A Comparison of Smoothing Approximation Methods for L1-regularized LR

L1-regularized classi ers are widely used to obtain sparse models; however, thenon-di erentiability of L1-regularized form causes more challenges in optimization. In this thesis, in order to eliminate the limited use of standard unconstrained methods in L1-regularized problems, smooth convex pproximations are used to replace the absolute form to make the problem twice-di erentiable. Thus we can use popular Newton methods to solve the reformulated problem. Results show that after approximation, the modified problem behaves in the middle of L1- and L2-regularized problems. To further investigate the pratical application of this approximation method, we also conduct experiments to compare with the state-of-art methods for olving L1- and L2-regularization problems.