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Massively Parallel Exact Inference for Hawkes Processes

arXiv:2604.01342v1 Announce Type: new 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

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Ahmer Raza, Hudson Smith · · 1 min read · 0 views
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arXiv:2604.01342v1 Announce Type: new 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 of millions of events, substantially beyond scales reported in prior work. We provide an open-source PyTorch library implementing our optimizations.

Executive Summary

This article presents a novel algorithm for maximum likelihood estimation of linear exponential Hawkes processes, leveraging massively parallel computation on GPUs to achieve significant speedups in scalability and complexity. By expressing the Hawkes process intensity as a product of sparse transition matrices, the authors exploit parallelization to reduce computational complexity from O(N^2) to O(N/P), where P is the number of parallel processors. This approach preserves the model's simplicity and interpretability while avoiding GPU memory constraints. The authors demonstrate orders-of-magnitude speedups on simulated and real datasets, scaling to unprecedented sizes. The open-source PyTorch library implementing these optimizations offers a valuable resource for researchers and practitioners.

Key Points

  • ▸ The authors develop a novel algorithm for maximum likelihood estimation of linear exponential Hawkes processes.
  • ▸ Massively parallel computation on GPUs reduces computational complexity from O(N^2) to O(N/P).
  • ▸ The approach preserves the model's simplicity and interpretability while avoiding GPU memory constraints.

Merits

Methodological Innovation

The authors introduce a novel algorithm that leverages massively parallel computation to achieve significant speedups in scalability and complexity.

Scalability and Complexity Reduction

The approach reduces computational complexity from O(N^2) to O(N/P), enabling the analysis of large datasets.

Preservation of Model Simplicity and Interpretability

The authors' approach preserves the simplicity and interpretability of the Hawkes process model, making it more accessible for researchers and practitioners.

Demerits

Limited Generalizability

The algorithm is specifically designed for linear exponential Hawkes processes, and its applicability to other types of Hawkes processes is uncertain.

Dependence on GPU Architecture

The algorithm's performance is heavily dependent on the specific GPU architecture, which may limit its portability to different hardware configurations.

Expert Commentary

The article presents a significant contribution to the field of statistical modeling, particularly in the context of point process modeling. The authors' algorithm offers a novel and efficient approach to maximum likelihood estimation of linear exponential Hawkes processes, leveraging massively parallel computation on GPUs to achieve significant speedups in scalability and complexity reduction. While the algorithm is specifically designed for linear exponential Hawkes processes, its potential applications in other areas of statistical modeling, such as machine learning and high-performance computing, are substantial. The preservation of model simplicity and interpretability ensures that the Hawkes process remains a valuable tool for understanding and modeling complex event data, with important implications for policy-making and decision-making in various fields.

Recommendations

  • ✓ Further research is needed to explore the applicability of the algorithm to other types of Hawkes processes and to generalize its performance across different GPU architectures.
  • ✓ The algorithm's potential applications in machine learning and high-performance computing should be further explored, with a focus on developing more scalable and efficient approaches to statistical modeling.

Sources

Original: arXiv - cs.LG

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