons17a, title = {{B}ayesian Inference of Log Determinants}, author = {Fitzsimons, J and Cutajar, K and Filippone, M and Osborne, M and Roberts, S}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {131--140}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/fitzsimons17a/fitzsimons17a.pdf}, url = {https://proceedings.mlr.press/r15/fitzsimons17a.html}, abstract = {The log determinant of a kernel matrix ap- pears in a variety of machine learning prob- lems, ranging from determinantal point pro- cesses and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often in- tractable when the size of the kernel matrix ex- ceeds a few thousands. In the spirit of proba- bilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we com- bine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain proba- bilistic estimates for the log determinant and its associated uncertainty within a given com- putational budget. Beyond its novelty and the- oretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budget- constrained evidence.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Bayesian Inference of Log Determinants %A J Fitzsimons %A K Cutajar %A M Filippone %A M Osborne %A S Roberts %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-fitzsimons17a %I PMLR %P 131--140 %U https://proceedings.mlr.press/r15/fitzsimons17a.html %V R15 %X The log determinant of a kernel matrix ap- pears in a variety of machine learning prob- lems, ranging from determinantal point pro- cesses and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often in- tractable when the size of the kernel matrix ex- ceeds a few thousands. In the spirit of proba- bilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we com- bine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain proba- bilistic estimates for the log determinant and its associated uncertainty within a given com- putational budget. Beyond its novelty and the- oretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budget- constrained evidence. %Z Reissued by PMLR on 04 October 2026.
APA
Fitzsimons, J., Cutajar, K., Filippone, M., Osborne, M. & Roberts, S.. (2017). Bayesian Inference of Log Determinants. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:131-140 Available from https://proceedings.mlr.press/r15/fitzsimons17a.html. Reissued by PMLR on 04 October 2026.

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