6 problems

Let $G$ satisfy the paper's general-graph regularity assumption, and let $\\{V_n\\}_{n \ge 1}$ satisfy the candidate-set assumption. For each initial source $v$, write…

Let $X(1),\ldots,X(N)$ be an i.i.d. sample, and let $\widehat H_i$, $i=1,\ldots,M$, be a permutation bootstrap sample of the estimator $\widehat H(j_1,j_2)$. Let the scales $j_1$,…

Let $\beta\geq -1$ and $\gamma>0$, and for $n\in\mathbb{N}$ set $N=\lceil n/\gamma\rceil$. Under $\mu_0$, draw $\mathbf{z}_1,\ldots,\mathbf{z}_N\sim N(0,I_n)$ independently. Under…

Sparse PCA runtime conjecture. For any $\lambda$ in the hard regime

Informal low-degree conjecture. For “nice” distributions $\mathbb{P}_n$ and $\mathbb{Q}_n$, if

Let $Y^*$ denote the true support matrix in the submatrix localization model. Assume $\mu\le 1$, $n_L=n_R=n$, $K_L=K_R=K$, and $K\ge c_1\log n$. Submatrix localization computationa…