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In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query.
On small random perturbations of dynamical systems
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John Milnor · 1976
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Nobuyuki Ikeda and Shinzo Watanabe · 1977
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Yasumasa Saisho · 1987
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Luigi Ambrosio and Carlo Mantegazza · 1998
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Stochastic analysis on manifolds , volume 38
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A note on the poincaré inequality for convex domains
Mario Bebendorf · 2003
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A theory of the term structure of interest rates
John C Cox, Jonathan E Ingersoll Jr, and Stephen A Ross · 2005
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The largest eigenvalue of small rank perturbations of hermitian random matrices
Sandrine Péché · 2006
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A simple proof of the poincaré inequality for a large class of probability measures including the log-concave case
Dominique Bakry, Franck Barthe, Patrick Cattiaux, and Arnaud Guillin · 2008
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A general two-scale criteria for logarithmic sobolev inequalities
Tony Lelièvre · 2009
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An introduction to random matrices, volume 118 of cambridge studies in advanced mathematics, 2010
Greg W Anderson, Alice Guionnet, and Ofer Zeitouni · 2010
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Mathematical methods for financial markets
Monique Jeanblanc, Marc Yor, and Marc Chesney · 2010
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A survey of ricci curvature for metric spaces and markov chains
Yann Ollivier · 2010
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Condition: The geometry of numerical algorithms , volume 349
Peter Bürgisser and Felipe Cucker · 2013
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Lie groups, Lie algebras, and their representations , volume 102
Veeravalli S Varadarajan · 2013
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Guaranteed matrix completion via non-convex factorization
Ruoyu Sun and Zhi-Quan Luo · 2016
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Arnak S Dalalyan · 2017
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 2017
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How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan · 2017
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Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis
Maxim Raginsky, Alexander Rakhlin, and Matus Telgarsky · 2017
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Sébastien Bubeck, Ronen Eldan, and Joseph Lehec · 2015
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Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Benjamin Recht · 2015
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
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Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition
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Rong Ge, Jason D Lee, and Tengyu Ma · 2016
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Ravid Shwartz-Ziv and Naftali Tishby · 2017
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A hitting time analysis of stochastic gradient langevin dynamics
Yuchen Zhang, Percy Liang, and Moses Charikar · 2017
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Optimality and sub-optimality of pca i: Spiked random matrix models
Amelia Perry, Alexander S Wein, Afonso S Bandeira, Ankur Moitra, et al · 2018
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Xiang Cheng, Peter L Bartlett, and Michael I Jordan · 2019
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Implicit generation and generalization in energy-based models
Yilun Du and Igor Mordatch · 2019
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Sampling can be faster than optimization
Yi-An Ma, Yuansi Chen, Chi Jin, Nicolas Flammarion, and Michael I Jordan · 2019
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Sampling for bayesian mixture models: Mcmc with polynomial-time mixing
Wenlong Mou, Nhat Ho, Martin J Wainwright, Peter L Bartlett, and Michael I Jordan · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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