eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-01-12
7:1
7:15
10.4230/LIPIcs.ITCS.2018.7
article
Non-Negative Sparse Regression and Column Subset Selection with L1 Error
Bhaskara, Aditya
Lattanzi, Silvio
We consider the problems of sparse regression and column subset selection under L1 error. For both problems, we show that in the non-negative setting it is possible to obtain tight and efficient approximations, without any additional structural assumptions (such as restricted isometry, incoherence, expansion, etc.). For sparse regression, given a matrix A and a vector b with non-negative entries, we give an efficient algorithm to output a vector x of sparsity O(k), for which |Ax - b|_1 is comparable to the smallest error possible using non-negative k-sparse x. We then use this technique to obtain our main result: an efficient algorithm for column subset selection under L1 error for non-negative matrices.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol094-itcs2018/LIPIcs.ITCS.2018.7/LIPIcs.ITCS.2018.7.pdf
Sparse regression
L1 error optimization
Column subset selection