Harald Oberhauser

Associate Professor and Tutorial Fellow 

Mathematical Institute 

University of Oxford 

Email
oberhauser at maths.ox.ac.uk


Phone +44 1865 615176 

Adress Mathematical Institute, Andrew Wiles Building, Woodstock Road, OX2 6GG

Research
I am interested in probability theory, stochastic processes, and their applications. In particular, I enjoy developing ideas from pure mathematics into tools for applications, and viceversa, in developing mathematics inspired by questions that arise in applications.
Most of my recent research does this in situations where stochastic analysis intersects with statistics, machine learning, algebra, geometry, or topology.
Recent Stuff (in reversed chronological order of the arXiv posting)
Hypercontractivity meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures
with Satoshi Hayakawa, Terry Lyons
Fast Bayesian Inference via Kernel Recombination
with Masaki Adachi, Satoshi Hayakawa, Martin Jørgensen, Michael A. Osborne. NeuRIPS 2022
Capturing Graphs with HypoElliptic Diffusions
with Csaba Toth, Darrick Lee, Celia Hacker. NeuRIPS 2022
A Topological Approach to Mapping Space Signatures
with Chad Giusti, Darrick Lee, Vidit Nanda. Submitted
Proper Scoring Rules, Gradients, Divergences, and Entropies for Paths and Time Series
with Patric Bonnier. Submitted
Markov Chain Approximations to SDEs by Recombination on Lattice Trees with Francesco Cosentino, Alessandro Abate. Submitted
Tangent Space and Dimension Estimation with the Wasserstein Distance with Uzu Lim, Vidit Nanda. Submitted
Positively Weighted Kernel Quadrature via Subsampling with Satoshi Hayakawa, Terry Lyons. NeuRIPS 2022
GridFree Computation of Probabilistic Safety with Malliavin Calculus with Francesco Cosentino, Alessandro Abate. IEEE Trans. on Aut. Control 2023+
Neural SDEs as InfiniteDimensional GANs with Patrick Kidger, James Foster, Xuechen Li, Terry Lyons. ICML 2021
Nonlinear Independent Component Analysis for Continuous Time Signals
with Alexander Schell. Annals of Statistics 2023+
Estimating the Probability that a Vector is in the Convex Hull with Satoshi Hayakawa, Terry Lyons. Prob. Theory and Rel. Fields 2023+
The shifted ODE method for underdamped Langevin MCMC with James Foster, Terry Lyons. Submitted
Seq2Tens: An Efficient Representation of Sequences by LowRank Tensor Projections with Csaba Toth, Patric Bonnier. ICLR 2021
Carathéodory Sampling for Stochastic Gradient Descent with Francesco Cosentino, Alessandro Abate. Submitted
A Randomized Algorithm to Reduce the Support of Discrete Measures with Francesco Cosentino, Alessandro Abate. NeuRIPs 2020 (spotlight paper)
Adapted Topologies and Higher Rank Signatures with Chong Liu, Patric Bonnier. Annals of Applied Probability 2022+
Signature Cumulants, Ordered Partitions, and Independence of Stochastic Processes with Patric Bonnier. Bernoulli 2019
Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariances with Csaba Toth. ICML 2020
A Free Boundary Characterisation of the Root Barrier for Markov Processes with Paul Gassiat, Christina Zou. Prob. Theory and Rel. Fields 2021
An optimal polynomial approximation of Brownian motion with James Foster. SIAM Journal on Numerical Analysis 2020
Signature Moments to Characterize Laws of Stochastic Processes
with Ilya Chevyrev. Journal of Machine Learning Research 2022
Persistence Paths and Signature Features in Topological Data Analysis
with Ilya Chevyrev, Vidit Nanda. Trans. Pattern Anal. and Machine Int. 2020
Kernels for Sequentially Ordered Data with Franz Kiraly. Journal of Machine Learning Research 2019
...for earlier stuff see
arXiv
Software used in some of the above papers
KSig a package for GPUaccelerated computation of the signature kernel and MMD for stochastic processes. Written by Csaba Toth
Python code for constructing
Positively weighted Kernel Quadrature Formulas. Written by Satoshi Hayakawa
Python code for measure reduction via recombination.
Written by Francesco Cosentino
Supervision
DPhil (=PhD) students James Foster (DPhil 20), Francesco Cosentino (DPhil'21), Alexander Schell (DPhil'22), Patric Bonnier, Csaba Toth, Uzu Lim, Satoshi Hayakawa
Postdoctoral Researchers James Foster (until 09/22), Darrick Lee
I am always looking for prospective DPhil (PhD) students and postdoctoral researcher with shared interests. There are two standard routes for DPhil applications: the
CDT in Random Dynamical Systems and the usual
DPhil program in mathematics. Both result in a DPhil degree but the CDT has several courses in the first year. You are welcome to get in touch before you apply but please be aware that application deadlines are relatively early.
For postdoctoral positions, there are several funding possibilities and it's essential to get in touch early since this has to go through internal Oxford admin before we can submit to a funding body.
Teaching
HT22 C8.2 Stochastic Analysis and Partial Differential Equations
Affiliations
I'm a
Tutorial Fellow at
St. Hugh's College.
My research is supported by
DataSig, the
Turing Institute, and
CIMDA.