Mutual information for low-rank even-order symmetric tensor estimation

Understand

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order.

• The proof applies the adaptive interpolation method originally invented for rank-one factorization.
• Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors.
• This requires new nontrivial ideas with respect to the current analysis in the literature.