NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process
Neha Gupta, Aditya Maheshwari
cs.LG, stat.ML
Submitted: 2026-07-13
Comments: 19 pages; 21 figures
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range
Terminology
Abstract
In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters (mu, gamma, alpha, beta) directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = 0.1634), followed by the LSTM (MSE = 0.1752), compared to MLE (MSE = 2.8032). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.
Sources
- Layer Normalization
- Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks
- A Comparison of Traditional and Deep Learning Methods for Parameter Estimation of the Ornstein-Uhlenbeck Process
- NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process
- Adam: A Method for Stochastic Optimization
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