4 problems

Let $q\in[0,1]$, and let $\hat{\mathcal{S}}$ estimate the principal subspace $\mathcal{S}$ under the same conditions as in the column sparse upper-bound corollary, with $R_q$ repla…

Optimality conjecture. The rates found in Theorem 4 are optimal.

Minimax volume conjecture. The minimax volume satisfies, up to a constant factor depending only on $n$,

One-sided estimation lower-bound conjecture. There exist constants $c_0,c,r>0$ such that, for every $s,n\in\mathbb{N}$ satisfying