论文标题
通用的Neyman-Pearson分类，具有已知假设
Universal Neyman-Pearson Classification with a Known Hypothesis
论文作者
论文摘要
我们提出了一个用于二进制Neyman-Pearson分类的通用分类器，其中已知无效分布，而仅训练序列可用于替代分布。提议的分类器在Hoeffding的分类器和似然比测试之间进行了插值，并获得了与似然比测试相同的误差概率预成分，即与已知两种分布相同的预先成品。此外，像Hoeffding的通用假设检验一样，提出的分类器被证明可以达到一旦训练与观察样本的比率超过一定值，就可以实现由似然比测试实现的最佳误差指数。我们提出了与观测比的下限和上限。此外，我们提出了一个顺序分类器，该分类器达到最佳错误指数折衷。
We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between Hoeffding's classifier and the likelihood ratio test and attains the same error probability prefactor as the likelihood ratio test, i.e., the same prefactor as if both distributions were known. In addition, like Hoeffding's universal hypothesis test, the proposed classifier is shown to attain the optimal error exponent tradeoff attained by the likelihood ratio test whenever the ratio of training to observation samples exceeds a certain value. We propose a lower bound and an upper bound to the training to observation ratio. In addition, we propose a sequential classifier that attains the optimal error exponent tradeoff.
