We generalize the log Gaussian Cox process (lgcp) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple lgcps, whose log intensities are given by linear combinations of latent functions drawn from Gaus-sian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate lgcp, core-gionalization models, and multi-task perma-nental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.
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