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。

一种基于双层优化的安全筛选规则和 ν 支持向量机

A Safe Screening Rule with Bi-level Optimization of $ν$ Support Vector  Machine

The l1-regularized logistic regression (or sparse logistic regression) is a
widely used method for simultaneous classification and feature selection.
Although many recent efforts have been devoted to its efficient implementation,
its application to high dimensional data still poses significant challenges. In
this paper, we present a fast and effective sparse logistic regression
screening rule (Slores) to identify the 0 components in the solution vector,
which may lead to a substantial reduction in the number of features to be
entered to the optimization. An appealing feature of Slores is that the data
set needs to be scanned only once to run the screening and its computational
cost is negligible compared to that of solving the sparse logistic regression
problem. Moreover, Slores is independent of solvers for sparse logistic
regression, thus Slores can be integrated with any existing solver to improve
the efficiency. We have evaluated Slores using high-dimensional data sets from
different applications. Extensive experimental results demonstrate that Slores
outperforms the existing state-of-the-art screening rules and the efficiency of
solving sparse logistic regression is improved by one magnitude in general.

本文提出了一种用于高维数据稀疏逻辑回归分类和特征选择的快速和有效的稀疏逻辑回归筛选规则（Slores），能够在解决稀疏逻辑回归问题的计算成本基础上实现数据集的一次扫描获得 0 组件，未来可与任何现有的稀疏逻辑回归引擎集成以提高效率。