Sparse Estimation with the Swept Approximated Message-Passing Algorithm
This work addresses a stability problem for researchers and practitioners using AMP in sparse estimation, offering an incremental improvement for specific applications.
The paper tackled the convergence issues of Approximate Message Passing (AMP) in non-ideal contexts by proposing a swept coefficient update scheme, which stabilizes AMP to achieve theoretically expected performance on problems where standard AMP diverges without unduly increasing computational costs for large-dimensional signals.
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contexts that do not exactly match its assumptions. We propose a new approach to stabilizing AMP in these contexts by applying AMP updates to individual coefficients rather than in parallel. Our results show that this change to the AMP iteration can provide theoretically expected, but hitherto unobtainable, performance for problems on which the standard AMP iteration diverges. Additionally, we find that the computational costs of this swept coefficient update scheme is not unduly burdensome, allowing it to be applied efficiently to signals of large dimensionality.