Knowl Inf Syst DOI 10.1007/s10115-017-1047-z REGULAR PAPER A new accelerated proximal technique for regression with high-dimensional datasets Mridula Verma 1 · K. K. Shukla 1 Received: 26 October 2016 / Revised: 3 March 2017 / Accepted: 17 March 2017 © Springer-Verlag London 2017 Abstract We consider the problem of minimization of the sum of two convex functions, one of which is a smooth function, while another one may be a nonsmooth function. Many high-dimensional learning problems (classification/regression) can be designed using such frameworks, which can be efficiently solved with the help of first-order proximal-based meth- ods. Due to slow convergence of traditional proximal methods, a recent trend is to introduce acceleration to such methods, which increases the speed of convergence. Such proximal gradient methods belong to a wider class of the forward–backward algorithms, which math- ematically can be interpreted as fixed-point iterative schemes. In this paper, we design few new proximal gradient methods corresponding to few state-of-the-art fixed-point iterative schemes and compare their performances on the regression problem. In addition, we propose a new accelerated proximal gradient algorithm, which outperforms earlier traditional meth- ods in terms of convergence speed and regression error. To demonstrate the applicability of our method, we conducted experiments for the problem of regression with several publicly available high-dimensional real datasets taken from different application domains. Empiri- cal results exhibit that the proposed method outperforms the previous methods in terms of convergence, accuracy, and objective function values. Keywords Nonsmooth convex minimization · Proximal methods · Regression 1 Introduction Many machine learning problems are designed using a regularized convex minimization framework, which is the sum of a smooth convex loss function f (·) and a nonsmooth convex regularization function g(·), both defined over d -dimensional real space R d , as, min x ∈R d F (x ) = f (x ) + g(x ). (1) B Mridula Verma mridula.rs.cse13@iitbhu.ac.in 1 Department of Computer Science and Engineering, IIT (BHU), Varanasi, India 123