Neural Tangent Kernel Maximum Mean Discrepancy
This addresses a long-standing challenge in online implementation for assimilating new samples, though it appears incremental as it adapts existing kernel MMD theories.
The authors tackled the high memory and computational complexity of Maximum Mean Discrepancy (MMD) statistics by connecting neural tangent kernel (NTK) with MMD, resulting in a more efficient approach for two-sample tests, validated on synthetic and real-world datasets.
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.