论文标题
稳健的多种伪造测试，矩限制的不确定性集
Robust Multi-Hypothesis Testing with Moment Constrained Uncertainty Sets
论文作者
论文摘要
研究了可靠的二元假设检验的问题。在这两个假设下，假定数据生成的分布属于瞬间构建的不确定性集。特别是，这些集合包含分布，其矩的矩围绕从训练样本获得的经验时刻为中心。目的是设计一个在不确定性集中所有分布中表现良好的测试，即最大程度地减少不确定性集的最坏情况误差概率。在有限的阿尔如图案例中，获得了最佳测试。在无限字母案例中，得出了使用来自字母的有限样本收敛到最佳值的最坏情况误差的典型近似值。进一步构建了一个测试以推广到整个字母。还提出了针对测试样品的指数一致测试。提供数值结果以证明所提出的可靠测试的性能。
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose moments are centered around the empirical moments obtained from training samples. The goal is to design a test that performs well under all distributions in the uncertainty sets, i.e., minimize the worst-case error probability over the uncertainty sets. In the finite-alphabet case, the optimal test is obtained. In the infinite-alphabet case, a tractable approximation to the worst-case error is derived that converges to the optimal value using finite samples from the alphabet. A test is further constructed to generalize to the entire alphabet. An exponentially consistent test for testing batch samples is also proposed. Numerical results are provided to demonstrate the performance of the proposed robust tests.
