The Layered Structure of Tensor Estimation and its Mutual Information
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We consider rank-one non-symmetric tensor esti- mation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using a new type of interpolation method developed in . We then show how to harness the structure in "layers" of tensor estimation in order to obtain a formula for the mutual information for the order 3 problem from the knowledge of the formula for the order 2 problem, still using the same kind of interpolation. Our proof technique straightforwardly general- izes and allows to rigorously obtain the mutual information at any order in a recursive way.