Harald Oberhauser - From Stochastic Analysis to Statistical Learning, Algebra, and Geometry

harald oberhause

Learning from vector-valued data is a well-developed subject. However, often one is faced with data that exhibits a much richer structure; for example sequential (time series), relationships (a graph), or a nonlinear smooth structure (manifold). To efficiently capture and make inferences based on such objects, tools from pure mathematics turn out to be very powerful. I will give a general overview and then briefly talk about three recent projects I was involved with.

  • Capturing Graphs with Hypo-elliptic Diffusions, with Csaba Toth, Darrick Lee, Celia Hacker. NeuRIPS 2022
  • Signature Moments to Capture Laws of Stochastic Processes, with Ilya Chevyrev, Journal of Machine Learning Research 2022
  • Tangent Space and Dimension Estimation, with Uzu Lim and Vidit Nanda, 2022