$A^*$ sampling with probability matching
Probabilistic methods often need to draw samples from a nontrivial distribution. sampling is a nice algorithm by building upon a top-down construction of a Gumbel process, where a large state space is divided into subsets and at each round sampling selects a subset to process. However, the selection rule depends on a bound function, which can be intractable. Moreover, we show that such a selection criterion can be inefficient. This paper aims to improve sampling by addressing these issues. To design a suitable selection rule, we apply emph{Probability Matching}, a widely used method for decision making, to sampling. We provide insights into the relationship between sampling and probability matching by analyzing a nontrivial special case in which the state space is partitioned into two subsets. We show that in this case probability matching is optimal within a constant gap. Furthermore, as directly applying probability matching to sampling is time consuming, we design an approximate version based on Monte-Carlo estimators. We also present an efficient implementation by leveraging special properties of Gumbel distributions and well-designed balanced trees. Empirical results show that our method saves a significantly amount of computational resources on suboptimal regions compared with sampling.
 It seems a good paper, containing with interesting ideas. However, the state-of-the-art discussion about sampling methods is formed by just one sentence. I suggest to add more references about adaptive rejection sampling and MCMC, discussing a bit more their differences, and the differences and connections with A* sampling. Also direct methods should be discussed. For this reasons, I also suggest to add references to related books as Devroye*s sampling book and other, more recent books devoted to describe independent random sampling methods.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
$A^*$ sampling with probability matching
Probabilistic methods often need to draw samples from a nontrivial distribution. sampling is a nice algorithm by building upon a top-down construction of a Gumbel process, where a large state space is divided into subsets and at each round sampling selects a subset to process. However, the selection rule depends on a bound function, which can be intractable. Moreover, we show that such a selection criterion can be inefficient. This paper aims to improve sampling by addressing these issues. To design a suitable selection rule, we apply emph{Probability Matching}, a widely used method for decision making, to sampling. We provide insights into the relationship between sampling and probability matching by analyzing a nontrivial special case in which the state space is partitioned into two subsets. We show that in this case probability matching is optimal within a constant gap. Furthermore, as directly applying probability matching to sampling is time consuming, we design an approximate version based on Monte-Carlo estimators. We also present an efficient implementation by leveraging special properties of Gumbel distributions and well-designed balanced trees. Empirical results show that our method saves a significantly amount of computational resources on suboptimal regions compared with sampling.
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>



 It seems a good paper, containing with interesting ideas. However, the state-of-the-art discussion about sampling methods is formed by just one sentence. I suggest to add more references about adaptive rejection sampling and MCMC, discussing a bit more their differences, and the differences and connections with A* sampling. Also direct methods should be discussed. For this reasons, I also suggest to add references to related books as Devroye*s sampling book and other, more recent books devoted to describe independent random sampling methods.
assistant
 It seems a good paper, containing with interesting ideas. However, the state-of-the-art discussion about sampling methods is formed by just one sentence. I suggest to add more references about adaptive rejection sampling and MCMC, discussing a bit more their differences, and the differences and connections with A* sampling. Also direct methods should be discussed. For this reasons, I also suggest to add references to related books as Devroye*s sampling book and other, more recent books devoted to describe independent random sampling methods.