A Bayesian framework for active learning

We describe a Bayesian framework for active learning for non-separable data, which incorporates a query density to explicitly model how new data is to be sampled. The model makes no assumption of independence between queried data-points; rather it updates model parameters on the basis of both observations and how those observations were sampled. A `hypothetical' look-ahead is employed to evaluate expected cost in the next time-step. We show the efficacy of this algorithm on the probabilistic high-low game which is a non-separable generalisation of the separable high-low game introduced by Seung et al. Our results indicate that the active Bayes algorithm performs significantly better than passive learning even when the overlap region is wide, covering over 30% of the feature space.