11 problems

Fix a sequence of subgraphs $\Gamma=(\Gamma_n)_n$, assume $p_n,q_n=\Theta(1)$, and consider the exact-recovery condition for the likelihood peeling algorithm … for any…

Exact-recovery threshold conjecture. For $d=4$ and $5$, the correct threshold for exact recovery is $\frac{2d-4}{2d-1}$. The paper establishes only bounds on this threshold: exact…

Abbe–Baccelli–Sankararaman conjecture. The above impossibility result is tight: exact recovery should be possible whenever

Abbe et al.'s tightness conjecture. The impossibility result is tight: exact recovery is achievable whenever

Let $d$-uniform hypergraph stochastic block model parameters be given by $\big(\mathbf{p}, \{Q_{\mathbf{T}}\}_{\mathbf{T} \in \mathcal{T}}\big)$, and let $\mathbf{A}$ denote the ob…

Let $X_i$ be observations from a Gaussian mixture model with noise covariance matrix $\boldsymbol\varepsilon_i\sim N(0,\Sigma)$, where the positive-definite covariance matrix…

Spectral-estimator conjecture. Under this condition, $\eta_1^0$ achieves exact recovery. The conjecture is motivated by the optimality of spectral estimation for exact recovery in…

Feldman et al.'s conjecture. The condition

Consider the stochastic block model for a $k$-uniform hypergraph with edge probabilities … where $\alpha>\beta>0$, and define … Exact recovery means recovering the planted partitio…

For any $\lambda>0$, $d\in\mathbb{N}$, and $0\leq b<a\leq 1$, let $\nu_d$ denote the volume of the unit Euclidean ball in $d$ dimensions, and let…

Consider the general stochastic block model in the setting of Colin et al., with linear-size communities and exact recovery, and let $k$ denote the number of communities. Exact-rec…