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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: weprove for logistic regression that PL outperforms margin-based AL even fornoiseless data and when using the Bayes optimal decision boundary for sampling.Insights from our proof indicate that this high-dimensional phenomenon isexacerbated when the separation between the classes is small. We corroboratethis intuition with experiments on 20 high-dimensional datasets spanning adiverse range of applications, from finance and histology to chemistry andcomputer vision.

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