Multiparameter Bernoulli factories

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1913

Renato Paes Leme, Jon Schneider

引用次数: 2

Abstract

We consider the problem of computing with many coins of unknown bias. We are given access to samples of n coins with unknown biases p1,…,pn and are asked to sample from a coin with bias f(p1,…,pn) for a given function f:[0,1]n→[0,1]. We give a complete characterization of the functions f for which this is possible. As a consequence, we show how to extend various combinatorial sampling procedures (most notably, the classic Sampford sampling for k-subsets) to the boundary of the hypercube.

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多参数伯努利工厂

我们考虑带有许多未知偏差的硬币的计算问题。我们可以访问n个偏差未知的硬币的样本p1，…，pn，并要求对给定函数f:[0,1]n→[0,1]从偏差为f(p1，…，pn)的硬币进行抽样。我们给出了函数f的一个完整的表征，使得这是可能的。因此，我们展示了如何将各种组合抽样过程(最值得注意的是k-子集的经典Sampford抽样)扩展到超立方体的边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.