Computer Science Events
[PAST EVENT] Iteratively Reweighted Least Squares for Data Science: New Formulations, Guarantees and Applications
Location
McGlothlin-Street Hall, Online on Zoom251 Jamestown Rd
Williamsburg, VA 23185Map this location
Abstract:
Iteratively Reweighted Least Squares (IRLS) is a simple algorithmic
framework for non-smooth optimization that has been studied since the
1930’s and has been widely used in approximation theory, statistics,
computer vision and beyond. Despite its popularity, a thorough
understanding of the framework had been elusive. In this talk, we
present several advances in both the theory and formulation of IRLS for
several problems in data science. We provide the first global linear
convergence results for IRLS applied to l1-norm minimization.
Furthermore, we formulate an optimal formulation for IRLS optimizing
non-convex spectral functions, for which we show fast local convergence
guarantees, and illustrate its data-efficiency and scalability compared
to the state-of-the-art for matrix completion problems, which are
foundational for modern recommender systems.
Using a low-rank property of a suitable block Hankel embedding, we
finally use IRLS to show that a shift operator encoding the topology of
a graph can be inferred from a near-optimal number of spatio-temporal
samples.
Bio:
Christian Kümmerle is Postdoctoral Fellow at Johns Hopkins University in
the Department of Applied Mathematics & Statistics. He is interested in
the mathematical foundations of machine learning and the development and
analysis of efficient algorithms for large scale data analysis.
His research leverages continuous optimization to address computational
and statistical challenges arising from data models involving graph,
sparsity and low-rank structures, leading to provable and efficient
algorithms.
He received B.Sc. and M.Sc. degrees in Mathematics from Technical
University of Munich in 2013 and 2015, respectively, after studies in
Munich, Paris and Charlottesville, VA, and completed his Ph.D. in
Mathematics at TU Munich in 2019 under the supervision of Felix Krahmer.
Contact
Pieter Peers