Sparse Spectral Bayesian Permanental Process with Generalized Kernel

Jeremy Sellier, Petros Dellaportas
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:2769-2791, 2023.

Abstract

We introduce a novel scheme for Bayesian inference on permanental processes which models the Poisson intensity as the square of a Gaussian process. Combining generalized kernels and a Fourier features-based representation of the Gaussian process with a Laplace approximation to the posterior, we achieve a fast and efficient inference that does not require numerical integration over the input space, allows kernel design and scales linearly with the number of events. Our method builds and improves upon the state-of-theart Laplace Bayesian point process benchmark of Walder and Bishop (2017), demonstrated on both synthetic, real-world temporal and large spatial data sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-sellier23a, title = {Sparse Spectral Bayesian Permanental Process with Generalized Kernel}, author = {Sellier, Jeremy and Dellaportas, Petros}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {2769--2791}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/sellier23a/sellier23a.pdf}, url = {https://proceedings.mlr.press/v206/sellier23a.html}, abstract = {We introduce a novel scheme for Bayesian inference on permanental processes which models the Poisson intensity as the square of a Gaussian process. Combining generalized kernels and a Fourier features-based representation of the Gaussian process with a Laplace approximation to the posterior, we achieve a fast and efficient inference that does not require numerical integration over the input space, allows kernel design and scales linearly with the number of events. Our method builds and improves upon the state-of-theart Laplace Bayesian point process benchmark of Walder and Bishop (2017), demonstrated on both synthetic, real-world temporal and large spatial data sets.} }
Endnote
%0 Conference Paper %T Sparse Spectral Bayesian Permanental Process with Generalized Kernel %A Jeremy Sellier %A Petros Dellaportas %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-sellier23a %I PMLR %P 2769--2791 %U https://proceedings.mlr.press/v206/sellier23a.html %V 206 %X We introduce a novel scheme for Bayesian inference on permanental processes which models the Poisson intensity as the square of a Gaussian process. Combining generalized kernels and a Fourier features-based representation of the Gaussian process with a Laplace approximation to the posterior, we achieve a fast and efficient inference that does not require numerical integration over the input space, allows kernel design and scales linearly with the number of events. Our method builds and improves upon the state-of-theart Laplace Bayesian point process benchmark of Walder and Bishop (2017), demonstrated on both synthetic, real-world temporal and large spatial data sets.
APA
Sellier, J. & Dellaportas, P.. (2023). Sparse Spectral Bayesian Permanental Process with Generalized Kernel. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:2769-2791 Available from https://proceedings.mlr.press/v206/sellier23a.html.

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