A Scalable Laplace Approximation for Neural Networks
We leverage recent insights from second-order optimisation for neural networks to construct a Kronecker factored Laplace approximation to the posterior over the weights of a trained network. Our approximation requires no modification of the training procedure, enabling practitioners to estimate the uncertainty of their models currently used in production without having to retrain them. We extensively compare our method to using Dropout and a diagonal Laplace approximation for estimating the uncertainty of a network. We demonstrate that our Kronecker factored method leads to better uncertainty estimates on out-of-distribution data and is more robust to simple adversarial attacks. Our approach only requires calculating two square curvature factor matrices for each layer. Their size is equal to the respective square of the input and output size of the layer, making the method efficient both computationally and in terms of memory usage. We illustrate its scalability by applying it to a state-of-the-art convolutional network architecture.
 This paper proposes a Laplace approximation to approximate the posterior distribution over the parameters of deep networks. The idea is interesting and the realization of the paper is good. The idea builds upon previous work in scalable Gauss-Newton methods for optimization in deep networks, notably Botev et al., ICML 2017. In this respect, I think that the novelty in the current submission is limited, as the approximation is essentially what proposed in Botev et al., ICML 2017. The Laplace approximation requires the Hessian of the posterior, so techniques developed for Gauss-Newton optimization can straightforwardly be applied to construct Laplace approximations. Having said that, the experimental evaluation is quite interesting and in-depth. I think it would have been interesting to report comparisons with factorized variational inference (Graves, 2011) as it is a fairly standard and widely adopted in Bayesian deep learning. This would have been an interesting way to support the claims on the poor approximation offered by standard variational inference. I believe that the independence assumption across layers is a limiting factor of the proposed approximation strategy. Intuitively, changes in the weights in a given layer should affect the weights in other layers, so I would expect the posterior distribution over all the weights to reflect this through correlations across layers. I wonder how these results can be generalized to relax the independence assumption.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A Scalable Laplace Approximation for Neural Networks
We leverage recent insights from second-order optimisation for neural networks to construct a Kronecker factored Laplace approximation to the posterior over the weights of a trained network. Our approximation requires no modification of the training procedure, enabling practitioners to estimate the uncertainty of their models currently used in production without having to retrain them. We extensively compare our method to using Dropout and a diagonal Laplace approximation for estimating the uncertainty of a network. We demonstrate that our Kronecker factored method leads to better uncertainty estimates on out-of-distribution data and is more robust to simple adversarial attacks. Our approach only requires calculating two square curvature factor matrices for each layer. Their size is equal to the respective square of the input and output size of the layer, making the method efficient both computationally and in terms of memory usage. We illustrate its scalability by applying it to a state-of-the-art convolutional network architecture.
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>



 This paper proposes a Laplace approximation to approximate the posterior distribution over the parameters of deep networks. The idea is interesting and the realization of the paper is good. The idea builds upon previous work in scalable Gauss-Newton methods for optimization in deep networks, notably Botev et al., ICML 2017. In this respect, I think that the novelty in the current submission is limited, as the approximation is essentially what proposed in Botev et al., ICML 2017. The Laplace approximation requires the Hessian of the posterior, so techniques developed for Gauss-Newton optimization can straightforwardly be applied to construct Laplace approximations. Having said that, the experimental evaluation is quite interesting and in-depth. I think it would have been interesting to report comparisons with factorized variational inference (Graves, 2011) as it is a fairly standard and widely adopted in Bayesian deep learning. This would have been an interesting way to support the claims on the poor approximation offered by standard variational inference. I believe that the independence assumption across layers is a limiting factor of the proposed approximation strategy. Intuitively, changes in the weights in a given layer should affect the weights in other layers, so I would expect the posterior distribution over all the weights to reflect this through correlations across layers. I wonder how these results can be generalized to relax the independence assumption.
assistant
 This paper proposes a Laplace approximation to approximate the posterior distribution over the parameters of deep networks. The idea is interesting and the realization of the paper is good. The idea builds upon previous work in scalable Gauss-Newton methods for optimization in deep networks, notably Botev et al., ICML 2017. In this respect, I think that the novelty in the current submission is limited, as the approximation is essentially what proposed in Botev et al., ICML 2017. The Laplace approximation requires the Hessian of the posterior, so techniques developed for Gauss-Newton optimization can straightforwardly be applied to construct Laplace approximations. Having said that, the experimental evaluation is quite interesting and in-depth. I think it would have been interesting to report comparisons with factorized variational inference (Graves, 2011) as it is a fairly standard and widely adopted in Bayesian deep learning. This would have been an interesting way to support the claims on the poor approximation offered by standard variational inference. I believe that the independence assumption across layers is a limiting factor of the proposed approximation strategy. Intuitively, changes in the weights in a given layer should affect the weights in other layers, so I would expect the posterior distribution over all the weights to reflect this through correlations across layers. I wonder how these results can be generalized to relax the independence assumption.