Efficient Inference in Multi-task Cox Process Models
This provides a more efficient and accurate method for researchers and practitioners working with multivariate point processes, such as in spatial statistics or event modeling.
The authors tackled the problem of modeling multiple correlated point data jointly by generalizing the log Gaussian Cox process framework to multi-task settings, developing an efficient variational inference algorithm that is orders of magnitude faster than existing benchmarks and achieves state-of-the-art performance.
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 Gaussian 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, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.