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Poster
Global Linear and Local Superlinear Convergence of IRLS for Non-Smooth Robust Regression
Liangzu Peng · Christian Kümmerle · Rene Vidal

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #310
in Poster Session 3 »
We advance both the theory and practice of robust $\ell_p$-quasinorm regression for $p \in (0,1]$ by using novel variants of iteratively reweighted least-squares (IRLS) to solve the underlying non-smooth problem. In the convex case, $p=1$, we prove that this IRLS variant converges globally at a linear rate under a mild, deterministic condition on the feature matrix called the stable range space property. In the non-convex case, $p\in(0,1)$, we prove that under a similar condition, IRLS converges locally to the global minimizer at a superlinear rate of order $2-p$; the rate becomes quadratic as $p\to 0$. We showcase the proposed methods in three applications: real phase retrieval, regression without correspondences, and robust face restoration. The results show that (1) IRLS can handle a larger number of outliers than other methods, (2) it is faster than competing methods at the same level of accuracy, (3) it restores a sparsely corrupted face image with satisfactory visual quality.
Keywords: Sparsity · Non-smooth optimization · Iteratively Reweighted Least-Squares · Robust Regression · Outliers · Convergence Rate Analysis
[ Paper]  [ Poster]  [ OpenReview] 

Author Information

Liangzu Peng (Johns Hopkins University)
Christian Kümmerle (University of North Carolina at Charlotte)
Rene Vidal (Mathematical Institute for Data Science, Johns Hopkins University, USA)

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