Learning Jump-Diffusion Dynamics from Irregularly-Sampled Data

Tim Jahn, Jannis Chemseddine, Paul Hagemann, Onno Pfohl, Christian Wald, Gabriele Steidl

Keywords: generative modelling, irregular time series, jump processes, stochastic differential equations

Abstract:

Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation.
For this, we find new generators of SDEs and jump processes for conditional interpolation which match the marginal distributions of the time series of interest.
Specifically, we can handle discontinuities of the underlying processes by parameterizing the jump kernel densities by scaled
Gaussians that allow for
closed form formulas and hence rapid evaluation of the corresponding
Kullback-Leibler divergence in the loss.
Unlike most other approaches, we explicitly account for both irregular and non-aligned sampling times in constructing the generators. We also clarify several theoretical aspects that lead to a more robust formulation of the model. We underline our theoretical results by numerical experiments involving combinations of jumps and SDE dynamics that illustrate the benefits of the proposed framework

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 11082