  We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by
identifying a new connection between neural tangent kernel (NTK) and MMD. This
connection enables us to develop a computationally efficient and
memory-efficient approach to compute the MMD statistic and perform NTK 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 assimilating new samples. Theoretically, such a connection
allows us to understand the NTK test statistic properties, such as the Type-I
error and testing power for performing the two-sample test, by adapting
existing theories for kernel MMD. Numerical experiments on synthetic and
real-world datasets validate the theory and demonstrate the effectiveness of
the proposed NTK-MMD statistic.
