Using Truncated Path Signatures as Features in Machine Learning

Summary

The article develops a supervised learning approach that represents streams of data as paths and uses truncated path signatures as model features. A path signature is a sequence of iterated integrals; the full signature identifies a bounded-variation path up to a stated equivalence. Since a computer can only store finitely many terms, the article cites a bound showing factorial decay in the magnitude of higher-order terms, motivating truncation while acknowledging that discarded terms may still lose information.

The proposed workflow embeds each data stream into a continuous path, computes its signature to a selected order, and fits a linear model. The implementation uses Lasso regression, with signature order and regularization strength as parameters. The mathematical results support the feature representation and approximation rationale, but this installment does not report a quantitative finance experiment or predictive performance. Its trading relevance remains to be tested in later applications, and practical results will depend on path construction, truncation choice, data, and validation.

Key ideas

• Path signatures convert streams of observations into vectors of iterated-integral features.
• The full signature distinguishes bounded-variation paths up to tree-like equivalence.
• A cited bound motivates truncation because higher-order signature terms decay factorially.
• The proposed estimator fits Lasso regression to truncated signatures.
• The article provides a modeling framework but no empirical trading results.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.