A Safe Screening Rule with Bi-level Optimization of $ν$ Support Vector
  Machine
Zhiji Yang Wanyi Chen Huan Zhang Yitian Xu Lei Shi Jianhua Zhao
Support vector machine (SVM) has achieved many successes in machine learning,
especially for a small sample problem. As a famous extension of the traditional
SVM, the $\nu$ support vector machine ($\nu$-SVM) has shown outstanding
performance due to its great model interpretability. However, it still faces
challenges in training overhead for large-scale problems. To address this
issue, we propose a safe screening rule with bi-level optimization for
$\nu$-SVM (SRBO-$\nu$-SVM) which can screen out inactive samples before
training and reduce the computational cost without sacrificing the prediction
accuracy. Our SRBO-$\nu$-SVM is strictly deduced by integrating the
Karush-Kuhn-Tucker (KKT) conditions, the variational inequalities of convex
problems and the $\nu$-property. Furthermore, we develop an efficient dual
coordinate descent method (DCDM) to further improve computational speed.
Finally, a unified framework for SRBO is proposed to accelerate many SVM-type
models, and it is successfully applied to one-class SVM. Experimental results
on 6 artificial data sets and 30 benchmark data sets have verified the
effectiveness and safety of our proposed methods in supervised and unsupervised
tasks.