Abstract:Accurately and efficiently estimating the variance of the Maximum Mean Discrepancy (MMD) remains challenging, particularly for unbalanced sample sizes. In this paper, we derive a finite-sample unbiased estimator of the MMD variance. To overcome the traditional $\mathcal{O}(N^2)$ computational bottleneck, we develop a recursive prefix-suffix accumulation scheme for the Laplace kernel, reducing the computational complexity to $\mathcal{O}(N \log N)$ while requiring $\mathcal{O}(N)$ memory. Experimental results verify the theoretical exactness and numerical stability of the proposed estimator and demonstrate its scalability on large datasets. Furthermore, the method proves effective for monitoring distributional convergence during the training of Time-series Generative Adversarial Networks (TimeGAN).
From: Shijie Zhong [view email]
[v1]
Tue, 20 Jan 2026 11:41:32 UTC (352 KB)
[v2]
Wed, 4 Feb 2026 14:41:27 UTC (353 KB)
[v3]
Wed, 16 Sep 2026 02:04:45 UTC (1,002 KB)
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