相关论文: The Signature Kernel is the solution of a Goursat …
Signature kernels have emerged as a powerful tool within kernel methods for sequential data. In the paper "The Signature Kernel is the solution of a Goursat PDE", the authors identify a kernel trick that demonstrates that, for continuously…
Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE. However,…
The signature kernel is a recent state-of-the-art tool for analyzing high-dimensional sequential data, valued for its theoretical guarantees and strong empirical performance. In this paper, we present a novel method for efficiently…
The signature kernel is a positive definite kernel for sequential and temporal data that has become increasingly popular in machine learning applications due to powerful theoretical guarantees, strong empirical performance, and recently…
The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this short survey…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
Suppose that $\gamma$ and $\sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $\gamma$…
The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular,…
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 effective way to capture sequentially ordered information,…
The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…
Signature-based methods have recently gained significant traction in machine learning for sequential data. In particular, signature kernels have emerged as powerful discriminators and training losses for generative models on time-series,…
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging…
We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal -- a setting that arises naturally in earthquake…
We develop a rough-path framework for two-parameter rough differential equations on rectangular and simplicial domains, motivated by the signature kernel and Schwinger--Dyson kernel equations. The theory is formulated in spaces of jointly…
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…
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 kernels on path-space. Specifically, we solve an optimal…
Path signatures provide a rich representation of sequential data, with strong theoretical guarantees and good performance in a variety of machine-learning tasks. While signatures have progressed from fixed feature extractors to trainable…
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…
Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A…
In this paper we introduce Keras Sig a high-performance pythonic library designed to compute path signature for deep learning applications. Entirely built in Keras 3, \textit{Keras Sig} leverages the seamless integration with the mostly…