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Binary Hypothesis Testing Game With Training Data

机译：带有训练数据的二元假设检验游戏

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摘要

We introduce a game-theoretic framework to study the hypothesis testing problem in the presence of an adversary aiming to prevent a correct decision. Specifically, this paper considers a scenario in which an analyst has to accept or reject the null hypothesis (H_0) characterized by a probability mass function (pmf) (P_X) based on the evidence provided by a test sequence. In turn, the goal of the adversary is to take a sequence generated according to a different pmf and modify it in such a way to induce a decision error. (P_X) is known only through one or more training sequences. We derive the asymptotic equilibrium of the game under the assumption that the analyst relies only on first order statistics of the test and training sequences, and compute the asymptotic payoff of the game when the length of the sequences tends to infinity. We introduce the concept of indistinguishability region, defined as the set of pmfs that can not be distinguished reliably from (P_X) in the presence of attacks. Two different scenarios are considered: in the first one the analyst and the adversary share the same training sequence, in the second scenario, they rely on independent sequences. The obtained results are compared with a version of the game in which the pmf (P_X) is perfectly known to both the analyst and the adversary.
机译：我们引入了一个博弈论的框架来研究存在一个旨在防止做出正确决定的对手时的假设检验问题。具体而言，本文考虑了一个场景，在该场景中，分析人员必须根据测试序列提供的证据，接受或拒绝以概率质量函数（pmf）（P_X）为特征的零假设（H_0）。反过来，对手的目标是采用根据不同pmf生成的序列，并以引起决策错误的方式对其进行修改。 （P_X）仅通过一个或多个训练序列已知。我们假设分析人员仅依赖于测试和训练序列的一阶统计量，得出游戏的渐近均衡，并在序列长度趋于无穷大时计算游戏的渐进收益。我们介绍了不可区分区域的概念，定义为在存在攻击时无法与（P_X）可靠区分的pmfs集。考虑了两种不同的方案：在第一种方案中，分析师和对手共享相同的训练序列，在第二种方案中，他们依赖于独立的序列。将获得的结果与该游戏的版本进行比较，在该版本中，分析师和对手都完全了解pmf（P_X）。

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