Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
This paper studies mixed linear regression and give a number of results. Under various deterministic conditions, they show that given a sufficiently warm start, iterative trimmed least squares converges to the true directions quickly. Their algorithm continues to work in the presence of adversarial corruptions. However the warm start is required to be quite close to the true solution. They give an SVD based initialization procedure that works in the non-noisy setting and when the examples come from a gaussian distribution. There has been much recent progress on mixed linear regression. Perhaps the most closely related paper is the work of Li-Liang. The main point of debate among the reviewers was, in light of what is known, how surprising are the results? Still, the results fill in some gaps in what was known for an important problem.