大规模并行精确推断用于Hawkes过程
Massively Parallel Exact Inference for Hawkes Processes
AI总结：
本文提出一种大规模并行算法，用于高效估计线性指数Hawkes过程，通过并行前缀扫描实现线性时间计算，降低复杂度至O(N/P)，并提供开源库。
摘要：
多变量Hawkes过程是一种广泛使用的自激发点过程，但最大似然估计的常规方法复杂度为O(N²)。本文展示Hawkes过程强度可表示为稀疏转移矩阵的乘积，允许线性时间关联乘法，从而通过并行前缀扫描计算。该方法将复杂度降至约O(N/P)，自然产生批处理方案以维持常数内存使用，避免GPU内存限制。重要的是，该方法在不增加任何假设或近似的情况下计算精确似然，保持模型的简洁性和可解释性。我们在模拟和真实数据集上展示了数量级的加速，扩展到数千节点和数千万事件，远超先前工作的规模。我们提供了一个开源的PyTorch库实现我们的优化。
英文摘要：
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 of millions of events, substantially beyond scales reported in prior work. We provide an open-source PyTorch library implementing our optimizations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
