[2604.01342] Massively Parallel Exact Inference for Hawkes Processes

Computer Science > Machine Learning arXiv:2604.01342 (cs) [Submitted on 1 Apr 2026] Title:Massively Parallel Exact Inference for Hawkes Processes Authors:Ahmer Raza, Hudson Smith View a PDF of the paper titled Massively Parallel Exact Inference for Hawkes Processes, by Ahmer Raza and Hudson Smith View PDF Abstract:Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster $O(N)$ recurrence, but prior work evaluates this recurrence sequentially, without exploiting parallelization on modern GPUs. We show that the Hawkes process intensity can be expressed as a product of sparse transition matrices admitting a linear-time associative multiply, enabling computation via a parallel prefix scan. This yields a simple yet massively parallelizable algorithm for maximum likelihood estimation of linear exponential Hawkes processes. Our method reduces the computational complexity to approximately $O(N/P)$ with $P$ parallel processors, and naturally yields a batching scheme to maintain constant memory usage, avoiding GPU memory constraints. Importantly, it computes the exact likelihood without any additional assumptions or approximations, preserving the simplicity and interpretability of the model. We demonstrate orders-of-magnitude speedups on simulated and real datasets, scaling to thousands of nodes and tens ...