in the related work and the experiments. If some of these concerns would be addressed in the rebuttal, I would be willing to upgrade my recommended score. Strengths: - The results seem to be correct. - In contrast to Huggins et al. (2016) and Tolochinsky & Feldman (2018), the coreset guarantee applies to the standard loss function of logistic regression and not to variations. - The (theoretical) algorithm (without the sketching algorithm for the QR decomposition) seems simple and practical. If space permits, the authors might consider explicitly specifying the algorithm in pseudo-code (so that practitioners do not have to extract it from the Theorems). - The authors include in the Supplementary Materials an example where uniform sampling fails even if the complexity parameter mu is bounded. - The authors show that the proposed approach obtains a better trade-off between error and absolute running time than uniform sampling and the approach by Huggins et al. (2016). Weaknesses: - Novelty: The sensitivity bound in this paper seems very similar to the one presented in [1] which is not cited in the manuscript. The paper [1] also uses a mix between sampling according to the data point weights and the l2-sampling with regards to the mean of the data to bound the sensitivity and then do importance sampling. Clearly, this paper treats a different problem (logistic regression vs k-means clustering) and has differences. However, this submission would be strengthened if the proposed approach would be compared to the one in [1]. In particular, I wonder if the idea of both additive and multiplicative errors in [1] could be applied in this paper (instead of restricting mu-complexity) to arrive at a coreset construction that does not require any assumptions on the data data set. [1] Scalable k-Means Clustering via Lightweight Coresets Olivier Bachem, Mario Lucic and Andreas Krause To Appear In International Conference on Knowledge Discovery and Data Mining (KDD), 2018. - Practical significance: The paper only contains a limited set of experiments, i.e., few data sets and no comparison to Tolochinsky & Feldman (2018). Furthermore, the paper does not compare against any non-coreset based approaches, e.g., SGD, SDCA, SAGA, and friends. It is not clear whether the proposed approach is useful in practice compared to these approaches. - Figure 1 would be much stronger if there were error bars and/or if there were more random trials that would (potentially) get rid of some of the (most likely) random fluctuations in the results.
- Figure 1 would be much stronger if there were error bars and/or if there were more random trials that would (potentially) get rid of some of the (most likely) random fluctuations in the results.