Bayesian Uncertainty Estimation for Batch Normalized Deep Networks
Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance.
 *Summary* The paper proposes using batch normalisation at test time to get the predictive uncertainty. The stochasticity of the prediction comes from different minibatches of training data that were used to normalise the activity/pre-activation values at each layer. This is justified by an argument that using batch norm is doing variational inference, so one should use the approximate posterior provided by batch norm at prediction time. Several experiments show Monte Carlo prediction at test time using batch norm is better than dropout. *Originality and significance* As far as I understand, almost learning algorithms similar to equation 2 can be recast as variational inference under equation 1. However, the critical questions are what is the corresponding prior, what is the approximating density, what are the additional approximations to obtain 2, and whether the approximation is a good approximation for getting closer to the posterior/obtain better prediction. It is not clear to me from the presentation what the q(w) density is -- whether this is explicit (as in vanilla Gaussian VI or MC dropout), or implicit (the stochasticity on the activity h due to batch norm induces an equivalence q on w). From a Bayesian perspective, it is also not satisfying to ignore the regularisation term by an empirical heuristic provided in the batch norm paper [small .lambda] -- what is the rationale of this? Can this be explained by comparing the variational free-energy. The experiments also do not compare to modern variational inference methods using the reparameterisation trick with Gaussian variational approximations (see Blundell et al 2016) or richer variational families (see e.g. Louizos and Welling, 2016, 2017). The VI method included in the PBP paper (Hernandez-Lobato and Adams, 2015) does not use the reparameterisation trick, which has been found to reduce variance and improve over Graves* VI method. *Clarity* The paper is in general well written and easy to understand. *Additional comments* Page 2: Monte Carlo Droput --> Dropout Page 3 related work: (Adams, 2015) should be (Hernandez-Lobato and Adams, 2015)
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Bayesian Uncertainty Estimation for Batch Normalized Deep Networks
Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance.
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>



 *Summary* The paper proposes using batch normalisation at test time to get the predictive uncertainty. The stochasticity of the prediction comes from different minibatches of training data that were used to normalise the activity/pre-activation values at each layer. This is justified by an argument that using batch norm is doing variational inference, so one should use the approximate posterior provided by batch norm at prediction time. Several experiments show Monte Carlo prediction at test time using batch norm is better than dropout. *Originality and significance* As far as I understand, almost learning algorithms similar to equation 2 can be recast as variational inference under equation 1. However, the critical questions are what is the corresponding prior, what is the approximating density, what are the additional approximations to obtain 2, and whether the approximation is a good approximation for getting closer to the posterior/obtain better prediction. It is not clear to me from the presentation what the q(w) density is -- whether this is explicit (as in vanilla Gaussian VI or MC dropout), or implicit (the stochasticity on the activity h due to batch norm induces an equivalence q on w). From a Bayesian perspective, it is also not satisfying to ignore the regularisation term by an empirical heuristic provided in the batch norm paper [small .lambda] -- what is the rationale of this? Can this be explained by comparing the variational free-energy. The experiments also do not compare to modern variational inference methods using the reparameterisation trick with Gaussian variational approximations (see Blundell et al 2016) or richer variational families (see e.g. Louizos and Welling, 2016, 2017). The VI method included in the PBP paper (Hernandez-Lobato and Adams, 2015) does not use the reparameterisation trick, which has been found to reduce variance and improve over Graves* VI method. *Clarity* The paper is in general well written and easy to understand. *Additional comments* Page 2: Monte Carlo Droput --> Dropout Page 3 related work: (Adams, 2015) should be (Hernandez-Lobato and Adams, 2015)
assistant
 *Summary* The paper proposes using batch normalisation at test time to get the predictive uncertainty. The stochasticity of the prediction comes from different minibatches of training data that were used to normalise the activity/pre-activation values at each layer. This is justified by an argument that using batch norm is doing variational inference, so one should use the approximate posterior provided by batch norm at prediction time. Several experiments show Monte Carlo prediction at test time using batch norm is better than dropout. *Originality and significance* As far as I understand, almost learning algorithms similar to equation 2 can be recast as variational inference under equation 1. However, the critical questions are what is the corresponding prior, what is the approximating density, what are the additional approximations to obtain 2, and whether the approximation is a good approximation for getting closer to the posterior/obtain better prediction. It is not clear to me from the presentation what the q(w) density is -- whether this is explicit (as in vanilla Gaussian VI or MC dropout), or implicit (the stochasticity on the activity h due to batch norm induces an equivalence q on w). From a Bayesian perspective, it is also not satisfying to ignore the regularisation term by an empirical heuristic provided in the batch norm paper [small .lambda] -- what is the rationale of this? Can this be explained by comparing the variational free-energy. The experiments also do not compare to modern variational inference methods using the reparameterisation trick with Gaussian variational approximations (see Blundell et al 2016) or richer variational families (see e.g. Louizos and Welling, 2016, 2017). The VI method included in the PBP paper (Hernandez-Lobato and Adams, 2015) does not use the reparameterisation trick, which has been found to reduce variance and improve over Graves* VI method. *Clarity* The paper is in general well written and easy to understand. *Additional comments* Page 2: Monte Carlo Droput --> Dropout Page 3 related work: (Adams, 2015) should be (Hernandez-Lobato and Adams, 2015)