Data Science and Analytics Thrust Seminar | Multivariate Poisson Intensity Estimation via Low-Rank Tensor Decomposition

In this talk, we introduce novel matrix- and tensor-based methods for estimating multivariate intensity functions in spatial point processes. By projecting a multivariate function onto a finite-dimensional tensor product subspace, we obtain a coefficient matrix or tensor with approximately low-rank structure, which we exploit via low-rank matrix or tensor decomposition. Compared to traditional nonparametric approaches, our methods significantly reduce estimation variance and improve estimation accuracy both theoretically and numerically. We develop theoretical tools to justify the statistical performance of our methods. This work represents the first application of matrix or tensor decompositions for intensity function estimation in spatial point processes. Extensive numerical results support our theoretical findings and demonstrate the effectiveness of our methods.