Fractional SDE-Net: Generation of Time Series Data with Long-term Memory

• URL: http://arxiv.org/abs/2201.05974v1
• Date: Sun, 16 Jan 2022 05:37:02 GMT
• Title: Fractional SDE-Net: Generation of Time Series Data with Long-term Memory
• Authors: Kohei Hayashi and Kei Nakagawa
• Abstract summary: We propose fSDE-Net: neural fractional Differential Equation Network. We derive the solver of fSDE-Net and theoretically analyze the existence and uniqueness of the solution. Our experiments demonstrate that the fSDE-Net model can replicate distributional properties well.
• Score: 10.267057557137665
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we focus on generation of time-series data using neural networks. It is often the case that input time-series data, especially taken from real financial markets, is irregularly sampled, and its noise structure is more complicated than i.i.d. type. To generate time series with such a property, we propose fSDE-Net: neural fractional Stochastic Differential Equation Network. It generalizes the neural SDE model by using fractional Brownian motion with Hurst index larger than half, which exhibits long-term memory property. We derive the solver of fSDE-Net and theoretically analyze the existence and uniqueness of the solution to fSDE-Net. Our experiments demonstrate that the fSDE-Net model can replicate distributional properties well.

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• Solving partial differential equations with sampled neural networks [1.8590821261905535]
  Approximation of solutions to partial differential equations (PDE) is an important problem in computational science and engineering. We discuss how sampling the hidden weights and biases of the ansatz network from data-agnostic and data-dependent probability distributions allows us to progress on both challenges.
  arXiv  Detail & Related papers  (2024-05-31T14:24:39Z)
• PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equations [49.80959046861793]
  We present PDETime, a novel LMTF model inspired by the principles of Neural PDE solvers. Our experimentation across seven diversetemporal real-world LMTF datasets reveals that PDETime adapts effectively to the intrinsic nature of the data.
  arXiv  Detail & Related papers  (2024-02-25T17:39:44Z)
• Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates [0.0]
  This paper presents the Delay-SDE-net, a neural network model based on delay differential equations (SDDEs) The use of SDDEs with multiple delays as modelling makes it a suitable model for time series with memory effects. We derive the theoretical error of the Delay-SDE-net and analyze the convergence rate numerically.
  arXiv  Detail & Related papers  (2023-03-14T14:31:38Z)
• Learning PDE Solution Operator for Continuous Modeling of Time-Series [1.39661494747879]
  This work presents a partial differential equation (PDE) based framework which improves the dynamics modeling capability. We propose a neural operator that can handle time continuously without requiring iterative operations or specific grids of temporal discretization. Our framework opens up a new way for a continuous representation of neural networks that can be readily adopted for real-world applications.
  arXiv  Detail & Related papers  (2023-02-02T03:47:52Z)
• LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data [47.49194807524502]
  We propose LordNet, a tunable and efficient neural network for modeling entanglements. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements can be well modeled by the LordNet.
  arXiv  Detail & Related papers  (2022-06-19T14:41:08Z)
• Time Series Forecasting with Ensembled Stochastic Differential Equations Driven by L\'evy Noise [2.3076895420652965]
  We use a collection of SDEs equipped with neural networks to predict long-term trend of noisy time series. Our contributions are, first, we use the phase space reconstruction method to extract intrinsic dimension of the time series data. Second, we explore SDEs driven by $alpha$-stable L'evy motion to model the time series data and solve the problem through neural network approximation.
  arXiv  Detail & Related papers  (2021-11-25T16:49:01Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• Score-Based Generative Modeling through Stochastic Differential Equations [114.39209003111723]
  We present a differential equation that transforms a complex data distribution to a known prior distribution by injecting noise. A corresponding reverse-time SDE transforms the prior distribution back into the data distribution by slowly removing the noise. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks. We demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
  arXiv  Detail & Related papers  (2020-11-26T19:39:10Z)

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.