Pool-based active learning in approximate linear regression

The goal of pool-based active learning is to choose the best input points to gather output values from a 'pool' of input samples. We develop two pool-based active learning criteria for linear regression. The first criterion allows us to obtain a closed-form solution so it is computationally very efficient. However, this solution is not necessarily optimal in the single-trial generalization error analysis. The second criterion can give a better solution, but it does not have a closed-form solution and therefore some additional search strategy is needed. To cope with this problem, we propose a practical procedure which enables us to efficiently search for a better solution around the optimal solution of the first method. Simulations with toy and benchmark datasets show that the proposed active learning method compares favorably with other active learning methods as well as the baseline passive learning scheme. Furthermore, the usefulness of the proposed active learning method is also demonstrated in wafer alignment in semiconductor exposure apparatus.