# Massively Parallel Exact Inference for Hawkes Processes

arXiv: https://arxiv.org/abs/2604.01342 · HTML: https://mlsanity.com/paper/2604.01342/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics](https://mlsanity.com/paper/1603.09449/) (2016)
- [Multivariate Hawkes Processes for Large-scale Inference](https://mlsanity.com/paper/1602.08418/) (2016)

## Built on by (most cited first, 1 of 1)

- [Credit Attribution in Timestamped Soccer Networks Using Multivariate Hawkes Processes](https://mlsanity.com/paper/2610.12775/) (2026)

## Abstract (arXiv)

Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as O(N2) 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 massively parallelizable algorithm for 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.