Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data

• URL: http://arxiv.org/abs/2402.14989v5
• Date: Fri, 22 Nov 2024 07:57:14 GMT
• Title: Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data
• Authors: YongKyung Oh, Dongyoung Lim, Sungil Kim,
• Abstract summary: Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods. We propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.
• Score: 3.686808512438363
• License:
• Abstract: Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

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)
• Towards stable real-world equation discovery with assessing differentiating quality influence [52.2980614912553]
  We propose alternatives to the commonly used finite differences-based method. We evaluate these methods in terms of applicability to problems, similar to the real ones, and their ability to ensure the convergence of equation discovery algorithms.
  arXiv  Detail & Related papers  (2023-11-09T23:32:06Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Non-adversarial training of Neural SDEs with signature kernel scores [4.721845865189578]
  State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. In this paper, we introduce a novel class of scoring rules on pathspace based on signature kernels.
  arXiv  Detail & Related papers  (2023-05-25T17:31:18Z)
• Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations [84.42837346400151]
  Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare. Existing causal inference approaches consider regular, discrete-time intervals between observations and treatment decisions. We propose a controllable simulation environment based on a model of tumor growth for a range of scenarios.
  arXiv  Detail & Related papers  (2022-06-16T17:15:15Z)
• Learning effective stochastic differential equations from microscopic simulations: combining stochastic numerics and deep learning [0.46180371154032895]
  We approximate drift and diffusivity functions in effective SDE through neural networks. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot.
  arXiv  Detail & Related papers  (2021-06-10T13:00:18Z)
• Accurate and Reliable Forecasting using Stochastic Differential Equations [48.21369419647511]
  It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. This paper develops SDE-HNN to characterize the interaction between the predictive mean and variance of HNNs for accurate and reliable regression. Experiments on the challenging datasets show that our method significantly outperforms the state-of-the-art baselines in terms of both predictive performance and uncertainty quantification.
  arXiv  Detail & Related papers  (2021-03-28T04:18:11Z)
• STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations [2.362412515574206]
  We present STENCIL-NET, an artificial neural network architecture for data-driven learning of problem- and resolution-specific local discretizations of nonlinear PDEs. Knowing the actual PDE is not necessary, as solution data is sufficient to train the network to learn the discrete operators. A once-trained STENCIL-NET model can be used to predict solutions of the PDE on larger domains and for longer times than it was trained for.
  arXiv  Detail & Related papers  (2021-01-15T15:43:41Z)
• Learning Continuous-Time Dynamics by Stochastic Differential Networks [32.63114111531396]
  We propose a flexible continuous-time recurrent neural network named Variational Differential Networks (VSDN) VSDN embeds the complicated dynamics of the sporadic time series by neural Differential Equations (SDE) We show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and tasks for sporadic time series.
  arXiv  Detail & Related papers  (2020-06-11T01:40:34Z)
• Stochasticity in Neural ODEs: An Empirical Study [68.8204255655161]
  Regularization of neural networks (e.g. dropout) is a widespread technique in deep learning that allows for better generalization. We show that data augmentation during the training improves the performance of both deterministic and versions of the same model. However, the improvements obtained by the data augmentation completely eliminate the empirical regularization gains, making the performance of neural ODE and neural SDE negligible.
  arXiv  Detail & Related papers  (2020-02-22T22:12:56Z)

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.