8 problems

Let $\theta>1$, let $d_0\geq 1$ be fixed, and use the spiked matrix model notation of Theorem, assuming and. Let $\bm R=\bm R^{(d)}\in\mathbb{R}^{d_0\times d}$ satisfy…

OAMP optimality conjecture. The predicted performance of the proposed optimal OAMP algorithm agrees with the replica-symmetric predictions for the associated Bayes-optimal estimato…

Let $\bm{x}$ be random as in the paper's spiked-prior assumption, let $p(y)$ be a density defining an additive noise channel $\mathcal{P}$, and let $F_{\mathcal{P}}$ denote its Fis…

Suppose $\boldsymbol{Y}=\boldsymbol{u}\boldsymbol{u}^{\mathsf T}+\boldsymbol{J}$, where $\boldsymbol{J}\sim\operatorname{GOE}(d)$ and $u_i\sim_{\mathrm{iid}}\pi_0$ for a distributi…

Let $\beta_{\mathrm{IT}}$ and $\beta_{\mathrm{wr}}$ denote the information-theoretic and weak-recovery thresholds, respectively, and consider the posterior distribution of the symm…

Let $\beta_{\text{IT}}$ be the information-theoretic threshold, let $J(\pi_{\Theta})$ denote the set of signal-to-noise parameters for which Bayes AMP is known to achieve asymptoti…

Deshpande–Montanari conjecture. The AMP results for $\lambda>1$ should continue to hold when AMP is initialized using the leading eigenvector of ${\boldsymbol Y}$, rather than inde…

Let $\MSE^{\rm AMP}_t$ be the asymptotic mean squared error of AMP at iteration $t$ for the spiked Wigner model, and let … be its limiting performance. AMP optimality conjecture. T…