Gaussian process modulated Cox processes under linear inequality constraints

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Gaussian process modulated Cox processes under linear inequality constraints

April 16 - 18, 2019 AISTATS, Naha, Okinawa, Japan

Authors: Andrés Felipe Lopez Lopera (he was an intern at when he did this work), ST John, and Nicolas Durrande

Abstract: Gaussian process (GP) modulated Cox processes are widely used to model point patterns in a great variety of applications. Existing approaches require a mapping (link function) between the real valued GP and the (positive) intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Furthermore, our approach can ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonocity is a feature of the process, our ability to include this in the inference improves results.

Probabilistic Modelling

Gaussian Processes

Cox Processes

Point Processes

Renewal Processes

Dimension Reduction

Truncated Gaussian Distribution

See paper

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