Semi-supervised Active Linear Regression

Labeled data often comes at a high cost as it may require recruiting human labelers or running costly experiments. At the same time, in many practical scenarios, one already has access to a partially labeled, potentially biased dataset that can help with the learning task at hand. Motivated by such settings, we formally initiate a study of ``semi-supervised active learning'' through the frame of linear regression. Here, the learner has access to a dataset $X \in \mathbb{R}^{(n_{\text{un}}+n_{\text{lab}}) \times d}$ composed of $n_{\text{un}}$ unlabeled examples that a learner can actively query, and $n_{\text{lab}}$ examples labeled a priori.