We consider the problem of recovering an invertible n x n matrix A and a sparse n x p random matrix X based on the observation of Y = AX (up to a scaling and permutation of columns of A and rows of X). Using only elem...
详细信息
We consider the problem of recovering an invertible n x n matrix A and a sparse n x p random matrix X based on the observation of Y = AX (up to a scaling and permutation of columns of A and rows of X). Using only elementary tools from the theory of empirical processes we show that a version of the er-spud algorithm by Spielman, Wang and Wright with high probability recovers A and X exactly, provided that p >= Cn log n, which is optimal up to the constant C.
We consider the problem of recovering an invertible n×n matrix A and a sparse n×p random matrix X based on the observation of Y = AX (up to a scaling and permutation of columns of A and rows of X). Using onl...
详细信息
We consider the problem of recovering an invertible n×n matrix A and a sparse n×p random matrix X based on the observation of Y = AX (up to a scaling and permutation of columns of A and rows of X). Using only elementary tools from the theory of empirical processes we show that a version of the er-spud algorithm by Spielman, Wang and Wright with high probability recovers A and X exactly, provided that p ≥ Cn log n, which is optimal up to the constant C.
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