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

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.

Subjectivity in Unsupervised Machine Learning Model Selection

Model selection is a necessary step in unsupervised machine learning. Despite numerous criteria and metrics, model selection remains subjective. A high degree of subjectivity may lead to questions about repeatability and reproducibility of various machine learning studies and doubts about the robustness of models deployed in the real world. Yet, the impact of modelers' preferences on model selection outcomes remains largely unexplored. This study uses the Hidden Markov Model as an example to investigate the subjectivity involved in model selection. We asked 33 participants and three Large Language Models (LLMs) to make model selections in three scenarios. Results revealed variability and inconsistencies in both the participants' and the LLMs' choices, especially when different criteria and metrics disagree. Sources of subjectivity include varying opinions on the importance of different criteria and metrics, differing views on how parsimonious a model should be, and how the size of a dataset should influence model selection. The results underscore the importance of developing a more standardized way to document subjective choices made in model selection processes.