Interpretability of Path Signatures in Statistical Learning

Establish a general theoretical explanation for why path signatures—defined as the sequence of iterated Stratonovich integrals of a path—provide effective feature representations in statistical learning, thereby resolving the interpretability gap regarding the success of signature-based methods across applications.

Background

Path signatures have been widely adopted as powerful features in machine learning and have shown notable success in applications within mathematical finance and beyond. Despite their empirical effectiveness, the theoretical reasons underlying their performance remain insufficiently explained.

This paper proposes an interpretability approach via signature perturbations in the context of commodity futures term structures, but it acknowledges that, in the general case, the broader question of why signatures work remains unclear. The open problem seeks a principled, comprehensive theory explaining the effectiveness of signature-based features.