7 problems

Let the covariance eigenvalues of the input distribution decay algebraically, and let $\cM_m(\cF;L^p_\mu)$ denote the minimax risk after $m$ noisy input-output samples for the rele…

Leighton–Samaniego's conjecture. The deterministic minimax risk is of this order:

Let $S$ be the number of states in a deterministic estimation procedure, let $R(S)$ denote the smallest asymptotic minimax risk achievable by such an $S$-state procedure, and let…

Let $r({\mathbf{X}}, {\mathbf{Z}}, K_0,s_0)$ be the design-dependent quantity defined by … Assume that the design satisfies a restricted eigenvalue (RE) assumption and that the fea…

Partial-contamination failure conjecture. For $\alpha\neq 1$, the results obtained in the case $\alpha=1$ are no longer true, for both upper and lower bounds. Nevertheless, correct…

Let $\ell_0[p_n]\subset\mathbb{R}^{N_n}$ be the class of nearly black vectors with at most $p_n$ nonzero coordinates, and suppose that the indirect problem has ordered noise levels…

Let $\mathcal P_r$ be the class of convex polytopes with at most $r$ vertices, let $\hat P_n^{(r)}$ be the estimator considered in the paper, and let…