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Recently, Approximate Message Passing (AMP) has been integrated with stochastic localization (diffusion model) by providing a computationally efficient estimator of the posterior mean.
Statistics of random processes: General theory , volume 394
Robert Shevilevich Liptser and Albert Nikolaevich Shiriaev · 1977
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Digital Image Processing (3rd Edition)
Rafael C. Gonzalez and Richard E. Woods · 2006
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Message passing algorithms for compressed sensing
David L. Donoho, Arian Maleki, and Andrea Montanari · 2009
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Mean field models for spin glasses: Volume I: Basic examples , volume 54
Michel Talagrand · 2010
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Magnetic resonance imaging: theory and practice
Marinus T. Vlaardingerbroek and Jacques A. Boer · 2010
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The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
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The lasso risk for gaussian matrices
Mohsen Bayati and Andrea Montanari · 2011
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Generalized approximate message passing for estimation with random linear mixing
Sundeep Rangan · 2011
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Graphical models concepts in compressed sensing
Andrea Montanari, YC Eldar, and G Kutyniok · 2012
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Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator
Xiaobo Qu, Yingkun Hou, Fan Lam, Jianhui Zhong, and Zhong Chen · 2013
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Convergence rate of Markov chain methods for genomic motif discovery
Dawn B. Woodard and Jeffrey S. Rosenthal · 2013
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Variational free energies for compressed sensing
Florent Krzakala, Andre Manoel, Eric W Tramel, and Lenka Zdeborová · 2014
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High-Dimensional Probability: An Introduction with Applications in Data Science
Roman Vershynin · 2018
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Optimal errors and phase transitions in high-dimensional generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2019
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Mutual information and optimality of approximate message-passing in random linear estimation
Jean Barbier, Nicolas Macris, Mohamad Dia, and Florent Krzakala · 2020
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State evolution for approximate message passing with non-separable functions
Raphael Berthier, Andrea Montanari, and Phan-Minh Nguyen · 2020
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The estimation error of general first order methods
Michael Celentano, Andrea Montanari, and Yuchen Wu · 2020
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Tap free energy, spin glasses and variational inference
Solving inverse problems in medical imaging with score-based generative models
Yang Song, Liyue Shen, Lei Xing, and Stefano Ermon · 2022
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Operator norm bounds on the correlation matrix of the sk model at high temperature
Christian Brennecke, Changji Xu, and Horng-Tzer Yau · 2023
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Diffusion posterior sampling for general noisy inverse problems
Hyungjin Chung, Jeongsol Kim, Michael T Mccann, Marc L Klasky, and Jong Chul Ye · 2023
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Universality of approximate message passing with semirandom matrices
Rishabh Dudeja, Yue M. Lu, and Subhabrata Sen · 2023
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Sampling, diffusions, and stochastic localization
Andrea Montanari · 2023
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Sampling from the sherrington-kirkpatrick gibbs measure via algorithmic stochastic localization
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Variational inference in high-dimensional linear regression
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Diffusion models are minimax optimal distribution estimators
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The tap free energy for high-dimensional linear regression
Jiaze Qiu and Subhabrata Sen · 2023
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Sampling with flows, diffusion, and autoregressive neural networks from a spin-glass perspective
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Minimax optimality of score-based diffusion models: Beyond the density lower bound assumptions
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