Timeline for Robust estimation of $Ax=b$

9 events

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Dec 5, 2020 at 18:31	comment	added	Daniel Shapero		To add to @FedericoPoloni's excellent answer, there are loads of other ways of solving L1-type problems besides IRLS. Proximal algorithms, such as FISTA, are often very effective and quite simple to implement.
Dec 5, 2020 at 17:48	comment	added	Mark L. Stone		I have now edited my answer.
Dec 5, 2020 at 17:43	comment	added	Mark L. Stone		Fair enough. But why no solve it as a Linear Programming Problem? Unlike a century ago, such solvers now exist.
Dec 5, 2020 at 17:41	comment	added	Federico Poloni		@MarkL.Stone No, IRLS is an iterative method to solve a L1 loss problem in which a L2 problem is solved at each iteration.
Dec 5, 2020 at 17:35	comment	added	Mark L. Stone		The problem statement says L1 loss, not least squares (L2) loss.
Dec 5, 2020 at 14:47	comment	added	Federico Poloni		QR. Anyway, are you sure SVD is that expensive? It should be at most a factor 2 slower than A^TWA.
Dec 5, 2020 at 14:44	comment	added	lalit		Thank you for your answer. I'll update on this. For m>>n, e.g., m=10000, n=100, SVD computation of W^(1/2) * A will be expensive both in terms of memory and time taken when compared to A^T * W * A. Can you suggest any method to reduce the computation time?
Dec 5, 2020 at 14:06	history	edited	Federico Poloni	CC BY-SA 4.0	added 105 characters in body
Dec 5, 2020 at 12:30	history	answered	Federico Poloni	CC BY-SA 4.0