NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process
This work addresses the problem of accurately estimating parameters in memory-dependent event processes for applications such as emergency response and financial analysis, representing an incremental improvement over existing methods.
The paper tackled parameter estimation for the fractional Poisson process, which models event arrivals with memory, and found that their LSTM-based approach reduced mean squared error by about 55.3% compared to traditional methods on synthetic data, while also performing reliably on real-world datasets like emergency calls and stock trading data.
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 $μ>0$ and $β\in(0,1)$ 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.