6 problems

Let an SST matrix be a matrix satisfying the strong stochastic transitivity condition, and consider its estimation under the Frobenius norm. Statistical-computational gap conjectur…

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 $P_{{\rm mis}}(d\bx\mid \bY)$ be the mismatched posterior, let $\bX$ be the planted signal, and let $M(\lambda,\lambda_*)$ be the function defined by … Here…

The model consists of a stochastic block model (SBM) whose groups may have asymmetric connection probabilities; the quantity $I_s$ denotes the information parameter appearing in th…

Let $n_1=n_2=n$, and let $\theta\in\mathcal{M}^{n,n}$ be the anti-Monge matrix constructed in the preceding proof, with $V(\theta)=V_0$ and with low-rank approximation error of ord…

In a mixed membership stochastic block model with $n$ vertices and $r$ communities, the expected matrix has rank at most $r$, and the information-theoretic lower bound for weak det…