Theoretical Statistics and Mathematics Unit, ISI Delhi

January 20, 2016 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Rodolphe Sepulchre,
University of Cambridge

Title:
The geometry of algorithms with rank and positivity constraints

Abstract of Talk

The talk will describe a Riemannian framework for large-scale computations over the
set of low-rank matrices. The foundation is geometric and the motivation
is algorithmic, with a bias towards efficient computations in large-scale problems.
We will explore how classical matrix factorizations connect the Riemannian geometry of the set of
fixed-rank matrices to two well-studied manifolds: the Grassmann manifold of linear subspaces and the cone
of positive definite matrices. The theory will be illustrated on various applications, including
low-rank Kalman filtering, linear regression with low-rank priors, matrix completion, and the choice of a suitable metric for Diffusion Tensor Imaging.