6 problems

Universality conjecture. Analogous phenomena persist for asymmetric spiked tensor models.

Consider an asymmetric spiked tensor maximum-likelihood problem with signal-to-noise ratio $\beta$. Let $(\lambda_*,{\bm{u}}_*^{(1)},\ldots,{\bm{u}}_*^{(d)})$ be the tuple associat…

Consider an asymmetric spiked tensor maximum-likelihood problem with signal-to-noise ratio $\beta$. Let $(\lambda_*,{\bm{x}}^{(1)}_*,\ldots,{\bm{x}}^{(d)}_*)$ denote the tuple asso…

Let ${\bm{\mathsfit{Y}}}$ be an asymmetric spiked tensor with signal-to-noise ratio $\beta$, and let the maximum-likelihood problem be the optimization problem in Eq. (objective).…

Tight algorithmic threshold conjecture. $d^{p/4}$ is the tight algorithmic threshold: below this threshold, no consistent estimates can be computed in polynomial time.

Consider the Bayesian spiked tensor estimation model studied in the paper, with the minimum mean squared error (MMSE) as the information-theoretic optimum and Approximate Message P…