实例介绍
【实例简介】Abstract—The standard linear regression (SLR) problem is to
recover a vector x0 from noisy linear observations y = Ax0 w.
The approximate message passing (AMP) algorithm recently
proposed by Donoho, Maleki, and Montanari is a computationally
efficient iterative approach to SLR that has a remarkable
property: for large i.i.d. sub-Gaussian matrices A, its periteration
behavior is rigorously characterized by a scalar stateevolution
whose fixed points, when unique, are Bayes optimal.
AMP, however, is fragile in that even small deviations from the
i.i.d. sub-Gaussian model can cause the algorithm to diverge. This
paper considers a “vector AMP” (VAMP) algorithm and shows
that VAMP has a rigorous scalar state-evolution that holds under
a much broader class of large random matrices A: those that are
right-rotationally invariant. After performing an initial singular
value decomposition (SVD) of A, the per-iteration complexity of
VAMP is similar to that of AMP. In addition, the fixed points of
VAMP’s state evolution are consistent with the replica prediction
of the minimum mean-squared error recently derived by Tulino,
Caire, Verd´ u, and Shamai
recover a vector x0 from noisy linear observations y = Ax0 w.
The approximate message passing (AMP) algorithm recently
proposed by Donoho, Maleki, and Montanari is a computationally
efficient iterative approach to SLR that has a remarkable
property: for large i.i.d. sub-Gaussian matrices A, its periteration
behavior is rigorously characterized by a scalar stateevolution
whose fixed points, when unique, are Bayes optimal.
AMP, however, is fragile in that even small deviations from the
i.i.d. sub-Gaussian model can cause the algorithm to diverge. This
paper considers a “vector AMP” (VAMP) algorithm and shows
that VAMP has a rigorous scalar state-evolution that holds under
a much broader class of large random matrices A: those that are
right-rotationally invariant. After performing an initial singular
value decomposition (SVD) of A, the per-iteration complexity of
VAMP is similar to that of AMP. In addition, the fixed points of
VAMP’s state evolution are consistent with the replica prediction
of the minimum mean-squared error recently derived by Tulino,
Caire, Verd´ u, and Shamai
【实例截图】
标签： 算法
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