4 problems

Let $p$ be the dimension, $n$ the sample size, and $d$ the tensor order. Consider estimating the order-$d$ moment or cumulant tensors of a sub-Gaussian random vector, with consiste…

Let $p$ be the dimension, $n$ the sample size, and $d$ the tensor order. Consider estimating order-$d$ moment or cumulant tensors of sub-Gaussian random vectors in spectral norm. E…

The statistical lower and upper bounds in the setting considered are respectively $\mathcal{O}(d^{-(m-1)})$ and $\widetilde{\mathcal{O}}(d^{-(m-1)})$, while the computational lower…

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