Learning a regression function via Tikhonov regularization

On One Property of Tikhonov Regularization Algorithm

For linear inverse problem with Gaussian random noise we show that Tikhonov regularization algorithm is minimax in the class of linear estimators and is asymptotically minimax in the sense of sharp asymptotic in the class of all estimators. The results are valid if some a priori information on a Fourier coefficients of solution is provided. For trigonometric basis this a priori information implies that the solution belongs to a ball in Besov space $B^r_{2\infty}$.

非线性统计逆问题中具有过平滑惩罚项的 Tikhonov 正则化

Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems

针对统计学习中含噪非线性不适定逆问题，本文采用 Hilbert 尺度下的 Tikhonov 正则化重建估计量，并基于算子与先验假设推导收敛速率及 RKHS 误差估计。

非线性统计逆学习问题的 Tikhonov 正则化收敛性分析

Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems

本文针对非线性统计逆学习问题，分析基于再生核 Hilbert 空间的 Tikhonov 正则化估计量，并给出由源条件定义的可容许解类别上的最优一致收敛速率。

基于机器学习的最优Tikhonov正则化方法 I：仿射流形

A Machine Learning Approach to Optimal Tikhonov Regularisation I: Affine Manifolds

本文提出基于监督学习的方法，用于近似高维函数，将噪声数据映射到最优Tikhonov正则化参数的近似值，假设逆问题解在低维线性子空间上集中分布且噪声为亚高斯。