5 problems

StoNet conjecture. The StoNet could enable the extension of benign overfitting theory from linear models to super-wide DNNs by leveraging its capability in sufficient dimension red…

Let $\mathcal{S}$ be the central subspace and let the hierarchical prior assign mass to subspaces of varying dimension, including dimensions greater than the intrinsic dimension…

Let $d_n=d$ and $d^*_n=d^*$ be fixed, and let $\mathcal{S}_n=\mathcal{S}$ denote the central subspace. Consider the hierarchical Bayes procedure described in the paper, whose poste…

Let $\mathbf{M}_{n(O)}$ be the matrix formed using the first $q$ variables for the exact oracle sparse dimension-reduction estimator, and let $\mathbf{M}_{n(q)}$ be the correspondi…

In a single-index regression, the linearity condition is the condition under which the conditional mean of the covariates given the index is linear in the index, and an adaptive es…