Fast Bayesian intensity estimation for the permanental process

Publication Type:
Conference Proceeding
34th International Conference on Machine Learning, ICML 2017, 2017, 7 pp. 5459 - 5471
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1701.03535v3.pdfAccepted Manuscript version4.89 MB
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Copyright © 2017 by the authors. 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 distribu-tion 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.
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