H
Harald Oberhauser
Researcher at University of Oxford
Publications - 69
Citations - 1010
Harald Oberhauser is an academic researcher from University of Oxford. The author has contributed to research in topics: Computer science & Rough path. The author has an hindex of 16, co-authored 59 publications receiving 814 citations. Previous affiliations of Harald Oberhauser include Technical University of Berlin & University of Cambridge.
Papers
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A (rough) pathwise approach to a class of non-linear stochastic partial differential equations
TL;DR: In this paper, the authors consider non-linear parabolic evolution equations of the form ∂ t u = F ( t, x, D u, D 2 u ) subject to noise of the order H ( x, D u ) ∘ d B where H is linear in Du and B denotes the Stratonovich differential of a multi-dimensional Brownian motion.
Journal Article
Kernels for sequentially ordered data
TL;DR: The experiments indicate that the signature-based sequential kernel framework may be a promising approach to learning with sequential data, such as time series, that allows to avoid extensive manual pre-processing.
Posted Content
Signature moments to characterize laws of stochastic processes
Ilya Chevyrev,Harald Oberhauser +1 more
TL;DR: This work uses the normalized sequence of moments, which characterizes the law of any finite-dimensional random variable, to define a metric for laws of stochastic processes, which can be efficiently estimated from finite samples, even if the stochastics processes themselves evolve in high-dimensional state spaces.
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Robust filtering: Correlated noise and multidimensional observation
TL;DR: In this paper, the authors use the theory of rough paths to show that if the signal and the observation noise are independent, then there exists a continuous map of continuous paths with uniform convergence topology such that the solution of the stochastic filtering problem can depend continuously on the observed data.
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Persistence Paths and Signature Features in Topological Data Analysis
TL;DR: In this article, a new feature map for barcodes is proposed to solve the problem of persistent homology computation by first realizing each barcode as a path in a convenient vector space, and then compute its path signature which takes values in the tensor algebra of that vector space.