Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures
arXiv:2606.15332v1 Announce Type: new Abstract: 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 fund
The continuous development in AI and machine learning pushes for more sophisticated ways to handle complex data types, such as continuous-time paths, leading to new models like probabilistic signature inversion.
This development proposes a novel approach to recovering complex data from truncated representations, which could enhance the precision and robustness of AI systems dealing with time-series data.
The ability to probabilistically infer full paths from incomplete signatures could lead to more robust and accurate AI models, especially in fields like forecasting, anomaly detection, and synthetic data generation.
- · Machine Learning Researchers
- · Time Series Data Analysts
- · AI Development Platforms
- · Traditional Deterministic Modeling Approaches
Improved accuracy in AI models trained on partial or truncated time-series data.
New applications in areas requiring the reconstruction or generation of dynamic processes from limited information.
Potential for more efficient training of AI models by using signatures as a compressed, yet informative, representation of complex paths.
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Read at arXiv cs.LG