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Kernel-Based Hypothesis Testing Explores Regularization vs. Convolution

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This paper explores kernel-based hypothesis testing, specifically focusing on the Maximum Mean Discrepancy (MMD) test. It investigates two distinct approaches: a convolution method for translation-invariant kernels on $\mathbb{R}^d$ and a regularization method for general measurable spaces. The research connects these by demonstrating that both methods achieve minimax optimality over Sobolev balls under $L^2$-separation when a specific condition on the kernel's spectral density is met. The study shows that for certain kernels like Matérn and Laplace, a fixed bandwidth with a vanishing regularization parameter can attain the Sobolev minimax rate. AI

RANK_REASON The item is an academic paper detailing theoretical advancements in statistical methods. [lever_c_demoted from research: ic=1 ai=0.4]

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Kernel-Based Hypothesis Testing Explores Regularization vs. Convolution

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The item is an academic paper detailing theoretical advancements in statistical methods. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Omar Hagrass, Bharath K. Sriperumbudur ·

    Regularization vs. Convolution in Kernel-Based Hypothesis Testing

    arXiv:2611.06778v1 Announce Type: cross Abstract: The maximum mean discrepancy (MMD) test is a popular nonparametric test on general domains. Two lines of work have studied its optimality through structurally different approaches. The first, a convolution approach on $\mathbb{R}^…

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