Rigorous State Evolution Analysis for Approximate Message Passing With Side Information

Liu, Hangjin; Rush, Cynthia; Baron, Dror

doi:10.1109/tit.2022.3220046

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…However, there are now many variants on the original AMP algorithm. Remaining within the realm of Gaussian design matrices, for example, works have extended the AMP analyses to non-separable denoising functions that do not act componentwise on their vector arguments and can therefore take advantage of correlation between entries of the unknown signal [6,28], to matrices with independent entries and a blockwise variance structure [13,23], or to incorporate additional side information on the signal in order to accommodate streaming estimation procedures [26]. As mentioned, GAMP is designed to accommodate general separable output distributions; similarly for GVAMP.…”

Section: Related Workmentioning

confidence: 99%

Exponentially Fast Concentration of Vector Approximate Message Passing to its State Evolution

Cademartori

Rush

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its iterates, for N × M design matrices A with i.i.d. Gaussian entries, the asymptotic distribution of the estimate at any iteration of the algorithm can be exactly characterized in the large system limit as M/N → δ ∈ (0, ∞) via a scalar recursion referred to as state evolution. In this paper, we show that appropriate functionals of the iterates, in fact, concentrate around their limiting values predicted by these asymptotic distributions with rates exponentially fast in N for a large class of AMP-style algorithms, including those that are used when high-dimensional generalized linear regression models are assumed to be the data-generating process, like the generalized AMP algorithm, or those that are used when the measurement matrix is assumed to be right rotationally invariant instead of i.i.d. Gaussian, like vector AMP and generalized vector AMP. In practice, these more general AMP algorithms have many applications, for example in in communications or imaging, and this work provides the first study of finite sample behavior of such algorithms. c 2k (k!) κ ′ with κ, κ ′ and c, c ′ being universal constants not depending on ǫ or N . While we do not specify κ, κ ′ explicitly in this informal statement, these will be small constant values (like κ = 16 and κ ′ = 22 from Theorem 1).

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Section: Related Workmentioning

confidence: 99%

Exponentially Fast Concentration of Vector Approximate Message Passing to its State Evolution

Cademartori

Rush

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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“…Our second contribution is to the AMP [20] community. The prior art has considered vector denoisers within AMP, and even SI-aided vector denoisers within AMP [30], including rigorous state evolution results [31]. However, combining these tools within generalized AMP (GAMP) is new, to the best of our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Group Testing with Side Information via Generalized Approximate Message Passing

Cao¹,

Goenka²,

Wong³

et al. 2022

Preprint

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Group testing can help maintain a widespread testing program using fewer resources amid a pandemic. In a group testing setup, we are given n samples, one per individual. Each individual is either infected or uninfected. These samples are arranged into m < n pooled samples, where each pool is obtained by mixing a subset of the n individual samples. Infected individuals are then identified using a group testing algorithm. In this paper, we incorporate side information (SI) collected from contact tracing (CT) into nonadaptive/single-stage group testing algorithms. We generate different types of possible CT SI data by incorporating different possible characteristics of the spread of disease. These data are fed into a group testing framework based on generalized approximate message passing (GAMP). Numerical results show that our GAMP-based algorithms provide improved accuracy. Compared to a loopy belief propagation algorithm, our proposed framework can increase the success probability by 0.25 for a group testing problem of n = 500 individuals with m = 100 pooled samples.

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A Non-Asymptotic Analysis of Generalized Vector Approximate Message Passing Algorithms With Rotationally Invariant Designs

Cademartori,

Rush

2024

IEEE Trans. Inform. Theory

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Rigorous State Evolution Analysis for Approximate Message Passing With Side Information

Cited by 4 publications

References 34 publications

Exponentially Fast Concentration of Vector Approximate Message Passing to its State Evolution

Exponentially Fast Concentration of Vector Approximate Message Passing to its State Evolution

Group Testing with Side Information via Generalized Approximate Message Passing

A Non-Asymptotic Analysis of Generalized Vector Approximate Message Passing Algorithms With Rotationally Invariant Designs

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