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方差轮廓下非独立同分布数据岭回归的高维分析AI 解读

High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed data. To this end, we suppose that the set of observed predictors (or features) is a random matrix with a variance profile and with dimensions growing at a proportional rate. Assuming a random effect model, we study the predictive risk of the…

非独立同分布数据与方差剖面下的高维随机特征岭回归AI 解读

Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=Σ^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $Σ$ is shared by all samples. In this paper, we move beyond this setting and study non-identically distributed data through a variance-profile model in which the training and test covariates have row-dependent diagonal covariance matrices $Σ_i=\diag(γ_{i1}^2,\ldots,γ_{ip}^2)$…

球面数据的 Monge-Kantorovich 分位数正则化估计AI 解读

Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applications that require out-of-sample estimates. To this end, we introduce a regularized estimator built from entropic optimal transport, by extending the definition of the entropic map to the spherical setting. We propose a stochastic algorithm to directly solve a continuous OT problem between the…