Accelerating Monte Carlo Bayesian Inference via Approximating Predictive Uncertainty over the Simplex
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always intractable, most efforts were made on finding an accurate approximation the true posterior. Even though a decent estimation of the model posterior is obtained, another approximation is required to compute the predictive distribution over the desired output. A common accurate solution is to use Monte Carlo (MC) integration. However, it needs to maintain a large number of samples, evaluate the model repeatedly and average multiple model outputs. In many real-world cases, this is computationally prohibitive. In this work, assuming that the exact posterior or a decent approximation is obtained, we propose a generic framework to approximate the output probability distribution induced by model posterior with a parameterized model and in an amortized fashion. The aim is to approximate the true uncertainty of a specific Bayesian model, meanwhile alleviating the heavy workload of MC integration at testing time. The proposed method is universally applicable to Bayesian classification models that allow for posterior sampling. Theoretically, we show that the idea of amortization incurs no additional costs on approximation performance. Empirical results validate the strong practical performance of our approach.
This paper studies the problem of avoiding Monte Carlo (MC) estimate for the predictive distribution during the test for Bayesian methods. MC estimate will incur multiple passes where the number of passes depends on the number of samples and therefore the cost can be huge. The authors propose One-Pass Uncertainty (OPU) methods to approximate the predictive distribution through distillation. Experiments on Bayesian neural networks are conducted to demonstrate the proposed method. Quality: The proposed method appears to be technically sound. The view of approximating the predictive distribution over simplex is interesting and may inspire future studies under this formulation. Although the restriction of the student distribution to be tractable seems to limit the design of the student model significantly. And this restrictive distribution family may cause large amortization error, as suggested by Lemma 1 in the paper. The experiments are well-conducted, and the proposed method is well-evaluated. Significance: This paper studies an important problem in Bayesian machine learning and the proposed method can be combined with many Bayesian methods to reduce the computational cost during the test. Originality: As far as I know, the method is novel. The related work is adequately cited. Clarity: This paper is well-written and easy to follow.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Accelerating Monte Carlo Bayesian Inference via Approximating Predictive Uncertainty over the Simplex
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always intractable, most efforts were made on finding an accurate approximation the true posterior. Even though a decent estimation of the model posterior is obtained, another approximation is required to compute the predictive distribution over the desired output. A common accurate solution is to use Monte Carlo (MC) integration. However, it needs to maintain a large number of samples, evaluate the model repeatedly and average multiple model outputs. In many real-world cases, this is computationally prohibitive. In this work, assuming that the exact posterior or a decent approximation is obtained, we propose a generic framework to approximate the output probability distribution induced by model posterior with a parameterized model and in an amortized fashion. The aim is to approximate the true uncertainty of a specific Bayesian model, meanwhile alleviating the heavy workload of MC integration at testing time. The proposed method is universally applicable to Bayesian classification models that allow for posterior sampling. Theoretically, we show that the idea of amortization incurs no additional costs on approximation performance. Empirical results validate the strong practical performance of our approach.
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 studies the problem of avoiding Monte Carlo (MC) estimate for the predictive distribution during the test for Bayesian methods. MC estimate will incur multiple passes where the number of passes depends on the number of samples and therefore the cost can be huge. The authors propose One-Pass Uncertainty (OPU) methods to approximate the predictive distribution through distillation. Experiments on Bayesian neural networks are conducted to demonstrate the proposed method. Quality: The proposed method appears to be technically sound. The view of approximating the predictive distribution over simplex is interesting and may inspire future studies under this formulation. Although the restriction of the student distribution to be tractable seems to limit the design of the student model significantly. And this restrictive distribution family may cause large amortization error, as suggested by Lemma 1 in the paper. The experiments are well-conducted, and the proposed method is well-evaluated. Significance: This paper studies an important problem in Bayesian machine learning and the proposed method can be combined with many Bayesian methods to reduce the computational cost during the test. Originality: As far as I know, the method is novel. The related work is adequately cited. Clarity: This paper is well-written and easy to follow.
assistant
This paper studies the problem of avoiding Monte Carlo (MC) estimate for the predictive distribution during the test for Bayesian methods. MC estimate will incur multiple passes where the number of passes depends on the number of samples and therefore the cost can be huge. The authors propose One-Pass Uncertainty (OPU) methods to approximate the predictive distribution through distillation. Experiments on Bayesian neural networks are conducted to demonstrate the proposed method. Quality: The proposed method appears to be technically sound. The view of approximating the predictive distribution over simplex is interesting and may inspire future studies under this formulation. Although the restriction of the student distribution to be tractable seems to limit the design of the student model significantly. And this restrictive distribution family may cause large amortization error, as suggested by Lemma 1 in the paper. The experiments are well-conducted, and the proposed method is well-evaluated. Significance: This paper studies an important problem in Bayesian machine learning and the proposed method can be combined with many Bayesian methods to reduce the computational cost during the test. Originality: As far as I know, the method is novel. The related work is adequately cited. Clarity: This paper is well-written and easy to follow.