Efficient Bayesian Inference for a Gaussian Process Density Model

Christian Donner, Manfred Opper
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:52-61, 2018.

Abstract

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P{ó}lya–Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model’s Gaussian process prior. The augmented posterior allows for efficient infer- ence by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and compar- isons with other density estimators are demon- strated on artificial and real datasets with up to several thousand data points.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-donner18a, title = {Efficient {B}ayesian Inference for a {G}aussian Process Density Model}, author = {Donner, Christian and Opper, Manfred}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {52--61}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/donner18a/donner18a.pdf}, url = {https://proceedings.mlr.press/r16/donner18a.html}, abstract = {We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P{ó}lya–Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model’s Gaussian process prior. The augmented posterior allows for efficient infer- ence by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and compar- isons with other density estimators are demon- strated on artificial and real datasets with up to several thousand data points.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Efficient Bayesian Inference for a Gaussian Process Density Model %A Christian Donner %A Manfred Opper %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-donner18a %I PMLR %P 52--61 %U https://proceedings.mlr.press/r16/donner18a.html %V R16 %X We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P{ó}lya–Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model’s Gaussian process prior. The augmented posterior allows for efficient infer- ence by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and compar- isons with other density estimators are demon- strated on artificial and real datasets with up to several thousand data points. %Z Reissued by PMLR on 04 October 2026.
APA
Donner, C. & Opper, M.. (2018). Efficient Bayesian Inference for a Gaussian Process Density Model. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:52-61 Available from https://proceedings.mlr.press/r16/donner18a.html. Reissued by PMLR on 04 October 2026.

Related Material