10 problems

MF-AOA asymptotic performance conjecture. In the limit $n\rightarrow\infty$, AMP algorithms such as the MF-AOA achieve a performance of approximately

Consider the generalized linear model with orthogonally invariant design, and let $\widehat{\beta}_{\mathrm{B}}=\mathbb{E}[\beta_*\mid X,y]$ be the posterior mean estimator. Let…

Let $\mathscr{U}$ be the universality class used in the paper, let $\mathscr{Q}$ be a matrix class, let OAMP/VAMP denote the stated algorithms, and let SE denote their state evolut…

In the spiked Wigner inference problem, let annealed Glauber dynamics refer to the Markov chain studied in the paper, and let weak recovery mean achieving nonzero correlation with…

PIIDG orthogonality conjecture. Then

Let $\bm{U}$ be an orthogonal matrix and let $\bm{U}_1$ be an $N\times(N-m)$ block of $\bm{U}$. Let $\bm{b}_1\in\mathbb{R}^{N-m}$ be a PIIDG vector, meaning a partially independent…

Let $X$ have prior distribution $P_0$, and consider the symmetric rank-one matrix estimation model with signal-to-noise parameter $\lambda$. For $\eta>0$, define … and set … Here…

MP-AMP cost conjecture. The total computation and communication cost scales as

Let $\bm{A}$ be unitarily invariant, and let $\bm{W}_t$ be given by the specified linear estimator. Define … with $v_0^2=\operatorname{E}\{X^2\}$, where $\Phi_t$ and $\Psi_t$ are t…

Consider a linear inverse problem in which an input signal ${\bf x}$, generated by a stationary ergodic source, is estimated from noisy measurements ${\bf y}$ and measurement matri…