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

2026-07-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

The NeuroMem-FHP framework introduces a deep learning approach for estimating parameters of the Fractional Hawkes Process (FHP), a self-exciting point process that models long-range dependence using a fractional Mittag-Leffler excitation kernel. This framework employs both Long Short-Term Memory (LSTM) and Transformer neural architectures to directly estimate the FHP parameters (μ,γ,α,β) from inter-arrival time sequences, bypassing computationally intensive likelihood optimization. On synthetic data, the Transformer achieved superior accuracy with a Mean Squared Error (MSE) of 0.1634, followed by LSTM at 0.1752, both significantly outperforming classical Maximum Likelihood Estimation (MLE) which yielded an MSE of 2.8032. The framework was validated on real-world AAPL NBBO transaction data and Montgomery County 911 emergency call records, demonstrating its ability to accurately reproduce empirical distribution, tail behavior, and temporal dependence structures.

Key takeaway

For Machine Learning Engineers modeling event-driven systems with long-memory dynamics, consider adopting the NeuroMem-FHP framework. Its Transformer-based approach provides significantly more accurate and efficient Fractional Hawkes Process parameter estimation than traditional MLE. You should preprocess inter-arrival times using logarithmic transformation and standardization, and use window sizes of at least 50 events for robust results. This method offers a powerful alternative for statistical inference and prediction in complex temporal processes.

Key insights

Deep learning, especially Transformers, offers a superior likelihood-free method for Fractional Hawkes Process parameter estimation, outperforming MLE.

Principles

• Long-range dependence in event processes requires specialized modeling.
• Likelihood-free deep learning can surpass traditional statistical methods.
• Self-attention mechanisms effectively capture complex temporal dependencies.

Method

The NeuroMem-FHP framework converts event timestamps to inter-arrival times, then feeds fixed-length windows into LSTM or Transformer models. These models predict FHP parameters (μ,γ,α,β) using Softplus and Sigmoid activations for constraint enforcement.

In practice

• Use Transformer models for FHP parameter estimation.
• Preprocess inter-arrival times with log transformation and standardization.
• Employ window sizes ≥50 for stable estimates.

Topics

• Fractional Hawkes Process
• Deep Learning
• Parameter Estimation
• Transformer Architecture
• Long-Range Dependence
• Likelihood-Free Methods

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.