50 citations · 159 across the 31 of their papers we have counts for
9 papers · 1 filter
Sparse Signature Coefficient Recovery via Kernels
Daniil Shmelev, Cristopher Salvi
Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effe…
Genus expansion for non-linear random matrix ensembles with applications to neural networks
Nicola Muca Cirone, Jad Hamdan, Cristopher Salvi
We present a unified approach to studying certain non-linear random matrix ensembles and associated random neural networks at initialization. This begins with a novel series expans…
SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings
Barbora Barancikova, Zhuoyue Huang, Cristopher Salvi
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…
Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals
Christian Holberg, Cristopher Salvi
We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event disc…
Lecture notes on rough paths and applications to machine learning
Thomas Cass, Cristopher Salvi
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 pri…
Log-PDE Methods for Rough Signature Kernels
Maud Lemercier, Terry Lyons, Cristopher Salvi
Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature ker…
A path-dependent PDE solver based on signature kernels
Alexandre Pannier, Cristopher Salvi
We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of k…
Theoretical Foundations of Deep Selective State-Space Models
Nicola Muca Cirone, Antonio Orvieto, Benjamin Walker +2
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs…
Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes
Georg Manten, Cecilia Casolo, Emilio Ferrucci +3
Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such proce…