  We propose a scalable framework for inference in an inhomogeneous Poisson
process modeled by a continuous sigmoidal Cox process that assumes the
corresponding intensity function is given by a Gaussian process (GP) prior
transformed with a scaled logistic sigmoid function. We present a tractable
representation of the likelihood through augmentation with a superposition of
Poisson processes. This view enables a structured variational approximation
capturing dependencies across variables in the model. Our framework avoids
discretization of the domain, does not require accurate numerical integration
over the input space and is not limited to GPs with squared exponential
kernels. We evaluate our approach on synthetic and real-world data showing that
its benefits are particularly pronounced on multivariate input settings where
it overcomes the limitations of mean-field methods and sampling schemes. We
provide the state of-the-art in terms of speed, accuracy and uncertainty
quantification trade-offs.
