|Rényi Entropy Bounds on the Active Learning Cost-Performance Tradeoff
|Vahid Jamali, University of Erlangen-Nuremberg, Germany, Germany; Antonia Tulino, University of Napoli Federico II, Italy, Italy; Jaime Llorca, Elza Erkip, New York University, New York, United States
|L.13: Online, Active, and Transfer Learning
|Statistics and Learning Theory
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|Semi-supervised classification, one of the most prominent fields in machine learning, studies how to combine the statistical knowledge of the often abundant unlabeled data with the often limited labeled data in order to maximize overall classification accuracy. In this context, the process of actively choosing the data to be labeled is referred to as active learning. In this paper, we initiate the non-asymptotic analysis of the optimal policy for semi-supervised classification with actively obtained labeled data. Considering a general Bayesian classification model, we provide the first characterization of the jointly optimal active learning and semi-supervised classification policy, in terms of the cost-performance tradeoff driven by the label query budget (number of data items to be labeled) and overall classification accuracy. Leveraging recent results on the Rényi Entropy, we derive tight information-theoretic bounds on such active learning cost-performance tradeoff.