Embedding and learning with signatures

Abstract

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered. Its basic principle is to represent multidimensional paths by a graded feature set of their iterated integrals, called the signature. This approach relies critically on an embedding principle, which consists in representing discretely sampled data as paths, i.e., functions from $[0,1]$ to ${\mathbb{R}}^d$. After a survey of machine learning methodologies for signatures, the influence of embeddings on prediction accuracy is investigated with an in-depth study of three recent and challenging datasets. It is shown that a specific embedding, called lead-lag, is systematically the strongest performer across all datasets and algorithms considered. Moreover, an empirical study reveals that computing signatures over the whole path domain does not lead to a loss of local information. It is concluded that, with a good embedding, combining signatures with other simple algorithms achieves results competitive with state-of-the-art, domain-specific approaches.

References in corpus (10)

• Scikit-learn: Machine Learning in Python
• Mobile Sensor Data Anonymization
• Sparse arrays of signatures for online character recognition
• Learning from the past, predicting the statistics for the future, learning an evolving system
• Extracting information from the signature of a financial data stream
• Discretely sampled signals and the rough Hoff process
• Signature moments to characterize laws of stochastic processes
• The iisignature library: efficient calculation of iterated-integral signatures and log signatures
• Application of the Signature Method to Pattern Recognition in the CEQUEL Clinical Trial
• Longitudinal Functional Data Analysis

Cited by in corpus (6)

• Neural Controlled Differential Equations for Irregular Time Series
• Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
• A Generalised Signature Method for Multivariate Time Series Feature Extraction
• Distribution Regression for Sequential Data
• Path Signatures on Lie Groups
• Path Imputation Strategies for Signature Models of Irregular Time Series