NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process

TL;DR

This paper introduces a recurrent neural network framework, specifically using LSTM, to accurately estimate parameters of the fractional Poisson process, capturing its memory effects and outperforming traditional methods on synthetic and real-world data.

Contribution

The paper presents a novel LSTM-based approach for parameter estimation in fractional Poisson processes, demonstrating significant accuracy improvements over existing methods.

Findings

Reduces MSE by 55.3% compared to traditional methods

Effectively models temporal dependencies in synthetic data

Accurately tracks parameter changes in real-world datasets

Abstract

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters $\mu >0$ and $\beta \in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3\% compared to the traditional method of moments (MOM) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.