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This research introduces a novel generative modeling framework capable of handling continuous-time processes with discontinuous trajectories from irregular data streams. By leveraging analytical formulas for jump bridges and scaled Gaussian parametrizations, the method enables simulation-free training of neural networks to match complex diffusion and jump dynamics. The work advances the theoretical foundations of machine learning for asynchronous time series, offering a robust solution for modeling real-world phenomena that exhibit sudden state changes.
A Jump-Diffusion Framework for Irregular Time Series Generation
arXiv:2505.23215v2 Announce Type: replace-cross Abstract: We propose a framework for generative modeling of continuous-time processes from irregularly and asynchronously recorded data. It is based on the matching of generators and accommodates discontinuous trajectories. Analytical formulas for diffusion and jump bridges yield a family of reference generators that a neural network is trained to match. The key ingredient is that, for our constructed jump bridge, a parametrization of the jump kernel densities by scaled Gaussians admits closed-form expressions for the Kullback-Leibler divergence, allowing simulation-free training.
Abstract:We propose a framework for generative modeling of continuous-time processes from irregularly and asynchronously recorded data. It is based on the matching of generators and accommodates discontinuous trajectories. Analytical formulas for diffusion and jump bridges yield a family of reference generators that a neural network is trained to match. The key ingredient is that, for our constructed jump bridge, a parametrization of the jump kernel densities by scaled Gaussians admits closed-form expressions for the Kullback-Leibler divergence, allowing simulation-free training.
Numerical Analysis (math.NA); Machine Learning (cs.LG)
arXiv:2505.23215 [math.NA]
(or arXiv:2505.23215v2 [math.NA] for this version)
https://doi.org/10.48550/arXiv.2505.23215 Focus to learn more arXiv-issued DOI via DataCite
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