Conformalized Signal Temporal Logic Inference under Covariate Shift
For researchers using STL in dynamical systems, this work addresses a practical limitation of existing conformal prediction methods by handling distribution shift, though the improvement is incremental.
This paper tackles the problem of STL inference under covariate shift, where training and deployment data distributions differ. The proposed framework uses weighted conformal prediction to provide validity guarantees, significantly improving symbolic learning reliability on trajectory datasets.
Signal Temporal Logic (STL) inference learns interpretable logical rules for temporal behaviors in dynamical systems. To ensure the correctness of learned STL formulas, recent approaches have incorporated conformal prediction as a statistical tool for uncertainty quantification. However, most existing methods rely on the assumption that calibration and testing data are identically distributed and exchangeable, an assumption that is frequently violated in real-world settings. This paper proposes a conformalized STL inference framework that explicitly addresses covariate shift between training and deployment trajectories dataset. From a technical standpoint, the approach first employs a template-free, differentiable STL inference method to learn an initial model, and subsequently refines it using a limited deployment side dataset to promote distribution alignment. To provide validity guarantees under distribution shift, the framework estimates the likelihood ratio between training and deployment distributions and integrates it into an STL-robustness-based weighted conformal prediction scheme. Experimental results on trajectory datasets demonstrate that the proposed framework preserves the interpretability of STL formulas while significantly improving symbolic learning reliability at deployment time.