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- W4313203595 abstract "We introduce a new discrete spatio-temporal Hawkes process model by formulating the general influence of the Hawkes process as a tensor kernel. Based on the low-rank structure assumption of the tensor kernel, we cast the estimation of the tensor kernel as a convex optimization problem using the Fourier transformed nuclear norm. We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. In particular, our upper bound of squared estimation error has the convergence rate of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$O(lnK/sqrt{K})$</tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$K$</tex-math></inline-formula> is the number of samples in the time horizon. The efficiency of our estimation is demonstrated with numerical simulations on synthetic data and the analysis of real-world data from Atlanta burglary incidents." @default.
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- W4313203595 date "2022-01-01" @default.
- W4313203595 modified "2023-09-28" @default.
- W4313203595 title "Tensor Kernel Recovery for Discrete Spatio-Temporal Hawkes Processes" @default.
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- W4313203595 doi "https://doi.org/10.1109/tsp.2022.3229642" @default.
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