Hadamard Powers and the Identification of Mixtures of Products

01/27/2021

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by   Spencer L. Gordon, et al.

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The Hadamard Power of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. We obtain several results concerning when a Hadamard Power has full column rank. This question in turn is central to the following problem: given a mixture of k product distributions on a list of binary random variables X_1,…,X_n, can the probability model be identified from the joint statistics of the X_i.