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Improving the Noise Estimation of Latent Neural Stochastic Differential Equations

arXiv 2412.17499 ↗First posted 23 Dec 2024cs.LG stat.MLcited by 0

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Abstract (arXiv)

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in such data, limiting their ability to capture stochastic dynamics accurately. We investigate this underestimation in detail and propose a straightforward solution: by including an explicit additional noise regularization in the loss function, we are able to learn a model that accurately captures the diffusion component of the data. We demonstrate our results on a conceptual model system that highlights the improved latent neural SDE's capability to model stochastic bistable dynamics.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 32 references that are in the map. First posted on arXiv 23 Dec 2024.

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References · 14

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  3. 2019Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishingcited by 191
  4. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  5. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
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  7. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  8. 2019Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Modelcited by 45
  9. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  10. 2020Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filteringcited by 33
  11. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
  12. 2020Identifying Latent Stochastic Differential Equationscited by 21
2 more
  1. 2023Latent SDEs on Homogeneous Spacescited by 16
  2. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10

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