Fundamental limits of symmetric lowrank matrix estimation
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Proceedings of the 2017 Conference on Learning Theory, PMLR 65:12971301, 2017.
Abstract
We consider the highdimensional inference problem where the signal is a lowrank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the lowrank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the signal remains constant. We unify and generalize a number of recent works on PCA, sparse PCA, submatrix localization or community detection by computing the informationtheoretic limits for these problems in the high noise regime. This allows to locate precisely the informationtheoretic thresholds for the above mentioned problems.
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