Macroscopic Analysis of Vector Approximate Message Passing in a Model Mismatch Setting

01/09/2020
by   Takashi Takahashi, et al.
0

Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally invariant ensembles, existing convergence and performance analyses have been limited mostly to cases in which the correct posterior distribution is available. Here, we extend the analyses for cases in which the correct posterior distribution is not used in the inference stage. We derive state evolution equations, which macroscopically describe the dynamics of VAMP, and show that their fixed point is consistent with the replica symmetric solution obtained by the replica method of statistical mechanics. We also show that the fixed point of VAMP can exhibit a microscopic instability, the critical condition of which agrees with that for breaking the replica symmetry. The results of numerical experiments support our findings.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/19/2020

Semi-analytic approximate stability selection for correlated data in generalized linear models

We consider the variable selection problem of generalized linear models ...
research
12/08/2021

Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing

We consider the problem of signal estimation in generalized linear model...
research
10/05/2021

Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization

We study a class of Approximate Message Passing (AMP) algorithms for sym...
research
02/16/2022

Analysis of Random Sequential Message Passing Algorithms for Approximate Inference

We analyze the dynamics of a random sequential message passing algorithm...
research
05/31/2023

Spontaneous symmetry breaking in generative diffusion models

Generative diffusion models have recently emerged as a leading approach ...
research
05/23/2019

Replicated Vector Approximate Message Passing For Resampling Problem

Resampling techniques are widely used in statistical inference and ensem...
research
07/03/2018

Approximate Survey Propagation for Statistical Inference

Approximate message passing algorithm enjoyed considerable attention in ...

Please sign up or login with your details

Forgot password? Click here to reset