5 problems

Let $p$ be the tensor order, let $n$ be the dimension, let $\theta_0$ denote the planted signal, and let $\theta_0$ be recovered from the observed spiked-tensor model with signal-t…

Approximate message passing (AMP) is an iterative inference algorithm whose performance under suitable assumptions is tracked in the high-dimensional limit by state evolution. In s…

Small-aspect-ratio channel equivalence conjecture. As $lpha\to0^+$, the asymptotic normalized mutual information of the original structured tensor estimation problem converges to t…

Let the model have information exponent at least $3$, and let weak recovery mean estimating the unknown vector with nontrivial correlation using samples. Computational hardness con…

Consider the $(\Delta_p,1/\Delta_2)$ phase diagram of the spiked matrix-tensor problem, and let the glassy-state analysis identify a line delimiting the region where stable one-ste…