Paper:
Ensembling multiple predictions is a widely-used technique to improve the accuracy of various machine learning tasks. In image classification tasks, for example, averaging the predictions for multiple patches extracted from the input image significantly improves accuracy. Using multiple networks trained independently to make predictions improves accuracy further. One obvious drawback of the ensembling technique is its higher execution cost during inference.This higher cost limits the real-world use of ensembling. In this paper, we first describe our insights on relationship between the probability of the prediction and the effect of ensembling with current deep neural networks; ensembling does not help mispredictions for inputs predicted with a high probability, i.e. the output from the softmax. This finding motivates us to develop a new technique called adaptive ensemble prediction, which achieves the benefits of ensembling with much smaller additional execution costs. Hence, we calculate the confidence level of the prediction for each input from the probabilities of the local predictions during the ensembling computation. If the prediction for an input reaches a high enough probability on the basis of the confidence level, we stop ensembling for this input to avoid wasting computation power. We evaluated the adaptive ensembling by using various datasets and showed that it reduces the computation cost significantly while achieving similar accuracy to the naive ensembling. We also showed that our statistically rigorous confidence-level-based termination condition reduces the burden of the task-dependent parameter tuning compared to the naive termination based on the pre-defined threshold in addition to yielding a better accuracy with the same cost.

Review:
The authors propose and evaluate an adaptive ensembling threshold using estimated confidence intervals from the t-distribution, rather than a static confidence level threshold. They show it can provide significant improvements in accuracy at the same cost as a naive threshold.
This paper has a nice simple idea at its core, but I don't think it's fully developed. There's a few major conceptual issues going on:
- The authors propose equation (3) as a stopping criterion because "computing CIs for all labels is costly." I don't see how this is true in any sense. The CI computation is literally just averages of a few numbers, which should be way less than the massive matrix multiplies needed to *generate* those numbers in the neural network. Computing pair-wise comparisons naively in O(n^2) time could potentially blow up if the number of output labels is massive, but then you should still be able to keep some running statistics to avoid having to do a quadratic number of comparisons (e.g. the threshold is just the highest bound of any CI you encounter, so you keep track of both the max predicted confidence and max CI so far...then you have your answer in O(n) time.) I think the real issue is that the authors state that the confidence interval computation code is written in Python. That is a huge knock against this paper: When writing a paper about inference time, it's just due diligence to do the most basic inference time optimizations (such as implementing an operation which should be effectively free in a C++ plugin.) 
- So by using (3) instead of the original proposed CI comparison that motivated this approach, the authors require that the predicted probability be greater than 1/2 + the CI at the given alpha level. This means that for problems with very large output spaces, getting enough probability mass to get over that 1/2 absolute threshold is potentially going to require a minimum number of evaluations and put a cap on the efficiency gain. This is what we see in Figure 3: for the few points evaluated, when the output space is large (ILSVRC 2012) there is no effective difference between the proposed method and a static threshold of 70%, indicating that the CI of 90% is roughly working out to be the 50% minimum + ~20% threshold from the CI. 
- Thus the experiments in this paper don't really add much value in understanding the benefits of this approach as currently written. For due diligence, there should be the following:
1. Show the distribution of computing thresholds from the CI.  Then compute, for a CI of 0.8, 0.9, etc., what is the effective threshold on average? Then for every *average threshold* from the CI method, apply that as a static threshold. Then you will get exactly the delta of your method over the static threshold method.
2. Do the same, but using the pairwise CI comparison method. 
3. The same again, but now show how effective this is as a function of the size of the output label space.  E.g. add these numbers to Table 1 and Table 2 (for every "our adaptive ensemble", put the equivalent static threshold.)
4. Implement the CI computation efficiently if you are going to report actual runtimes. Note that for a paper like this, I don't think the runtimes are as important as the # of evaluations in the ensemble, so this is less important.
- With the above experiments I think this would be a good paper.