SigDiffusions: Score-Based Diffusion Models for Long Time Series via Log-Signature Embeddings
<|reference_start|>SigDiffusions: Score-Based Diffusion Models for Long Time Series via Log-Signature Embeddings: Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models to generate long multivariate time series. Viewing a time series as the discretization of an underlying continuous process, we introduce SigDiffusion, a novel diffusion model operating on log-signature embeddings of the data. The forward and backward processes gradually perturb and denoise log-signatures preserving their algebraic structure. To recover a signal from its log-signature, we provide new closed-form inversion formulae expressing the coefficients obtained by expanding the signal in a given basis (e.g. Fourier or orthogonal polynomials) as explicit polynomial functions of the log-signature. Finally, we show that combining SigDiffusion with these inversion formulae results in highly realistic time series generation, competitive with the current state-of-the-art on various datasets of synthetic and real-world examples.<|reference_end|>
@article{barancikova2024sigdiffusions:,
    title={SigDiffusions: Score-Based Diffusion Models for Long Time Series via
  Log-Signature Embeddings},
    author={Barbora Barancikova, Zhuoyue Huang, Cristopher Salvi},
    journal={arXiv preprint arXiv:2406.10354},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.10354},
    primaryClass={cs.LG}
}