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

• URL: http://arxiv.org/abs/2512.05893v1
• Date: Fri, 05 Dec 2025 17:14:07 GMT
• Title: NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process
• Authors: Neha Gupta, Aditya Maheshwari,
• Abstract summary: We propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP)<n>The Long Short-Term Memory (LSTM) network estimates the key parameters $>0$ and $in(0,1)$ from sequences of inter-arrival times.<n>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.
• Score: 2.376995292379181
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $μ>0$ 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.

Related papers

• A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models [0.0]
  We introduce a neural-network-based approximation of the posterior distribution framework.<n>Our model employs a lightweight 1D Convolutional Residual Network trained end-to-end on Gillespie-simulated SPN realizations.<n>On synthetic SPNs with 20% missing events, our surrogate recovers rate-function coefficients with an RMSE = 0.108 and substantially runs faster than traditional Bayesian approaches.
  arXiv  Detail & Related papers  (2025-07-14T18:31:19Z)
• Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks [0.0]
  We present a purely deep neural network-based approach for estimating long memory parameters of time series models. Parameters, such as the Hurst exponent, are critical in characterizing the long-range dependence, roughness, and self-similarity of processes.
  arXiv  Detail & Related papers  (2024-10-03T03:14:58Z)
• Minimally Supervised Learning using Topological Projections in Self-Organizing Maps [55.31182147885694]
  We introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs) Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are assigned to key best matching units (BMU) Our results indicate that the proposed minimally supervised model significantly outperforms traditional regression techniques.
  arXiv  Detail & Related papers  (2024-01-12T22:51:48Z)
• Deep learning the Hurst parameter of linear fractional processes and assessing its reliability [0.0]
  The study focuses on three types of processes: fractional Brownian motion (fBm), fractional Ornstein-Uhlenbeck (fOU) process, and linear fractional stable motions (lfsm) The work involves a fast generation of extensive datasets for fBm and fOU to train the LSTM network on a large volume of data in a feasible time. It finds that LSTM outperforms the traditional statistical methods in the case of fBm and fOU processes; however, it has limited accuracy on lfsm processes.
  arXiv  Detail & Related papers  (2024-01-03T15:42:45Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation for Time Series [45.76310830281876]
  We propose Quantile Sub-Ensembles, a novel method to estimate uncertainty with ensemble of quantile-regression-based task networks. Our method not only produces accurate imputations that is robust to high missing rates, but also is computationally efficient due to the fast training of its non-generative model.
  arXiv  Detail & Related papers  (2023-12-03T05:52:30Z)
• Efficient Parametric Approximations of Neural Network Function Space Distance [6.117371161379209]
  It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. We consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks.
  arXiv  Detail & Related papers  (2023-02-07T15:09:23Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Bayesian Neural Network Language Modeling for Speech Recognition [59.681758762712754]
  State-of-the-art neural network language models (NNLMs) represented by long short term memory recurrent neural networks (LSTM-RNNs) and Transformers are becoming highly complex. In this paper, an overarching full Bayesian learning framework is proposed to account for the underlying uncertainty in LSTM-RNN and Transformer LMs.
  arXiv  Detail & Related papers  (2022-08-28T17:50:19Z)
• Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network [0.0]
  In this study, we evaluate the performance of NLLS, the RNN-based method and a multilayer perceptron (MLP) on datasets rat and human brain. We showed that the proposed RNN-based fitting approach had the advantage of highly reduced computation time over NLLS.
  arXiv  Detail & Related papers  (2022-03-01T16:33:15Z)
• Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data with Spatial Information [52.635997570873194]
  This work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to process complex multi-dimensional time series data with spatial information. The proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.
  arXiv  Detail & Related papers  (2021-01-12T20:08:18Z)
• HiPPO: Recurrent Memory with Optimal Polynomial Projections [93.3537706398653]
  We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale.
  arXiv  Detail & Related papers  (2020-08-17T23:39:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.