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Gaussian process (GP) modulated Cox processes are widely used to model pointpatterns. Existing approaches require a mapping (link function) between theunconstrained GP and the positive intensity function. This commonly yieldssolutions that do not have a closed form or that are restricted to specificcovariance functions. We introduce a novel finite approximation of GP-modulatedCox processes where positiveness conditions can be imposed directly on the GP,with no restrictions on the covariance function. Our approach can also ensureother types of inequality constraints (e.g. monotonicity, convexity), resultingin 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 datathat our framework accurately infers the intensity functions. Wheremonotonicity is a feature of the process, our ability to include this in theinference improves results.

Gaussian Process Modulated Cox Processes under Linear Inequality Constraints