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.

提出了一个安全的筛选规则和双层优化方法用于处理大规模问题，其中使用支持向量机（Support Vector Machine，SVM）的扩展方法 nu-SVM，以及通过高效的双坐标下降优化算法提高计算速度。在人工数据集和基准数据集上的实验结果验证了这些方法在有监督和无监督任务中的有效性和安全性。