论文标题
多参数Bernoulli工厂
Multiparameter Bernoulli Factories
论文作者
论文摘要
我们考虑了许多未知偏差硬币计算的问题。我们将获得样品访问$ n $硬币，其中\ emph {unknown}偏见$ p_1，\ dots，p_n $，并被要求从具有偏见$ f（p_1，\ dots，p_n）$的硬币中对给定函数$ f：[0,1]我们给出了函数$ f $的完整表征。结果，我们展示了如何将各种组合采样程序（最著名的是$ k $ -subsets的经典Sampford采样）扩展到HyperCube的边界。
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given function $f:[0,1]^n \rightarrow [0,1]$. 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.
