Log-PDE Methods for Rough Signature Kernels

Understand

Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis.

• For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE.
• However, existing PDE solvers only use increments as input data, leading to first order approximation errors.
• These approaches become computationally intractable for highly oscillatory input paths, as they have to be resolved at a fine enough scale to accurately recover their signature kernel, resulting in significant time and memory complexities.