BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Variable selection and classification with large-scale presence on ly data - Garvesh Raskutti (University of Wisconsin-Madison) DTSTART:20180119T114500Z DTEND:20180119T123000Z UID:TALK97909@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Co-author: Hyebin Song (University of Wisconsin-Madison )

In various real-world problems\, we are pres ented with positive and unlabelled data\, referred to as presence-only res ponses where the \; number of covariates $p$ is large. The combination of presence-only responses and high dimensionality presents both statisti cal and computational challenges. In this paper\, we develop the \\emph{PU lasso} algorithm for variable selection and classification with positive a nd unlabelled responses. Our algorithm involves using the majorization-min imization (MM) framework which is a generalization of the well-known expec tation-maximization (EM) algorithm. In particular to make our algorithm sc alable\, we provide two computational speed-ups to the standard EM algorit hm. We provide a theoretical guarantee where we first show that our algori thm is guaranteed to converge to a stationary point\, and then \ ;prove that any stationary point achieves the minimax optimal mean-squared error of $\\frac{s \\log p}{n}$\, where $s$ is the sparsity of the true p arameter. We also demonstrate through simulations that our algorithm out-p erforms state-of-the-art algorithms in the moderate $p$ settings in terms of classification performance. Finally\, we demonstrate that our PUlasso a lgorithm performs well on a biochemistry example.

Rel ated Links LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR