Large deviations in the perceptron model and consequences for active learning

Active learning (AL) is a branch of machine that deals with problems where unlabeled data abundant yet obtaining labels expensive. The algorithm has the possibility querying limited number samples to obtain corresponding labels, subsequently used for supervised learning. In this work, we consider task choosing subset be labeled from fixed finite pool samples. We assume random matrix and ground truth generated by single-layer teacher neural network. employ replica methods analyze large deviations accuracy achieved after on original pool. These then provide optimal achievable performance boundaries any AL algorithm. show can efficiently approached simple message-passing algorithms. also comparison some other popular active strategies.