Paper:
Active Bias: Training More Accurate Neural Networks by Emphasizing High Variance Samples
Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD): the variance in predicted probability of the correct class across iterations of minibatch SGD, and the proximity of the correct class probability to the decision threshold. Extensive experimental results on six datasets show that our methods reliably improve accuracy in various network architectures, including additional gains on top of other popular training techniques, such as residual learning, momentum, ADAM, batch normalization, dropout, and distillation.
other times, as illustrated in Figure 1. This preference is consistent with common variance reduction strategies in active learning [43].
Previous studies suggest that finding informative unlabeled samples to label is related to selecting already-labeled samples to optimize the model parameters [14]. As reported in the previous studies [42,6], models can sometimes achieve lower generalization error after being trained with only a subset of actively selected training data. In other words, focusing on informative samples can be beneficial even when all labels are available.
We propose two lightweight methods that actively emphasize uncertain samples to improve minibatch SGD for classification. One method measures the variance of prediction probabilities, while the other one estimates the closeness between the prediction probabilities and the decision threshold. For logistic regression, both methods can be proven to reduce the uncertainty in the model parameters under reasonable approximations.
We present extensive experiments on CIFAR 10, CIFAR 100, MNIST (image classification), Question Type (sentence classification), CoNLL 2003, and OntoNote 5.0 (Named entity Recognition), as well as on different architectures, including multiple class logistic regression, fully-connected networks, convolutional neural networks (CNNs) [26], and residual networks [16]. The results show that active bias makes neural networks more robust without prior knowledge of noise, and reduces the generalization error by 1% -18% even on training sets having few (if any) annotation errors.

Review:
The paper proposes a novel way of sampling (or weighing) data-points during training of neural networks. The idea is, that one would like to sample data-point more often which could be potentially classified well but are hard to learn (in contrast to outliers or wrongly labeled ones). To `find' them the authors propose two (four if split into sampling and weighing) schemes: The first one (SGD-*PV) proposes to weigh data-points according to the variance of the predictive probability of the true label plus its confidence interval under the assumption that the prediction probability is Gaussian distributed. The second one (SGD-*TC), as far as I understand, encodes if the probability of choosing the correct label given past prediction probabilities is close to the decision threshold. 
The statistics needed (means and variances of p) can be computed on-the-fly during a burn-in phase of the optimizer; they can be obtained from a forward pass of the network which is computed anyways. The authors test their methods on various architectures and dataset and compare to a range of baselines.
The paper motivates the problem well and the introduction is clearly written (Figure 1 is very helpful, too). The technical sections 3.2 (up to the logReg example) and 3.3 are very dense;  moving table 1 (and or 2) to the appendix and elaborating a bit more (especially on 3.3) would be very helpful.
Major Questions:
- I do not understand how SGD-*PV prefers uncertain example over hard ones, i.e. why should hard samples have lower predictive variance than uncertain ones? Hard ones might be labeled incorrectly, but the probability might still fluctuate.
- In 3.3 P(i|H, S_e, D) is largest around \bar{p}=0.5. Does that mean the method implicitly assumes 2 output classes only? If not, I would like to know how P encodes closeness to a threshold for multiple classes.
- In 3.2 the authors assume that p is Gaussian distributed. Is this meant across occurrences in the mini-batch? I would also like the authors to comment a bit more on this assumption, also since clearly p is not Gaussian distributed (it ranges between 0 and 1). Would it be possible to impose this assumption on log(p) instead to get a better fit?
- how many samples do you typically collect for p? as many as epochs? is this the reason you need a burn in time? or is there another reason why it is good to first burn-in and then start the proposed sampling/weighing schemes?
Further comments:
- since the authors propose a practical algorithm it would be nice to include a sentence about memory requirement or other non-trivial implementation details (in case there are some). 
- As mentioned above, I encourage the authors to expand the technical section (3.2 before the logReg example and especially 3.3) since it is very dense.
- It is very nice that the authors compare against many baselines
- It is nice that the authors are transparent about how the learning rates etc. are chosen.
(*after rebuttal*: The rebuttal clarified most of my questions. If the paper gets accepted I encourage the authors to also clarity the points in the paper (to eases the reading process) as they promise in the rebuttal, especially i) the presentation above the logistic regression example in Section 3.2 (maybe a pointer that the assumptions will be discussed below). At that point they are quite ad-hoc and it is hard (and not beneficial for the flow of thoughts) to trace back later ii) closeness to threshold: recap shortly what \bar{p} was (it took me a while to find it again) iii) the meaning of the burn-in phase. iv) A sentence about implementation which points to the Appendix. In good faith that this will be done I increased the score.)