Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures
The signature transform is a principled feature map for continuous-time paths, valued for its uniqueness and universality. Recovering a path from its truncated signature is, however, structurally ill-posed because the truncated signature map is not injective. We therefore reframe truncated signature inversion as a probabilistic problem -- learning the conditional distribution of a path given its truncated signature -- and adopt a signature-conditioned flow matching model as a practical estimator. This probabilistic formulation elucidates the fundamental difficulty of inversion: Bayes reconstruction error quantifies the irreducible uncertainty remaining after conditioning on a statistic. W...
| Authors | Junoh Kang, Kiseop Lee, Bohyung Han |
|---|---|
| Primary category | cs.LG |
| Published | 13 June 2026 |
| Last updated at source | 13 June 2026 |
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