Logistic regression with l_1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interior-point method for solving large-scale l_1-regularized logistic regression problems. Small problems with up to a thousand or so features and examples can be solved in seconds on a PC; medium sized problems, with tens of thousands of features and examples, can be solved in tens of seconds (assuming some sparsity in the data). A variation on the basic method, that uses a preconditioned conjugate gradient method to compute the search step, can solve very large problems, with a million features and examples (e.g., the 20 Newsgroups data set), in a few tens of minutes, on a PC. Using warm-start techniques, a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently.

Joint work with Kwangmoo Koh and Seung-Jean Kim

Thursday, April 5, 2007
3:00 pm - 4:15 pm
Wu & Chen Auditorium