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高维推断中的合成数据正则化AI 解读

To address the challenges of obtaining reliable inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via a weighted likelihood based on synthetic data generated from a simpler, more stable model. This method provides a theoretically sound and practically effective alternative to parameter penalization. We establish key theoretical properties…

稀疏回归中一般载荷的线性泛函检验：分离率与计算障碍AI 解读

We study the problem of testing $H_0: ξ^\topβ=t_0$ in high-dimensional sparse linear regression with Gaussian random design and unknown design covariance. The loading vector $ξ$ is arbitrary, and the exact sparsity level $k$ is unknown but bounded by a known value $k_u$. Tests are required to control Type I error uniformly over the $k_u$-sparse null, while power is evaluated against $k$-sparse alternatives. We construct a computationally efficient mixed test that gives an…

大维度下谱算法的学习曲线与良性过拟合AI 解读

Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of spectral algorithms in the large-dimensional setting where the sample size and dimension are of comparable order, i.e., $n \asymp d^γ$ for some $γ>0$. We first consider inner-product kernels on the sphere $\mathbb{S}^{d-1}$ and establish a sharp…