用LSTM估计带记忆的分数泊松过程参数，精度提升55%。
NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process
- 用LSTM建模事件间隔时间的时序依赖关系，估计μ和β参数
- 合成数据上比传统方法误差降低55.3%，跨训练条件稳定
- 在真实应急呼叫与股票交易数据中有效捕捉日周期与参数变化
本文提出一种基于循环神经网络（RNN）的框架，用于估计具有记忆性和长程依赖性的分数泊松过程（FPP）的参数。通过长短期记忆（LSTM）网络，从事件间隔时间序列中估计关键参数 $μ>0$ 与 $β∈(0,1)$，有效建模其时间依赖性。在合成数据上的实验表明，该方法相比传统的矩方法（MOM）将均方误差（MSE）降低了约55.3%，且在不同训练条件下表现可靠。我们进一步在两个真实高频数据集上验证：宾夕法尼亚州蒙哥马利县的紧急呼叫记录与苹果公司（AAPL）股票交易数据。结果表明，LSTM能有效追踪每日模式与参数动态变化，证实其在复杂时间依赖数据上的有效性。
原文摘要 · Abstract (English)
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.
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