Journal of Machine Learning Research 18 (2017) 1-49 Submitted 5/16; Revised 1/17; Published 3/17 A Unified Formulation and Fast Accelerated Proximal Gradient Method for Classification Naoki Ito naoki
[email protected] Department of Mathematical Informatics The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan Akiko Takeda
[email protected] Department of Mathematical Analysis and Statistical Inference The Institute of Statistical Mathematics 10-3 Midori-cho, Tachikawa, Tokyo 190-8562 Japan Kim-Chuan Toh
[email protected] Department of Mathematics National University of Singapore Blk S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore Editor: Moritz Hardt Abstract Binary classification is the problem of predicting the class a given sample belongs to. To achieve a good prediction performance, it is important to find a suitable model for a given dataset. However, it is often time consuming and impractical for practitioners to try various classification models because each model employs a different formulation and algorithm. The difficulty can be mitigated if we have a unified formulation and an efficient universal algorithmic framework for various classification models to expedite the comparison of performance of different models for a given dataset. In this paper, we present a unified formulation of various classification models (including C-SVM, `2-SVM, ν-SVM, MM-FDA, MM-MPM, logistic regression, distance weighted discrimination) and develop a general optimization algorithm based on an accelerated proximal gradient (APG) method for the formulation. We design various techniques such as backtracking line search and adaptive restarting strategy in order to speed up the practical convergence of our method.