Trajectory Generator Matching for Time Series

TL;DR

This paper introduces a novel generative modeling approach for irregularly sampled time series, leveraging trajectory flow matching to handle discontinuities and improve the modeling of complex stochastic processes.

Contribution

It proposes new SDE and jump process generators inspired by trajectory flow matching, capable of modeling irregular and discontinuous time series with closed-form divergence calculations.

Findings

Handles irregularly sampled data effectively

Models discontinuities using scaled Gaussian jump kernels

Provides closed-form KL divergence for training

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, inspired by trajectory flow matching, that have 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 of the corresponding Kullback-Leibler divergence in the loss. Unlike most other approaches, we are able to handle irregularly sampled time series.