Empirical confidence estimates for classification by deep neural networks
How well can we estimate the probability that the classification predicted by a deep neural network is correct (or in the Top 5)? It is well-known that the softmax values of the network are not estimates of the probabilities of class labels. However, there is a misconception that these values are not informative. We define the notion of implied loss and prove that if an uncertainty measure is an implied loss, then low uncertainty means high probability of correct (or Top-k) classification on the test set. We demonstrate empirically that these values can be used to measure the confidence that the classification is correct. Our method is simple to use on existing networks: we proposed confidence measures for Top-k which can be evaluated by binning values on the test set.
The paper provides a comparison of several uncertainty measures that have been proposed for neural networks. The goal of the work is to alleviate the lack of clear interpretability of softmax outputs as measures of uncertainty in neural networks for multi-class classification (in particular, here image classification). The authors propose the use of expected Bayes factors as aggregate measures of how much information is conveyed by a measure of uncertainty, and compares several proposed approaches based on this measure on CIFAR-10/100 and ImageNet-1k. The authors also discuss the application of uncertainty measures to detect mislabeled or ambiguous images, detecting out-of-distribution samples and adversarial examples. Passing by, the authors propose a measure based on the norm of the gradient to detect adversarial examples that seems to work well. There are interesting ideas in the paper. The use of Bayes factors for measuring the quality of the uncertainty estimates, and the comparison of various existing methods on that measure seems useful. The experiments on various tasks also have their own merits.The extension to top-k uncertainty is also interesting. On the other hand, I found the paper difficult to follow because the contributions are scattered over the paper and the appendices without clear link. A lot of space is devoted to the definition of the implied risk, which does not bring much to the overall interpretation of the results. The criterion for detecting adversarial examples based on the norm of the gradient appears at the end of the paper somewhat independently from what was before, and the definition and computation of the Expected Bayes factor is entirely deferred to Appendices, which makes the main paper not really self-contained. The paper also lacks a conclusion. The various uncertainty measures seem to perform differently depending on the datasets, and it is unclear what the authors recommend in the end. Overall, it seems to me that with a bit of restructuration, the paper would be an interesting contribution -- for instance in terms of the assessment of dropout variance vs direct model entropy. It seems to me though that for now the paper lacks coherence and clarity in the message. ====== after author rebuttal The rebuttal answer most of my concerns, and I raised my score to weak accept. Overall, even if there is no clear evidence that one method to evaluate uncertainty is consistently better than the others, I feel that the idea of using Bayes factors to compare uncertainty measures is possibly impactful.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Empirical confidence estimates for classification by deep neural networks
How well can we estimate the probability that the classification predicted by a deep neural network is correct (or in the Top 5)? It is well-known that the softmax values of the network are not estimates of the probabilities of class labels. However, there is a misconception that these values are not informative. We define the notion of implied loss and prove that if an uncertainty measure is an implied loss, then low uncertainty means high probability of correct (or Top-k) classification on the test set. We demonstrate empirically that these values can be used to measure the confidence that the classification is correct. Our method is simple to use on existing networks: we proposed confidence measures for Top-k which can be evaluated by binning values on the test set.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The paper provides a comparison of several uncertainty measures that have been proposed for neural networks. The goal of the work is to alleviate the lack of clear interpretability of softmax outputs as measures of uncertainty in neural networks for multi-class classification (in particular, here image classification). The authors propose the use of expected Bayes factors as aggregate measures of how much information is conveyed by a measure of uncertainty, and compares several proposed approaches based on this measure on CIFAR-10/100 and ImageNet-1k. The authors also discuss the application of uncertainty measures to detect mislabeled or ambiguous images, detecting out-of-distribution samples and adversarial examples. Passing by, the authors propose a measure based on the norm of the gradient to detect adversarial examples that seems to work well. There are interesting ideas in the paper. The use of Bayes factors for measuring the quality of the uncertainty estimates, and the comparison of various existing methods on that measure seems useful. The experiments on various tasks also have their own merits.The extension to top-k uncertainty is also interesting. On the other hand, I found the paper difficult to follow because the contributions are scattered over the paper and the appendices without clear link. A lot of space is devoted to the definition of the implied risk, which does not bring much to the overall interpretation of the results. The criterion for detecting adversarial examples based on the norm of the gradient appears at the end of the paper somewhat independently from what was before, and the definition and computation of the Expected Bayes factor is entirely deferred to Appendices, which makes the main paper not really self-contained. The paper also lacks a conclusion. The various uncertainty measures seem to perform differently depending on the datasets, and it is unclear what the authors recommend in the end. Overall, it seems to me that with a bit of restructuration, the paper would be an interesting contribution -- for instance in terms of the assessment of dropout variance vs direct model entropy. It seems to me though that for now the paper lacks coherence and clarity in the message. ====== after author rebuttal The rebuttal answer most of my concerns, and I raised my score to weak accept. Overall, even if there is no clear evidence that one method to evaluate uncertainty is consistently better than the others, I feel that the idea of using Bayes factors to compare uncertainty measures is possibly impactful.
assistant
The paper provides a comparison of several uncertainty measures that have been proposed for neural networks. The goal of the work is to alleviate the lack of clear interpretability of softmax outputs as measures of uncertainty in neural networks for multi-class classification (in particular, here image classification). The authors propose the use of expected Bayes factors as aggregate measures of how much information is conveyed by a measure of uncertainty, and compares several proposed approaches based on this measure on CIFAR-10/100 and ImageNet-1k. The authors also discuss the application of uncertainty measures to detect mislabeled or ambiguous images, detecting out-of-distribution samples and adversarial examples. Passing by, the authors propose a measure based on the norm of the gradient to detect adversarial examples that seems to work well. There are interesting ideas in the paper. The use of Bayes factors for measuring the quality of the uncertainty estimates, and the comparison of various existing methods on that measure seems useful. The experiments on various tasks also have their own merits.The extension to top-k uncertainty is also interesting. On the other hand, I found the paper difficult to follow because the contributions are scattered over the paper and the appendices without clear link. A lot of space is devoted to the definition of the implied risk, which does not bring much to the overall interpretation of the results. The criterion for detecting adversarial examples based on the norm of the gradient appears at the end of the paper somewhat independently from what was before, and the definition and computation of the Expected Bayes factor is entirely deferred to Appendices, which makes the main paper not really self-contained. The paper also lacks a conclusion. The various uncertainty measures seem to perform differently depending on the datasets, and it is unclear what the authors recommend in the end. Overall, it seems to me that with a bit of restructuration, the paper would be an interesting contribution -- for instance in terms of the assessment of dropout variance vs direct model entropy. It seems to me though that for now the paper lacks coherence and clarity in the message. ====== after author rebuttal The rebuttal answer most of my concerns, and I raised my score to weak accept. Overall, even if there is no clear evidence that one method to evaluate uncertainty is consistently better than the others, I feel that the idea of using Bayes factors to compare uncertainty measures is possibly impactful.