Lecture notes on rough paths and applications to machine learning

T Cass, C Salvi - arxiv preprint arxiv:2404.06583, 2024 - arxiv.org
These notes expound the recent use of the signature transform and rough path theory in
data science and machine learning. We develop the core theory of the signature from first …

Sigdiffusions: Score-based diffusion models for long time series via log-signature embeddings

B Barancikova, Z Huang, C Salvi - arxiv preprint arxiv:2406.10354, 2024 - arxiv.org
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 …

Rank and symmetries of signature tensors

F Galuppi, P Santarsiero - arxiv preprint arxiv:2407.20405, 2024 - arxiv.org
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the
path. In this paper we propose a systematic study of basic properties of signature tensors …

Rough kernel hedging

NM Cirone, C Salvi - arxiv preprint arxiv:2501.09683, 2025 - arxiv.org
Building on the functional-analytic framework of operator-valued kernels and un-truncated
signature kernels, we propose a scalable, provably convergent signature-based algorithm …