10 problems

RIE optimality conjecture. In the denoising or universal phase, it is statistically not possible to outperform the RIE for denoising $\bX\bX^\intercal$.

High-SNR Bayesian advantage conjecture. As in the case of discrete priors, the non-rotationally invariant nature of the prior should be exploitable to construct a Bayesian estimato…

Semerjian's universality conjecture. For a large system, the MI and MMSE for any such prior $P_X$ should match, for all $\lambda\geq 0$ and $\alpha>0$, their values in the Gaussian…

Spectral-gap condition conjecture. The condition $\sigma_2^*<1$ is implied by the criticality condition.

Wishart denoising universality conjecture. The asymptotic Bayes-optimal estimator and its associated mean square error do not depend on the details of the laws of the entries of…

Universality conjecture. The optimality of the low-degree polynomial estimators holds beyond strictly orthogonally invariant priors; in particular, this universality phenomenon inc…

Let $\tilde{\mathbf{u}}_j$ and $\tilde{\mathbf{u}}_k$ be the residual unit singular vectors arising in the spiked-model decomposition, and let $\mathbf{A}$ be a matrix. The relevan…

Let $X$ be an $m\times n$ noise matrix with $q=\min(m,n)$ and singular values $\sigma_i(X)$, and let $b$ be the right edge of its limiting singular-value distribution with D-transf…

Let $X$ be an $m\times n$ noise matrix with singular values $\sigma_i(X)$, and let $b$ be the right spectral edge of its limiting singular-value distribution with D-transform…

Let $\mathbf{X}$ be a low-rank matrix observed in the matrix denoising model, let $\rho$ denote its asymptotic rank fraction, and let $\mathcal{M}(\rho\mid\mathbf{X})$ and…