带拒绝选项的多重假设检验
On Multiple Hypothesis Testing with Rejection Option
摘要：
我们研究了问题的多重假设检验（HT）鉴于拒绝选项。HT的模型有许多不同的应用。考虑了关于源分布的M个假设的检验误差，并考虑了拒绝所有这些假设的选项。源是离散和任意变化的（AVS）。研究了错误概率指数/可靠性与拒绝决策的错误接受和真实分布的错误拒绝之间的权衡，并概述了最优决策策略。主要结果是专门为离散无记忆源（DMS）和进一步研究。分析所暗示的一个有趣的见解是这样一种现象（可以用监督/无监督学习来理解），即在M个假设分布内的最佳区分中，人们总是允许比决定拒绝假设集时更低的错误。几何解释的最佳决策方案给出了当前和已知的边界在多HT AVS的。
英文摘要：
We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all those hypotheses are considered. The source is discrete and arbitrarily varying (AVS). The tradeoffs among error probability exponents/reliabilities associated with false acceptance of rejection decision and false rejection of true distribution are investigated and the optimal decision strategies are outlined. The main result is specialized for discrete memoryless sources (DMS) and studied further. An interesting insight that the analysis implies is the phenomenon (comprehensible in terms of supervised/unsupervised learning) that in optimal discrimination within M hypothetical distributions one permits always lower error than in deciding to decline the set of hypotheses. Geometric interpretations of the optimal decision schemes are given for the current and known bounds in multi-HT for AVS's.
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