5 problems

Let $\mathcal{B}$ be a class of candidate parameter vectors in a generalized linear model, and let $\theta_{\widehat\beta}$ be an estimator constructed from the candidates. A sharp…

Improved constant conjecture. The constant term $2(p+1)I_p$ can be replaced by $(p+1)I_p$; that is, for every $M$,

Let $\mathcal{M}$ be a collection of models, let $\widehat{s}_m$ be the estimator associated with $m\in\mathcal{M}$, and let $\mathcal{R}$ and $\widehat{\mathcal{R}}_n$ denote the…

Maximum regularized likelihood estimators are considered in the general prediction setting, including regression, where assumptionless oracle inequalities have been established and…

Let $s$, $M$, and $T$ denote the sparsity, number of groups, and number of tasks, respectively, and let the risk be measured using prediction error with squared loss … The relevant…