Confidence Calibration in Deep Neural Networks through Stochastic Inferences
We propose a generic framework to calibrate accuracy and confidence (score) of a prediction through stochastic inferences in deep neural networks. We first analyze relation between variation of multiple model parameters for a single example inference and variance of the corresponding prediction scores by Bayesian modeling of stochastic regularization. Our empirical observation shows that accuracy and score of a prediction are highly correlated with variance of multiple stochastic inferences given by stochastic depth or dropout. Motivated by these facts, we design a novel variance-weighted confidence-integrated loss function that is composed of two cross-entropy loss terms with respect to ground-truth and uniform distribution, which are balanced by variance of stochastic prediction scores. The proposed loss function enables us to learn deep neural networks that predict confidence calibrated scores using a single inference. Our algorithm presents outstanding confidence calibration performance and improves classification accuracy with two popular stochastic regularization techniques---stochastic depth and dropout---in multiple models and datasets; it alleviates overconfidence issue in deep neural networks significantly by training networks to achieve prediction accuracy proportional to confidence of prediction.
 The authors propose a generic framework to calibrate predictions in deep-neural-network-based classifiers. They do this using a new variance-weighted loss function that does not introduce additional (hyper-)parameters. Results on various datasets using various architectures demonstrate how the framework result in models with well calibrated predictions, i.e., not under or overconfident probabilistic estimates of labels. In Section 3.3, .theta is, I think, not a deterministic parameter, though the authors may refer to the fact that it is learned as a point estimate. Equation (7) should be conditioned on .theta. In section 3.3, expected predictions and their variances can be approximated by MC not "calculated" as the authors write. In Figure 1 (right), the authors should use the same range for x and y axis to make more evident that the models are poorly calibrated. A diagonal line may also make the deviations from perfect calibration easier to see. In Section 4.2, the authors do not provide a theoretical justification for the choice of the variances as the weights for the loss function in (9). Other than that the proposed loss is very similar to that in (10). Also the authors do not properly justify/discuss the use of the Bhattacharyya coefficient as the variance metric or why T=5 samples are enough to get a good estimate of .alpha. The experiments although relatively extensive are not very convincing because results in Table 1 are to be expected (given CI is an average of multiple .beta values), and Table 2 shows that TS case 2 has better calibration results (ECE) than VWCI, although VWCI has in general better accuracy (at the cost of some calibration loss). It is not clear why the authors do not show calibration plots like in Figure 1(right) or Figure 4 in Guo et al, 2017.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Confidence Calibration in Deep Neural Networks through Stochastic Inferences
We propose a generic framework to calibrate accuracy and confidence (score) of a prediction through stochastic inferences in deep neural networks. We first analyze relation between variation of multiple model parameters for a single example inference and variance of the corresponding prediction scores by Bayesian modeling of stochastic regularization. Our empirical observation shows that accuracy and score of a prediction are highly correlated with variance of multiple stochastic inferences given by stochastic depth or dropout. Motivated by these facts, we design a novel variance-weighted confidence-integrated loss function that is composed of two cross-entropy loss terms with respect to ground-truth and uniform distribution, which are balanced by variance of stochastic prediction scores. The proposed loss function enables us to learn deep neural networks that predict confidence calibrated scores using a single inference. Our algorithm presents outstanding confidence calibration performance and improves classification accuracy with two popular stochastic regularization techniques---stochastic depth and dropout---in multiple models and datasets; it alleviates overconfidence issue in deep neural networks significantly by training networks to achieve prediction accuracy proportional to confidence of prediction.
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 authors propose a generic framework to calibrate predictions in deep-neural-network-based classifiers. They do this using a new variance-weighted loss function that does not introduce additional (hyper-)parameters. Results on various datasets using various architectures demonstrate how the framework result in models with well calibrated predictions, i.e., not under or overconfident probabilistic estimates of labels. In Section 3.3, .theta is, I think, not a deterministic parameter, though the authors may refer to the fact that it is learned as a point estimate. Equation (7) should be conditioned on .theta. In section 3.3, expected predictions and their variances can be approximated by MC not "calculated" as the authors write. In Figure 1 (right), the authors should use the same range for x and y axis to make more evident that the models are poorly calibrated. A diagonal line may also make the deviations from perfect calibration easier to see. In Section 4.2, the authors do not provide a theoretical justification for the choice of the variances as the weights for the loss function in (9). Other than that the proposed loss is very similar to that in (10). Also the authors do not properly justify/discuss the use of the Bhattacharyya coefficient as the variance metric or why T=5 samples are enough to get a good estimate of .alpha. The experiments although relatively extensive are not very convincing because results in Table 1 are to be expected (given CI is an average of multiple .beta values), and Table 2 shows that TS case 2 has better calibration results (ECE) than VWCI, although VWCI has in general better accuracy (at the cost of some calibration loss). It is not clear why the authors do not show calibration plots like in Figure 1(right) or Figure 4 in Guo et al, 2017.
assistant
 The authors propose a generic framework to calibrate predictions in deep-neural-network-based classifiers. They do this using a new variance-weighted loss function that does not introduce additional (hyper-)parameters. Results on various datasets using various architectures demonstrate how the framework result in models with well calibrated predictions, i.e., not under or overconfident probabilistic estimates of labels. In Section 3.3, .theta is, I think, not a deterministic parameter, though the authors may refer to the fact that it is learned as a point estimate. Equation (7) should be conditioned on .theta. In section 3.3, expected predictions and their variances can be approximated by MC not "calculated" as the authors write. In Figure 1 (right), the authors should use the same range for x and y axis to make more evident that the models are poorly calibrated. A diagonal line may also make the deviations from perfect calibration easier to see. In Section 4.2, the authors do not provide a theoretical justification for the choice of the variances as the weights for the loss function in (9). Other than that the proposed loss is very similar to that in (10). Also the authors do not properly justify/discuss the use of the Bhattacharyya coefficient as the variance metric or why T=5 samples are enough to get a good estimate of .alpha. The experiments although relatively extensive are not very convincing because results in Table 1 are to be expected (given CI is an average of multiple .beta values), and Table 2 shows that TS case 2 has better calibration results (ECE) than VWCI, although VWCI has in general better accuracy (at the cost of some calibration loss). It is not clear why the authors do not show calibration plots like in Figure 1(right) or Figure 4 in Guo et al, 2017.