Improving importance estimation in pool-based batch active learning for approximate linear regression

Pool-based batch active learning is aimed at choosing training inputs from a ‘pool’ of test inputs so that the generalization error is minimized. P-ALICE (Pool-based Active Learning using Importance-weighted least-squares learning based on Conditional Expectation of the generalization error) is a state-of-the-art method that can cope with model misspecification by weighting training samples according to the importance (i.e., the ratio of test and training input densities). However, importance estimation in the original P-ALICE is based on the assumption that the number of training samples to gather is small, which is not always true in practice. In this paper, we propose an alternative scheme for importance estimation based on the inclusion probability, and show its validity through numerical experiments.