Gaussian process modulated Cox processes under linear inequality constraints

Andrés F. López-Lopera (1, 2, 3, 4) , St John (5) , Nicolas Durrande (5)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
2 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
3 FAYOL-ENSMSE - Institut Henri Fayol
4 FAYOL-ENSMSE - Département Génie mathématique et industriel
5 PROWLER

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained 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. Our approach can also 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 monotonicity is a feature of the process, our ability to include this in the inference improves results.

Domaines: Autres [stat.ML]; Modélisation et simulation

Andrés F. López-Lopera, St John, Nicolas Durrande. Gaussian process modulated Cox processes under linear inequality constraints. 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Apr 2019, Okinawa, Japan. pp.1997-2006. ⟨hal-02103761⟩