# FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels

arXiv: https://arxiv.org/abs/2210.04635 · HTML: https://mlsanity.com/paper/2210.04635/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 17 of 17)

- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding](https://mlsanity.com/paper/1705.08006/) (2017)
- [Noise-Contrastive Estimation for Multivariate Point Processes](https://mlsanity.com/paper/2011.00717/) (2020)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Efficient Non-parametric Bayesian Hawkes Processes](https://mlsanity.com/paper/1810.03730/) (2018)
- [Multivariate Convolutional Sparse Coding for Electromagnetic Brain Signals](https://mlsanity.com/paper/1805.09654/) (2018)
- [Scalable Bayesian Inference for Excitatory Point Process Networks](https://mlsanity.com/paper/1507.03228/) (2015)
- [Tracking Dynamic Point Processes on Networks](https://mlsanity.com/paper/1409.0031/) (2014)
- [Learning Hawkes Processes from Short Doubly-Censored Event Sequences](https://mlsanity.com/paper/1702.07013/) (2017)
- [Benefits from Superposed Hawkes Processes](https://mlsanity.com/paper/1710.05115/) (2017)
- [Modeling networks of spiking neurons as interacting processes with memory of variable length](https://mlsanity.com/paper/1502.06446/) (2015)
- [DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG Signals](https://mlsanity.com/paper/2112.06652/) (2021)
- [A flexible, random histogram kernel for discrete-time Hawkes processes](https://mlsanity.com/paper/2208.02921/) (2022)
- [Exponential Kernels with Latency in Hawkes Processes: Applications in Finance](https://mlsanity.com/paper/2101.06348/) (2021)

## Built on by (most cited first, 5 of 5)

- [Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability](https://mlsanity.com/paper/2305.19694/) (2023)
- [Flexible Parametric Inference for Space-Time Hawkes Processes](https://mlsanity.com/paper/2406.06849/) (2024)
- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)
- [Unmixing Noise from Hawkes Process to Model Learned Physiological Events](https://mlsanity.com/paper/2406.16938/) (2024)
- [Sparklen: A Statistical Learning Toolkit for High-Dimensional Hawkes Processes in Python](https://mlsanity.com/paper/2502.18979/) (2025)

## Abstract (arXiv)

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ℓ2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.