Skip to main content
Browse by:
GROUP

Until further notice, in-person public events have been canceled. This includes recruitment events, tours, student programs, reunions, performances, conferences and social events.
Event listings include how to access online content. Contact event sponsor with questions.
Please note that all visitors to campus must comply with Duke’s community safety measures, which include wearing a mask,
check https://returnto.duke.edu/campus-visitors/ before coming to campus, and follow direction provided by campus personnel.

Learning & Exploiting Low-Dimensional Structure in High-Dimensional Data

Duke Math
Icon calendar
Thursday, February 27, 2020
Icon time
3:15 pm - 4:15 pm
Icon speaker
Didong Li (Duke)
Icon series
Probability Seminar

Data lying in a high dimensional ambient space are commonly thought to have a much lower intrinsic dimension. In particular, the data may be concentrated near a lower-dimensional subspace or manifold. There is an immense literature focused on approximating the unknown subspace and the unknown density, and exploiting such approximations in clustering, data compression, and building of predictive models. Most of the literature relies on approximating subspaces and densities using a locally linear, and potentially multiscale, dictionary with Gaussian kernels. In this talk, we propose a simple and general alternative, which instead uses pieces of spheres, or spherelets, to locally approximate the unknown subspace. I will also introduce a curved kernel called the Fisher-Gaussian (FG) kernel which outperforms multivariate Gaussians in many cases. Theory is developed showing that spherelets can produce lower covering numbers and mean square errors for many manifolds, as well as the posterior consistency of the Dirichlet process mixture of the FG kernels. Time permitting, I will also talk about an ongoing project about stochastic differential geometry.