[Colloquium] TODAY: Gilad Lerman Colloquium

[Nati Srebro]

REMINDER: Colloquium at 11AM TODAY

Speaker:  Gilad Lerman (Minnesota)

Title: Robust Computation of Linear Models

TODAY, September 24th, 11AM in TTIC 5th floor conference room

Abstract:

Consider a dataset of vector-valued observations that consists of a
modest number of noisy inliers, which are explained well by a
low-dimensional subspace, along with a large number of outliers, which
have no linear structure. We describe a convex optimization problem
that can reliably fit a low-dimensional model to this type of data.
When the inliers are contained in a low-dimensional subspace we
provide a rigorous theory that describes when this optimization can
recover the subspace exactly. We present an efficient algorithm for
solving this optimization problem, whose computational cost is
comparable to that of the non-truncated SVD. We also show that the
sample complexity of the proposed subspace recovery is of the same
order as PCA subspace recovery and we consequently obtain some
nontrivial robustness to noise.

 This presentation is based on three joint works: 1) with Teng Zhang,
2) with Michael McCoy, Joel Tropp and Teng Zhang, and 3) with Matthew
Coudron.

Bio: Gilad Lerman is an associate professor at the School of
Mathematics at the University of Minnesota. He is interested in
geometric data modeling, computational harmonic analysis, machine
learning and related applications. He is a receipt of the NSF career
award.