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Matroid Regression

Király, FJ; Theran, L; (2014) Matroid Regression. arXiv , Article arXiv:1403.0873 [math.ST]. Green open access

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Abstract

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estimates for any solution method. At the heart of our approach is the so-called regression matroid, a combinatorial object associated to sparsity patterns, which allows to replace inversion of the large matrix with the inversion of a kernel matrix that is constant size. We show that our method provides the best linear unbiased estimator (BLUE) for this setting and the minimum variance unbiased estimator (MVUE) under Gaussian noise assumptions, and furthermore we show that the size of the kernel matrix which is to be inverted can be traded off with accuracy.

Type: Article
Title: Matroid Regression
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/1403.0873
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: math.ST, math.ST, cs.DM, cs.LG, stat.ME, stat.ML, stat.TH
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1517414
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