A Unified Formulation and Fast Accelerated Proximal Gradient Method for Classification

Naoki Ito, Akiko Takeda, Kim-Chuan Toh; 18(16):1−49, 2017.

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, $\ell_2$-SVM, $\nu$-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. We also give a theoretical convergence guarantee for the proposed fast APG algorithm. Numerical experiments show that our algorithm is stable and highly competitive to specialized algorithms designed for specific models (e.g., sequential minimal optimization (SMO) for SVM).

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