Functional Bayesian Neural Networks for Model Uncertainty Quantification
In this paper, we extend the Bayesian neural network to functional Bayesian neural network with functional Monte Carlo methods that use the samples of functionals instead of samples of networks* parameters for inference to overcome the curse of dimensionality for uncertainty quantification. Based on the previous work on Riemannian Langevin dynamics, we propose the stochastic gradient functional Riemannian dynamics for training functional Bayesian neural network. We show the effectiveness and efficiency of our proposed approach with various experiments.
 The idea of extending Riemannian Langevin dynamics to functional spaces is elegant, however it is extremely hard to follow the proposed method as details are kept to a minimum. The finite approximation of the posterior distribution is a function of the parameters theta, however it displays parameters lambda. The couple of sentences: "Then by sampling λ, we sample a functional f equivalently. The Riemannian Langevin dynamics on the functional space can thus be written as: (6)" come without a single explanation. Minor comments * Max and Whye is the casual version for reference Welling and Teh. * proper nouns in References should be capitalized
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Functional Bayesian Neural Networks for Model Uncertainty Quantification
In this paper, we extend the Bayesian neural network to functional Bayesian neural network with functional Monte Carlo methods that use the samples of functionals instead of samples of networks* parameters for inference to overcome the curse of dimensionality for uncertainty quantification. Based on the previous work on Riemannian Langevin dynamics, we propose the stochastic gradient functional Riemannian dynamics for training functional Bayesian neural network. We show the effectiveness and efficiency of our proposed approach with various experiments.
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<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 idea of extending Riemannian Langevin dynamics to functional spaces is elegant, however it is extremely hard to follow the proposed method as details are kept to a minimum. The finite approximation of the posterior distribution is a function of the parameters theta, however it displays parameters lambda. The couple of sentences: "Then by sampling λ, we sample a functional f equivalently. The Riemannian Langevin dynamics on the functional space can thus be written as: (6)" come without a single explanation. Minor comments * Max and Whye is the casual version for reference Welling and Teh. * proper nouns in References should be capitalized
assistant
 The idea of extending Riemannian Langevin dynamics to functional spaces is elegant, however it is extremely hard to follow the proposed method as details are kept to a minimum. The finite approximation of the posterior distribution is a function of the parameters theta, however it displays parameters lambda. The couple of sentences: "Then by sampling λ, we sample a functional f equivalently. The Riemannian Langevin dynamics on the functional space can thus be written as: (6)" come without a single explanation. Minor comments * Max and Whye is the casual version for reference Welling and Teh. * proper nouns in References should be capitalized