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Matérn 回归的非渐近分析：目标与核长度尺度的作用AI 解读

Theoretical guarantees for kernel regression are typically formulated in terms of smoothness, but practical accuracy depends critically on how the design resolution compares with the target and kernel lengthscales. We develop a finite-sample theory for Matérn regression on periodic domains with quasi-uniform designs, covering noiseless interpolation and noisy kernel ridge regression. Our minimax result shows that accurate recovery requires a design dense enough to resolve…

带 Gamma 超先验的逆问题：一种变分推断方法AI 解读

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to \textit{maximum a posteriori} estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse…