Linear Regression with an Unknown Permutation: Statistical and Computational Limits

9 Aug 2016Ashwin PananjadyMartin J. WainwrightThomas A. Courtade

Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $\Pi^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise. We analyze the problem of permutation recovery in a random design setting in which the entries of the matrix $A$ are drawn i.i.d... (read more)

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