A1761
Title: A coefficient space projection approach for penalized regression problems
Authors: Zicheng Liu - The Chinese University of Hong Kong (Hong Kong)
Gan Yuan - City University of Hong Kong (Hong Kong) [presenting]
Chun Yip Yau - Chinese University of Hong Kong (Hong Kong)
Abstract: A new approach views a penalized least squares (PLS) problem as a projection problem in a linearly-transformed space of regression coefficients. Specifically, the least squares criterion is expressed as an $\ell_2$-distance from a point to the ordinary least squares estimator, and the feasible region of the PLS problem is characterized as a geometric object under the transformed space. The penalized least squares problem can then be solved by projecting the ordinary least squares estimator onto this geometric object. The coefficient space projection approach is applied to develop a general method for deriving solution path algorithms for solving PLS problems with convex penalty functions, extending the scope of existing path algorithms. As a particular example, the general method yields the first solution path algorithm for the elastic net problem.
