用轨迹匹配方法生成不规则采样的时间序列，能处理突发跳跃。
Trajectory Generator Matching for Time Series
- 基于轨迹流匹配设计新型SDE与跳过程生成器
- 支持不规则采样数据，可精确建模跳跃性随机过程
- 适合金融、医疗等含突发变化的时间序列分析
从不规则观测中准确建模连续时间随机过程仍是重大挑战。本文借鉴图像生成的生成建模思想，推进时间序列生成的边界。我们提出受轨迹流匹配启发的新一代SDE与跳过程生成器，其边缘分布与目标时间序列一致。通过参数化缩放高斯跳跃核密度，实现损失函数中KL散度的闭式解。与多数方法不同，本方法可直接处理不规则采样时间序列。
原文摘要 · Abstract (English)
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.
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