Fast Bayesian Intensity Estimation for the Permanental Process

Christian J. Walder, Adrian N. Bishop
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3579-3588, 2017.

Abstract

The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-walder17a, title = {Fast {B}ayesian Intensity Estimation for the Permanental Process}, author = {Christian J. Walder and Adrian N. Bishop}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3579--3588}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/walder17a/walder17a.pdf}, url = {https://proceedings.mlr.press/v70/walder17a.html}, abstract = {The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.} }
Endnote
%0 Conference Paper %T Fast Bayesian Intensity Estimation for the Permanental Process %A Christian J. Walder %A Adrian N. Bishop %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-walder17a %I PMLR %P 3579--3588 %U https://proceedings.mlr.press/v70/walder17a.html %V 70 %X The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.
APA
Walder, C.J. & Bishop, A.N.. (2017). Fast Bayesian Intensity Estimation for the Permanental Process. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3579-3588 Available from https://proceedings.mlr.press/v70/walder17a.html.

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