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2017 Poisson intensity estimation with reproducing kernels
Seth Flaxman, Yee Whye Teh, Dino Sejdinovic
Electron. J. Statist. 11(2): 5081-5104 (2017). DOI: 10.1214/17-EJS1339SI


Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space. In this paper we develop a new, computationally tractable Reproducing Kernel Hilbert Space (RKHS) formulation for the inhomogeneous Poisson process. We model the square root of the intensity as an RKHS function. Whereas RKHS models used in supervised learning rely on the so-called representer theorem, the form of the inhomogeneous Poisson process likelihood means that the representer theorem does not apply. However, we prove that the representer theorem does hold in an appropriately transformed RKHS, guaranteeing that the optimization of the penalized likelihood can be cast as a tractable finite-dimensional problem. The resulting approach is simple to implement, and readily scales to high dimensions and large-scale datasets.


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Seth Flaxman. Yee Whye Teh. Dino Sejdinovic. "Poisson intensity estimation with reproducing kernels." Electron. J. Statist. 11 (2) 5081 - 5104, 2017.


Received: 1 June 2017; Published: 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06825041
MathSciNet: MR3738206
Digital Object Identifier: 10.1214/17-EJS1339SI

Primary: 46E22 , 60G55 , 62G05

Keywords: computational statistics , inhomogeneous Poisson processes , intensity estimation , nonparametric statistics , ‎reproducing kernel Hilbert ‎space , spatial statistics


Vol.11 • No. 2 • 2017
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