SigDiffusions: Score-Based Diffusion Models for Long Time Series via Log-Signature Embeddings

• URL: http://arxiv.org/abs/2406.10354v1
• Date: Fri, 14 Jun 2024 18:04:06 GMT
• Title: SigDiffusions: Score-Based Diffusion Models for Long Time Series via Log-Signature Embeddings
• Authors: Barbora Barancikova, Zhuoyue Huang, Cristopher Salvi,
• Abstract summary: We introduce SigDiffusion, a novel diffusion model operating on log-signatures of the data. To recover a signal from its log-signature formulae, we provide new closed-form inversion formulae. We show that combining SigDiffusion with these formulae results in highly realistic time series generation.
• Score: 3.801509221714223
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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