A Safe Screening Rule with Bi-level Optimization of $ν$ Support Vector Machine
This work addresses efficiency challenges in SVM training for large-scale applications, though it is incremental as it builds on existing ν-SVM methods.
The paper tackles the high training overhead of ν-SVM for large-scale problems by proposing a safe screening rule with bi-level optimization (SRBO-ν-SVM) that pre-screens inactive samples, reducing computational cost without sacrificing accuracy, as verified on 36 datasets.
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 $ν$ support vector machine ($ν$-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 $ν$-SVM (SRBO-$ν$-SVM) which can screen out inactive samples before training and reduce the computational cost without sacrificing the prediction accuracy. Our SRBO-$ν$-SVM is strictly deduced by integrating the Karush-Kuhn-Tucker (KKT) conditions, the variational inequalities of convex problems and the $ν$-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.