SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910846904434688 |
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| author | Barancikova, Barbora Huang, Zhuoyue Salvi, Cristopher |
| author_facet | Barancikova, Barbora Huang, Zhuoyue Salvi, Cristopher |
| contents | 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 discretisation 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 while 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 SigDiffusions with these inversion formulae results in high-quality long time series generation, competitive with the current state-of-the-art on various datasets of synthetic and real-world examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings Barancikova, Barbora Huang, Zhuoyue Salvi, Cristopher Machine Learning 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 discretisation 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 while 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 SigDiffusions with these inversion formulae results in high-quality long time series generation, competitive with the current state-of-the-art on various datasets of synthetic and real-world examples. |
| title | SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2406.10354 |