Margin-based sampling in high dimensions: When being active is less efficient than staying passive

• URL: http://arxiv.org/abs/2212.00772v2
• Date: Fri, 2 Jun 2023 12:45:17 GMT
• Title: Margin-based sampling in high dimensions: When being active is less efficient than staying passive
• Authors: Alexandru Tifrea, Jacob Clarysse, Fanny Yang
• Abstract summary: Recent empirical evidence suggests that margin-based active learning can sometimes perform even worse than passive learning. We prove for logistic regression that PL outperforms margin-based AL even for noiseless data. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small.
• Score: 76.71565772067113
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is widely believed that given the same labeling budget, active learning (AL) algorithms like margin-based active learning achieve better predictive performance than passive learning (PL), albeit at a higher computational cost. Recent empirical evidence suggests that this added cost might be in vain, as margin-based AL can sometimes perform even worse than PL. While existing works offer different explanations in the low-dimensional regime, this paper shows that the underlying mechanism is entirely different in high dimensions: we prove for logistic regression that PL outperforms margin-based AL even for noiseless data and when using the Bayes optimal decision boundary for sampling. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small. We corroborate this intuition with experiments on 20 high-dimensional datasets spanning a diverse range of applications, from finance and histology to chemistry and computer vision.

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