Jul 24, 2023
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It is widely believed that given the same labeling budget, active learning (AL)algorithms like margin-based active learning achieve better predictiveperformance than passive learning (PL), albeit at a higher computational cost.Recent empirical evidence suggests that this added cost might be in vain, asmargin-based AL can sometimes perform even worse than PL. While existing worksoffer different explanations in the low-dimensional regime, this paper showsthat the underlying mechanism is entirely different in high dimensions: we provefor logistic regression that PL outperforms margin-based AL even for noiselessdata and when using the Bayes optimal decision boundary for sampling. Insightsfrom our proof indicate that this high-dimensional phenomenon is exacerbatedwhen the separation between the classes is small. We corroborate this intuitionwith experiments on 20 high-dimensional datasets spanning a diverse range ofapplications, from finance and histology to chemistry and computer vision.It is widely believed that given the same labeling budget, active learning (AL)algorithms like margin-based active learning achieve better predictiveperformance than passive learning (PL), albeit at a higher computational cost.Recent empirical evidence suggests that this added cost might be in vain, asmargin-based AL can sometimes perform even worse than PL. While existing worksoffer different explanations in the low-dimensional regime, this paper showsthat the underlying mechanism is entirely d…
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