Robust SDE Parameter Estimation Under Missing Time Information Setting
This addresses a practical problem for researchers and practitioners in domains like finance, health, and systems biology where timestamped data may be unavailable due to privacy or corruption, though it appears incremental as it builds on existing SDE methods.
The paper tackles parameter estimation for stochastic differential equations when temporal ordering information is missing or corrupted, introducing a framework that simultaneously recovers temporal order and estimates parameters. Experiments on synthetic and real-world datasets demonstrate the method's effectiveness in extending parameter estimation to settings with missing temporal order.
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.