On the Effectiveness of Active Learning by Uncertainty Sampling in Classification of High-Dimensional Gaussian Mixture Data

Active learning aims to reduce the cost of labeling through selective sampling. Despite reported empirical success over passive learning, many popular active learning heuristics such as uncertainty sampling still lack satisfying theoretical guarantees. Towards closing the gap between practical use and theoretical understanding in active learning, we propose to characterize the exact behavior of uncertainty sampling for high-dimensional Gaussian mixture data, in a modern regime of big data where the numbers of samples and features are commensurately large. Through a sharp characterization of the learning results, our analysis sheds light on the important question of when uncertainty sampling works better than passive learning. Our results show that the effectiveness of uncertainty sampling is not always ensured. In fact it depends crucially on the choice of i) an adequate initial classifier used to start the active sampling process and ii) a proper loss function that allows an adaptive treatment of samples queried at various