Matroid Regression
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 socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 DOI:
 10.48550/arXiv.1403.0873
 arXiv:
 arXiv:1403.0873
 Bibcode:
 2014arXiv1403.0873K
 Keywords:

 Mathematics  Statistics Theory;
 Computer Science  Discrete Mathematics;
 Computer Science  Machine Learning;
 Statistics  Methodology;
 Statistics  Machine Learning