Sparse Spectral Bayesian Permanental Process with Generalized Kernel
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
Text
Sellier and Dellaportas. "Sparse Spectral Bayesian Permanental Process with Generalized Kernel." Artificial Intelligence and Statistics, 2023.Markdown
[Sellier and Dellaportas. "Sparse Spectral Bayesian Permanental Process with Generalized Kernel." Artificial Intelligence and Statistics, 2023.](https://mlanthology.org/aistats/2023/sellier2023aistats-sparse/)BibTeX
@inproceedings{sellier2023aistats-sparse,
title = {{Sparse Spectral Bayesian Permanental Process with Generalized Kernel}},
author = {Sellier, Jeremy and Dellaportas, Petros},
booktitle = {Artificial Intelligence and Statistics},
year = {2023},
pages = {2769-2791},
volume = {206},
url = {https://mlanthology.org/aistats/2023/sellier2023aistats-sparse/}
}