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We propose a scalable framework for inference in an inhomogeneous Poissonprocess modeled by a continuous sigmoidal Cox process that assumes thecorresponding intensity function is given by a Gaussian process (GP) priortransformed with a scaled logistic sigmoid function. We present a tractablerepresentation of the likelihood through augmentation with a superposition ofPoisson processes. This view enables a structured variational approximationcapturing dependencies across variables in the model. Our framework avoidsdiscretization of the domain, does not require accurate numerical integrationover the input space and is not limited to GPs with squared exponentialkernels. We evaluate our approach on synthetic and real-world data showing thatits benefits are particularly pronounced on multivariate input settings whereit overcomes the limitations of mean-field methods and sampling schemes. Weprovide the state of-the-art in terms of speed, accuracy and uncertaintyquantification trade-offs.

Structured Variational Inference in Continuous Cox Process Models