Robust SDE Parameter Estimation Under Missing Time Information Setting

TL;DR

This paper introduces a novel method for estimating SDE parameters when temporal order information is missing or corrupted, by reconstructing the order and then applying maximum likelihood estimation, validated on synthetic and real data.

Contribution

It proposes a new framework that jointly recovers temporal order and estimates SDE parameters, extending applicability to privacy-sensitive and incomplete data scenarios.

Findings

Effective reconstruction of temporal order from unordered observations.

Accurate SDE parameter estimation in missing or corrupted time settings.

Validated on diverse synthetic and real-world datasets.

Abstract

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.