A Safe Screening Rule with Bi-level Optimization of ν Support Vector Machine
arxiv(2024)
摘要
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.
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