[PAST EVENT] Iteratively Reweighted Least Squares for Data Science: New Formulations, Guarantees and Applications

February 9, 2022
9am - 10am
McGlothlin-Street Hall, Online on Zoom
251 Jamestown Rd
Williamsburg, VA 23185Map this location


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



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


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.


Pieter Peers