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 vice-versa, generating mathematical theory to understand questions that arise in applications....at least that's what I tell myself. Most of my recent research does this in the context where stochastic analysis meets statistics and machine learning, but increasingly also includes some excursions into algebra, geometry, and topology.

Recent Stuff (in reversed chronological order of the arXiv posting)

  • Fast Bayesian Inference via Kernel Recombination with Masaki Adachi, Satoshi Hayakawa, Martin Jørgensen, Michael A. Osborne. NeuRIPS 2022
  • Capturing Graphs with Hypo-Elliptic 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
  • Grid-Free Computation of Probabilistic Safety with Malliavin Calculus with Francesco Cosentino, Alessandro Abate. Submitted
  • Neural SDEs as Infinite-Dimensional GANs with Patrick Kidger, James Foster, Xuechen Li, Terry Lyons. ICML 2021
  • Nonlinear Independent Component Analysis for Continuous Time Signals with Alexander Schell. Submitted
  • Estimating the Probability that a given Vector is in the Convex Hull of a Random Sample with Satoshi Hayakawa, Terry Lyons. Submitted
  • The shifted ODE method for underdamped Langevin MCMC with James Foster, Terry Lyons. Submitted
  • Seq2Tens: An Efficient Representation of Sequences by Low-Rank 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 GPU-accelerated 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), Christina Zou, Patric Bonnier, Csaba Toth, Alexander Schell, Uzu Lim, Satoshi Hayakawa
    Postdoctoral Researchers James Foster (until 09/22), Darrick Lee

    I am always looking for prospective DPhil (PhD) students. There are two standard routes for 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.

    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 Oxford-Man Institute, the Turing Institute, and CIMDA.