Neural Tangent Kernel Maximum Mean Discrepancy

Xiuyuan Cheng; Yao Xie

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arXiv · 2106.03227

Neural Tangent Kernel Maximum Mean Discrepancy

Xiuyuan Cheng·Yao Xie

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Abstract

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.

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BibTeX RIS

Xiuyuan Cheng, Yao Xie. 2021-06-06. Neural Tangent Kernel Maximum Mean Discrepancy. https://arxiv.org/abs/2106.03227

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