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Sampling from the posterior is a key technical problem in Bayesian statistics.
The description of a random field by means of conditional probabilities and conditions of its regularity
Roland L. Dobrushin · 1968
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Robert Shevilevich Liptser and Al’bert Nikolaevich Shiriaev · 1977
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Fundamentals of statistical exponential families: with applications in statistical decision theory
Lawrence D Brown · 1986
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Markov chain Monte Carlo in practice
Walter R Gilks, Sylvia Richardson, and David Spiegelhalter · 1995
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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An introduction to variational methods for graphical models
Michael I Jordan, Zoubin Ghahramani, Tommi S Jaakkola, and Lawrence K Saul · 1999
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On the distribution of the largest eigenvalue in principal components analysis
Iain M Johnstone · 2001
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
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Compressed sensing
David L Donoho · 2006
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Markov chain Monte Carlo: stochastic simulation for Bayesian inference
Dani Gamerman and Hedibert F Lopes · 2006
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Limitations of markov chain monte carlo algorithms for bayesian inference of phylogeny
Elchanan Mossel and Eric Vigoda · 2006
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Reconstruction for models on random graphs
Antoine Gerschenfeld and Andrea Montanari · 2007
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An introduction to compressive sampling
Emmanuel J Candès and Michael B Wakin · 2008
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Graphical models, exponential families, and variational inference
Martin J Wainwright and Michael I Jordan · 2008
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An introduction to random matrices
Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni · 2009
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Information, physics, and computation
Marc Mezard and Andrea Montanari · 2009
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Approximate bayesian computation (abc) in practice
Katalin Csilléry, Michael GB Blum, Oscar E Gaggiotti, and Olivier François · 2010
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Inverse problems: a bayesian perspective
Andrew M Stuart · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2011
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Bernstein–von mises theorems for gaussian regression with increasing number of regressors
Dominique Bontemps · 2011
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Statistics for high-dimensional data: methods, theory and applications
Peter Bühlmann and Sara Van De Geer · 2011
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Angular synchronization by eigenvectors and semidefinite programming
Amit Singer · 2011
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The computational hardness of counting in two-spin models on d-regular graphs
Allan Sly and Nike Sun · 2012
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Thin shell implies spectral gap up to polylog via a stochastic localization scheme
Ronen Eldan · 2013
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Handbook of Monte Carlo methods
Dirk P Kroese, Thomas Taimre, and Zdravko I Botev · 2013
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The Sherrington-Kirkpatrick model
Dmitry Panchenko · 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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Information-theoretically optimal sparse pca
Yash Deshpande and Andrea Montanari · 2014
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Universality in polytope phase transitions and message passing algorithms
Mohsen Bayati, Marc Lelarge, and Andrea Montanari · 2015
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, and Lenka Zdeborová · 2016
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, Lenka Zdeborová, et al · 2016
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Inapproximability of the partition function for the antiferromagnetic ising and hard-core models
Andreas Galanis, Daniel Štefankovič, and Eric Vigoda · 2016
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Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
Michael Celentano, Zhou Fan, and Song Mei · 2021
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Universality of approximate message passing algorithms
Wei Kuo Chen and Wai-Kit Lam · 2021
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TAP free energy, spin glasses and variational inference
Zhou Fan, Song Mei, and Andrea Montanari · 2021
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Estimation of low-rank matrices via approximate message passing
Andrea Montanari and Ramji Venkataramanan · 2021
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2021
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Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
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Yun Yang, Martin J Wainwright, and Michael I Jordan · 2016
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Variational inference: A review for statisticians
David M Blei, Alp Kucukelbir, and Jon D McAuliffe · 2017
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
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Asymptotic mutual information for the balanced binary stochastic block model
Yash Deshpande, Emmanuel Abbe, and Andrea Montanari · 2017
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Markov chains and mixing times
David A Levin and Yuval Peres · 2017
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Fundamental limits of low-rank matrix estimation
Léo Miolane · 2017
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Group synchronization on grids
Emmanuel Abbe, Laurent Massoulie, Andrea Montanari, Allan Sly, and Nikhil Srivastava · 2018
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Sitan Chen, Sinho Chewi, Jerry Li, Yuanzhi Li, Adil Salim, and Anru R Zhang · 2022
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Localization schemes: A framework for proving mixing bounds for markov chains
Yuansi Chen and Ronen Eldan · 2022
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Sudakov-Fernique post-AMP, and a new proof of the local convexity of the TAP free energy
Michael Celentano · 2022
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Hongrui Chen, Holden Lee, and Jianfeng Lu · 2022
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Hamilton–Jacobi equations for inference of matrix tensor products
Hong-Bin Chen and Jiaming Xia · 2022
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Convergence of denoising diffusion models under the manifold hypothesis
Valentin De Bortoli · 2022
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Spectral universality of regularized linear regression with nearly deterministic sensing matrices
Rishabh Dudeja, Subhabrata Sen, and Yue M Lu · 2022
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Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke · 2022
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A spectral condition for spectral gap: fast mixing in high-temperature ising models
Ronen Eldan, Frederic Koehler, and Ofer Zeitouni · 2022
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Analysis of high-dimensional distributions using pathwise methods
Ronen Eldan · 2022
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Approximate message passing algorithms for rotationally invariant matrices
Zhou Fan · 2022
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Sampling approximately low-rank ising models: Mcmc meets variational methods
Frederic Koehler, Holden Lee, and Andrej Risteski · 2022
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Convergence for score-based generative modeling with polynomial complexity
Holden Lee, Jianfeng Lu, and Yixin Tan · 2022
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Equivalence of approximate message passing and low-degree polynomials in rank-one matrix estimation
Andrea Montanari and Alexander S Wein · 2022
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Fundamental limits of low-rank matrix estimation with diverging aspect ratios
Andrea Montanari and Yuchen Wu · 2022
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The TAP free energy for high-dimensional linear regression
Jiaze Qiu and Subhabrata Sen · 2022
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Michael Celentano, Zhou Fan, Licong Lin, and Song Mei · 2023
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Sampling from mean-field gibbs measures via diffusion processes
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke · 2023
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Sampling, diffusions, and stochastic localization
Andrea Montanari · 2023
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Song Mei and Yuchen Wu · 2023
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Sampling from the random linear model via stochastic localization up to the amp threshold
Han Cui, Zhiyuan Yu, and Jingbo Liu · 2024
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Sampling from spherical spin glasses in total variation via algorithmic stochastic localization
Brice Huang, Andrea Montanari, and Huy Tuan Pham · 2024
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