cs.LGApr 1, 2026

Massively Parallel Exact Inference for Hawkes Processes

Authors: Ahmer Raza, Hudson Smith

Organizations: Clemson University

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as O(N2)O(N^2) in the number of events. The canonical linear exponential Hawkes process admits a faster O(N)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)O(N/P) with PP 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.

Figures & tables

Figure 1: Scaling of our method across various sequence lengths, showing average epoch time (left) and peak memory usage (right). The gray region indicates where batching is enabled to maintain constant memory (with batch size 219=2^{19}=524,288$$ ). Dashed black lines indicate the maximum epoch time and memory usage across all runs, respectively. Diagonal gridlines with unit power (slope 1 on log-log plot) are shown for reference.
Figure 2: Comparison between our method (black) and other implementations of the intensity computation. The red dotted lines indicate the 24-hour walltime limit (86.4 seconds per epoch for 1000 epochs) and the maximum available memory (80 GiB), respectively. Crosses indicate that the next run either ran out of memory or exceeded 24 hours.
 Relative ℓ2\ell_{2} Error
NodesN/M2N/M^{2}Log-Lik.μ\muA\mathcal{A}γ\gamma
10100000-2.0171.71×10−31.71\times 10^{-3}1.80×10−21.80\times 10^{-2}1.17×10−11.17\times 10^{-1}
50400-2.8287.18×10−37.18\times 10^{-3}1.64×10−21.64\times 10^{-2}8.36×10−38.36\times 10^{-3}
100100-3.1201.96×10−21.96\times 10^{-2}2.76×10−22.76\times 10^{-2}1.09×10−21.09\times 10^{-2}
25016-4.5364.72×10−24.72\times 10^{-2}3.89×10−23.89\times 10^{-2}9.36×10−39.36\times 10^{-3}
5004-4.7121.34×10−11.34\times 10^{-1}1.20×10−11.20\times 10^{-1}1.51×10−21.51\times 10^{-2}
Table 1: Synthetic parameter recovery results. Per-event log-likelihood is reported, and N/M2N/M^{2} is the number of events per interaction parameter.
 Avg. Epoch Time
SubsetNodesEventsLog Lik.OursLazy MHP
Bail Out83564,1383.6120.06 s0.47 s
Miami Heat1,173133,4511.6800.21 s1.60 s
Amy Winehouse1,561226,2472.0430.34 s3.30 s
Arab Spring1,377400,1992.7960.46 s4.60 s
Greece1,9251,077,1252.2801.24 s—
Table 2: Summary of MemeTracker subsets and fitted Hawkes process models. Per-event log-likelihood is reported. Lazy MHP results are obtained from [ 21 ] and are omitted for subsets not considered in the paper.
Crime TypesEvents ( NN )Avg. Epoch TimeLog-Likelihood
All7,834,6281.012 s1.012
Selected4,761,8200.605 s0.428
Theft2,071,6260.296 s-0.189
Battery1,420,7390.200 s-1.565
Assault563,5350.082 s-2.720
Burglary414,0730.072 s-2.454
Table 3: Summary of Chicago crime data and the fitted Hawkes models with M=22M=22 nodes.
Figure 3: Interaction matrix for all crime types learned from Chicago crime data. Choropleth maps showing influence of particularly influential districts (District 7 and District 10).
More in this topic

Hawkes Processes

See all 14 papers

Explore similar work

CardsList

  1. NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

    Jul 13, 2026Neha Gupta, Aditya MaheshwariTemporal Point ProcessesParameter Estimation

    Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore 453556, India.

  2. Multivariate Spatio-Temporal Neural Hawkes Processes

    Feb 27, 2026Christopher Chukwuemeka, Hojun You, Mikyoung JunTemporal Point Processes

  3. Martingale Posterior Cox Processes

    Oct 17, 2026Joshua Rooijakkers, Edwin FongTemporal Point ProcessesBayesian Inference

    Imperial College London · University of Hong Kong