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 is an element of R-(n (+n lab))(un) (x) (d) composed of n(un) unlabeled examples that a learner can actively query, and n lab examples labeled a priori. Denoting the true labels by Y is an element of R-n (+n lab)(un), the learner's objective is to find (beta) over cap is an element of Rd such that,