Signature Kernel

Signature kernels are positive definite kernels designed to measure similarity between sequential data, particularly time series, by leveraging the information contained in their iterated integrals (signatures). Current research focuses on efficient computation of these kernels, including the development of novel algorithms to overcome computational bottlenecks associated with high-dimensional or oscillatory data, and their application within machine learning models such as Neural Stochastic Differential Equations (Neural SDEs) and Gaussian process regression. This approach offers significant advantages in various fields, enabling improved forecasting accuracy (e.g., in finance and logistics) and more efficient analysis of complex, high-dimensional time series data.