在时间信息缺失时，通过反向过程不对称性恢复顺序并估计SDE参数。
Robust SDE Parameter Estimation Under Missing Time Information Setting
- 利用前后过程不对称性设计评分匹配准则，推断观测对的时间顺序。
- 通过排序重建完整时间序列，在合成与真实数据上实现高精度参数估计。
- 适用于隐私保护等时间信息缺失场景，拓展SDE应用边界。
随机微分方程（SDE）在金融、健康和系统生物学等领域的动态过程建模中展现出强大能力。然而，传统参数估计依赖精确的时间戳观测序列。当时间顺序被破坏、丢失或出于隐私目的隐藏时，现有方法通常失效。本文研究了时间顺序可恢复的条件，提出一种新框架：同时重构时间信息并估计SDE参数。该方法利用前向与后向过程的不对称性，推导出评分匹配准则，以判断观测对的正确时间顺序；随后通过排序算法恢复全局时间顺序，并基于重构序列使用最大似然法估计参数。我们在合成数据和真实数据集上进行了广泛实验，验证了该方法在时间顺序缺失场景下的有效性，扩展了SDE参数估计的应用范围。
原文摘要 · Abstract (English)
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs typically relies on accurately timestamped observational sequences. When temporal ordering information is corrupted, missing, or deliberately hidden (e.g., for privacy), existing estimation methods often fail. In this paper, we investigate the conditions under which temporal order can be recovered and introduce a novel framework that simultaneously reconstructs temporal information and estimates SDE parameters. Our approach exploits asymmetries between forward and backward processes, deriving a score-matching criterion to infer the correct temporal order between pairs of observations. We then recover the total order via a sorting procedure and estimate SDE parameters from the reconstructed sequence using maximum likelihood. Finally, we conduct extensive experiments on synthetic and real-world datasets to demonstrate the effectiveness of our method, extending parameter estimation to settings with missing temporal order and broadening applicability in sensitive domains.
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