Bayesian Active Learning for Classification and Preference Learning

TLDR

Information‑theoretic active learning has been widely studied for probabilistic models, with tractable optimal policies for simple regression but more difficult for classification with nonparametric models, leading current approaches to rely on approximations for tractability. The authors propose an information‑gain approach based on predictive entropies for Gaussian Process classification. The method makes minimal approximations to the full objective and extends to Gaussian Process preference learning by reformulating binary preference as a classification problem. Experiments demonstrate that the approach performs favorably against many popular active‑learning algorithms with comparable or lower computational cost, and matches decision‑theoretic methods that use more information but are computationally heavier.

Abstract

Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with nonparametric models, the optimal solution is harder to compute. Current approaches make approximations to achieve tractability. We propose an approach that expresses information gain in terms of predictive entropies, and apply this method to the Gaussian Process Classifier (GPC). Our approach makes minimal approximations to the full information theoretic objective. Our experimental performance compares favourably to many popular active learning algorithms, and has equal or lower computational complexity. We compare well to decision theoretic approaches also, which are privy to more information and require much more computational time. Secondly, by developing further a reformulation of binary preference learning to a classification problem, we extend our algorithm to Gaussian Process preference learning.