Robust SDE Parameter Estimation Under Missing Time Information Setting

2026-01-28

AI Summary

This work addresses the challenge of parameter estimation for stochastic differential equations (SDEs) when timestamps are missing, disordered, or deliberately obscured—a scenario under which conventional methods fail. The authors propose a novel framework that jointly reconstructs the observation sequence and estimates SDE parameters without relying on temporal ordering information. By exploiting the asymmetry between forward and backward diffusion processes, the method first infers the relative order of observation pairs via a score-matching criterion. A total-order reconstruction algorithm then recovers the complete time series, enabling subsequent parameter learning through maximum likelihood estimation. This approach represents the first robust solution for joint time-sequence reconstruction and SDE parameter estimation in the absence of time labels, significantly improving modeling accuracy on both synthetic and real-world datasets and thereby extending the applicability of SDEs to privacy-sensitive and other timestamp-constrained settings.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• stochastic differential equations
• parameter estimation
• missing time information
• temporal order
• privacy

Innovation

• stochastic differential equations
• temporal order recovery
• score matching
• parameter estimation
• missing time information