Expected Signature Kernels for Rough Paths
Read the original on arXiv Statistics ML →The paper introduces the expected signature kernel as a similarity measure for probability laws on path space, directly applicable to signature maximum mean discrepancies. It characterizes this kernel for group-valued inhomogeneous Lévy processes by solving an extended Goursat-type system, providing exact solutions in the continuous case and well‑posed infinite‑dimensional systems with error‑controlled truncations for jump processes. The authors also show that conditioning on sampled quadratic variations yields an unbiased, lower‑variance statistic for conditionally Gaussian martingales, and present computable finite‑grid implementations that improve variance and test power.
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