Improving the Noise Estimation of Latent Neural Stochastic Differential Equations
This addresses a specific limitation in generative modeling for stochastic time series, but it is incremental as it builds on existing latent neural SDE methods.
The paper tackled the problem of latent neural stochastic differential equations underestimating noise in stochastic time series data, resulting in a model that accurately captures the diffusion component by adding noise regularization to the loss function.
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.