Inferring the causal structure underlying stochastic dynamical systems from observational
data holds great promise in domains ranging from science and health to finance. Such …

We develop a provably convergent kernel-based solver for path-dependent PDEs (PPDEs).
Our numerical scheme leverages signature kernels, a recently introduced class of kernels …

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 …

Random developments of a path into a matrix Lie group $ G_N $ have recently been used to
construct signature-based kernels on path space. Two examples include developments into …

The signature of a path, introduced by KT Chen [10] in 1954, has been extensively studied in
recent years. The fundamental 2010 paper [20] of Hambly and Lyons showed that the …

Signature kernels are at the core of several machine learning algorithms for analysing
multivariate time series. The kernel of two bounded variation paths (such as piecewise linear …

The signature of a $ p $-weakly geometric rough path summarises a path up to a
generalised notion of reparameterisation. The quotient space of equivalence classes on …

Nonparametric regression of stochastic processes estimates statistical relationships
between multidimensional, time-dependent data without relying on specific parametric …

For any compact Lie group $ G $, we introduce a novel notion of average signature
$\mathbb A (G) $ valued in its tensor Lie algebra, by taking the average value of the …

Rough path theory is a branch of mathematics arising out of stochastic analysis. One of the
main tools of rough path analysis is the signature, which captures the evolution of an …