This manuscript proposes a novel method for Bayesian batch active learning through sparse subset approximation and a convenient set of reductions to arrive at a tractable algorithm. This method is validated and explored through a series of special cases (linear regression and classification), illustrations, and experiments. Overall the method appears to be competitive with the state of the art. Overall this manuscript is well written, insightful, and enjoyable to read. The proposed approach outlined on page 3 is elegant, appears to work well in practice, and the approach may be useful in other settings.

The reviewers concluded that this paper offers valuable contributions and addresses an important practical problem. The authors also conduct an extensive set of experiments. However, I would strongly encourage the authors to consider the baseline suggested by R2, which is simple and requested by all other reviewers. A second baseline worth considering is to phantasize evaluation, akin what folks to do in Bayesian optmization. While this would not be attractive computationally, it encourages diverse batches. It would be interesting to see how the proposed method compares to this.

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters.

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters.