69 citations · 354 across the 45 of their papers we have counts for
47 papers
The Singular Values of Lévy's Area Matrix
Danilo Jr Dela Cruz, Harald Oberhauser
The matrix of Lévy's areas of -dimensional Brownian motion is a fundamental object in stochastic analysis. In this article, we study the singular values of this ske…
Orthogonal polynomials on path-space
Ilya Chevyrev, Emilio Ferrucci, Darrick Lee +3
We consider the orthogonalisation of the signature of a stochastic process as the analogue of orthogonal polynomials on path-space. Under an infinite radius of convergence assumpti…
A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting
Masaki Adachi, Satoshi Hayakawa, Martin Jørgensen +3
Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealin…
Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach
Masaki Adachi, Satoshi Hayakawa, Martin Jørgensen +4
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic tr…
The Signature Kernel
Darrick Lee, Harald Oberhauser
The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and s…
Kernelized Cumulants: Beyond Kernel Mean Embeddings
Patric Bonnier, Harald Oberhauser, Zoltán Szabó
In , it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In thi…