VAMP with Vector-Valued Diagonalization

Fischer, Robert F. H.; Sippel, Carmen; Goertz, Norbert

doi:10.1109/icassp40776.2020.9053763

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…The paper also proves that for log-concave priors, the variances of the extrinsic distributions are always positive. In [5], an alternative method for implementing VAMP is presented, which avoids the need to approximate the extrinsic distribution covariances as multiples of the identity matrix. This approach considers prior distributions with nonlog-concave probability density functions and introduces a correction term to ensure the non-negativity of the extrinsic variances.…”

Section: A Prior Workmentioning

confidence: 99%

Approximate Message Passing for Not So Large niid Generalized Linear Models

Zhao,

Xiao,

Slock

2023

2023 IEEE 24th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

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Many signal processing problems involve a Generalized Linear Model (GLM), which is a linear model in which the unknowns may be non-identically independently distributed (n.i.i.d.). Vector Approximate Message Passing (VAMP) is a computationally efficient belief propagation technique used for Bayesian inference. However, the posterior variances obtained from (limited complexity) VAMP are only exact when an independent and identically distributed (i.i.d.) prior is assumed, due to the averaging operations involved. In many problems, it is desirable to not only get estimates of the unknowns but also correct posterior distributions. Whereas VAMP and esp. AMP is applicable to problems of high dimensions, in many applications the dimensions are not very high, allowing for more complex operations. Also, in finite dimensions, the asymptotic regime leading to correct variances under certain measurement matrix model assumptions does not hold. To address these challenges, we propose a revisited version of VAMP, called reVAMP, which provides both a multivariate Gaussian posterior approximation (including inter-parameter correlations) and accurate posterior marginals which only require the extrinsic distributions to become Gaussian.

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Section: A Prior Workmentioning

confidence: 99%

Approximate Message Passing for Not So Large niid Generalized Linear Models

Zhao,

Xiao,

Slock

2023

2023 IEEE 24th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

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“…The introduced procedures are very powerful recovery algorithms. However, for VAMPind numerical issues with the variances have been reported [5], causing a degradation in performance. Furthermore, also VAMPavg underlies a drop in performance, when a non-uniform power distribution over the components of x is present [20].…”

Section: Stabilization Techniquesmentioning

confidence: 99%

“…This means, we estimate the signal x from an observation y in Gaussian noise, given by the channel (1), where we assume that x is Gaussian distributed. This assumption might be far from reality, if, e.g., discrete priors as in [5], [20] are used. The fractional approach can be seen as a way to compensate for that inaccuracy.…”

Section: A Estimation Theoretic Interpretationmentioning

confidence: 99%

“…The main problem in VAMPind, that causes stability problems is the fact that the subtraction (11) of the precision parameter (see (13)) Λ \c j = Λ s,j −Λ \s j turns frequently negative, resulting in negative (extrinsic) variances, which have no reasonable meaning. Even with clipping, a degradation in performance may be visible in comparison to the average case VAMPavg for certain scenarios [5]. The fractional version stated above, adjusts the update to Λ \c j = Λ s,j − Λ \s j /e.…”

Section: Numerical Considerationsmentioning

confidence: 99%

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Stabilization Techniques for Iterative Algorithms in Compressed Sensing

Sippel,

Fischer

2021

Preprint

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Algorithms for signal recovery in compressed sensing (CS) are often improved by stabilization techniques, such as damping, or the less widely known so-called fractional approach, which is based on the expectation propagation (EP) framework. These procedures are used to increase the steadystate performance, i.e., the performance after convergence, or assure convergence, when this is otherwise not possible. In this paper, we give a thorough introduction and interpretation of several stabilization approaches. The effects of the stabilization procedures are examined and compared via numerical simulations and we show that a combination of several procedures can be beneficial for the performance of the algorithm.

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Unbiasing in Iterative Reconstruction Algorithms for Discrete Compressed Sensing

Fischer

Sippel

2022

Applied and Numerical Harmonic Analysis

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VAMP with Vector-Valued Diagonalization

Cited by 5 publications

References 11 publications

Approximate Message Passing for Not So Large niid Generalized Linear Models

Approximate Message Passing for Not So Large niid Generalized Linear Models

Stabilization Techniques for Iterative Algorithms in Compressed Sensing

Unbiasing in Iterative Reconstruction Algorithms for Discrete Compressed Sensing

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