论文标题
最小体积置信集的几何形状
Geometry of the Minimum Volume Confidence Sets
论文作者
论文摘要
置信度集合的计算对于数据科学和机器学习至关重要，它是A/B测试的主力，并基于强化学习算法的操作和分析。本文研究了多项式参数的最小体积置信集的几何形状。当使用基于边界和渐近近似的更标准置信集和间隔时，学习算法可以表现出改善的样品复杂性。先前的工作表明，最小体积置信集是由精确p值定义的不连续函数的级别集。虽然置信度集是最佳的，因为它们的平均体积最小，但集合中单点的成员的计算对于适度大小的问题来说是挑战。由于置信度集是不连续函数的级别集，因此其几何形状几乎没有什么明显的。本文通过列举和涵盖精确p值函数的连续区域来研究设定的最小体积置信度的几何形状。这解决了A/B测试中的一个基本问题：给定两个多项式结果，一个人如何确定其相应的最小体积置信度是否不相交？我们在有限的环境中回答这个问题。
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. This paper studies the geometry of the minimum-volume confidence sets for the multinomial parameter. When used in place of more standard confidence sets and intervals based on bounds and asymptotic approximation, learning algorithms can exhibit improved sample complexity. Prior work showed the minimum-volume confidence sets are the level-sets of a discontinuous function defined by an exact p-value. While the confidence sets are optimal in that they have minimum average volume, computation of membership of a single point in the set is challenging for problems of modest size. Since the confidence sets are level-sets of discontinuous functions, little is apparent about their geometry. This paper studies the geometry of the minimum volume confidence sets by enumerating and covering the continuous regions of the exact p-value function. This addresses a fundamental question in A/B testing: given two multinomial outcomes, how can one determine if their corresponding minimum volume confidence sets are disjoint? We answer this question in a restricted setting.
