Conformalized Signal Temporal Logic Inference under Covariate Shift

TL;DR

This paper introduces a conformalized STL inference method that effectively manages covariate shift, ensuring reliable and interpretable temporal logic rules in dynamical systems under distributional changes.

Contribution

It presents a novel framework combining differentiable STL inference with likelihood ratio-based conformal prediction to handle covariate shift.

Findings

Improves STL inference reliability under covariate shift.

Maintains interpretability of learned STL formulas.

Enhances robustness of symbolic learning at deployment.

Abstract

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.