# A Safe Screening Rule with Bi-level Optimization of nu Support Vector Machine

arXiv: https://arxiv.org/abs/2403.01769 · HTML: https://mlsanity.com/paper/2403.01769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [Anomaly Detection using One-Class Neural Networks](https://mlsanity.com/paper/1802.06360/) (2018)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Towards Explaining Anomalies: A Deep Taylor Decomposition of One-Class Models](https://mlsanity.com/paper/1805.06230/) (2018)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Scaling SVM and Least Absolute Deviations via Exact Data Reduction](https://mlsanity.com/paper/1310.7048/) (2013)

## Abstract (arXiv)

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.