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The Layered Structure of Tensor Estimation and its Mutual Information (1709.10368v3)
Published 29 Sep 2017 in cs.IT, cond-mat.dis-nn, math-ph, math.IT, and math.MP
Abstract: We consider rank-one non-symmetric tensor estimation 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 [1]. 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 generalizes and allows to rigorously obtain the mutual information at any order in a recursive way.