We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a connection between neural tangent kernel (NTK) and MMD statistic. This connection enables us to develop a computationally efficient and memory-efficient approach to compute the MMD statistic and perform neural network based two-sample tests towards addressing the long-standing challenge of memory and computational complexity of the MMD statistic, which is essential for online implementation to assimilate new samples. Theoretically, such a connection allows us to understand the properties of the new test statistic, such as Type-I error and testing power for performing the two-sample test, by leveraging analysis tools for kernel MMD. Numerical experiments on synthetic and real-world datasets validate the theory and demonstrate the effectiveness of the proposed NTK-MMD statistic.

翻译：我们通过确定神经正切内核(NTK)和MMD统计之间的联系,提出了一个新颖的神经网络最大平均差异(MMD)统计数据。这种连接使我们能够开发一种计算高效和记忆高效的方法来计算MMD统计数据,并进行基于双层神经网络测试,以应对MMD统计数据的记忆和计算复杂性的长期挑战,这对于在线实施新样本同化至关重要。理论上,这种连接使我们能够了解新的测试统计数据的特性,例如类型一错误和进行双模版测试的测试能力,方法是利用分析工具来计算MMMD。合成和真实世界数据集的数值实验验证了该理论,并展示了拟议的NTK-MD统计数据的有效性。