Active Learning of Hyperparameters: An Expected Cross Entropy Criterion for Active Model Selection

In standard active learning, the learner’s goal is to reduce the predictive uncertainty with as little data as possible. We consider a slightly dierent problem: the learner’s goal is to uncover latent properties of the model|e.g., which features are relevant (\active feature selection"), or the choice of hyper parameters|with as little data as possible. While the two goals are clearly related, we give examples where following the predictive uncertainty objective is suboptimal for uncovering latent parameters. We propose novel measures of information gain about the latent parameter, based on the divergence between the prior and expected posterior distribution over the latent parameter in question. Notably, this is dierent from applying Bayesian experimental design to latent variables: we give explicit examples showing that the latter objective is prone to get stuck in local minima, unlike its application the standard predictive uncertainty. Extensive evaluations show that active learning using our measures signicantly accelerates the uncovering of latent model parameters, as compared to standard version space approaches (Query-by-committee) as well as predictive uncertainty measures.