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Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference.
Stein’s lemma for the reparameterization trick with exponential family mixtures
Wu Lin, Mohammad E. Khan, and Mark Schmidt · 1910
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An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w ∗ w^{\ast} -algebras
Donald Bures · 1969
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Square-root algorithms for the continuous-time linear least squares estimation problem
Martin Morf, Bernard Levy, and Thomas Kailath · 1977
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On the limited memory BFGS method for large scale optimization
Dong C. Liu and Jorge Nocedal · 1989
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Riemannian geometry
Manfredo P. do Carmo · 1992
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Ensemble learning for multi-layer networks
David Barber and Christopher Bishop · 1997
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The variational formulation of the Fokker–Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Dynamics of labyrinthine pattern formation in magnetic fluids: a mean-field theory
Felix Otto · 1998
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A numerical method for the optimal time-continuous mass transport problem and related problems
Jean-David Benamou and Yann Brenier · 1999
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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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Bayesian model selection for support vector machines, Gaussian processes and other kernel classifiers
Matthias Seeger · 1999
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Methods of information geometry , volume 191 of Translations of Mathematical Monographs
Shun-ichi Amari and Hiroshi Nagaoka · 2000
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A new method for the nonlinear transformation of means and covariances in filters and estimators
Simon J. Julier, Jeffrey K. Uhlmann, and Hugh F. Durrant-Whyte · 2000
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The geometry of dissipative evolution equations: the porous medium equation
Felix Otto · 2001
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Constrained steepest descent in the 2-Wasserstein metric
Eric A. Carlen and Wilfrid Gangbo · 2003
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Topics in optimal transportation , volume 58 of Graduate Studies in Mathematics
Cédric Villani · 2003
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Unsupervised variational Bayesian learning of nonlinear models
Antti Honkela and Harri Valpola · 2004
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Unscented filtering and nonlinear estimation
Simon J. Julier and Jeffrey K. Uhlmann · 2004
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Pattern recognition and machine learning
Christopher M. Bishop · 2006
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On unscented Kalman filtering for state estimation of continuous-time nonlinear systems
Simo Särkkä · 2007
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Gradient flows in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Graphical models, exponential families, and variational inference
Martin J. Wainwright and Michael I. Jordan · 2008
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Cubature Kalman filters
Ienkaran Arasaratnam and Simon Haykin · 2009
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On a constrained 2-D Navier–Stokes equation
Emanuele Caglioti, Mario Pulvirenti, and Frédéric Rousset · 2009
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The variational Gaussian approximation revisited
Manfred Opper and Cédric Archambeau · 2009
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Optimal transport , volume 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
Cédric Villani · 2009
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Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
José A. Carrillo, Marco Di Francesco, Alessio Figalli, Thomas Laurent, and Dejan Slepčev · 2011
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On a nonlinear, nonlocal parabolic problem with conservation of mass, mean and variance
Adrian Tudorascu and Marcus Wunsch · 2011
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Confinement in nonlocal interaction equations
José A. Carrillo, Marco Di Francesco, Alessio Figalli, Thomas Laurent, and Dejan Slepčev · 2012
Cited alongside, same era.
Variational Bayesian inference with stochastic search
John Paisley, David M. Blei, and Michael I. Jordan · 2012
Cited alongside, same era.
Gaussian Kullback–Leibler approximate inference
Edward Challis and David Barber · 2013
Cited alongside, same era.
Analysis and geometry of Markov diffusion operators , volume 348 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
Dominique Bakry, Ivan Gentil, and Michel Ledoux · 2014
Cited alongside, same era.
Black box variational inference
Rajesh Ranganath, Sean Gerrish, and David M. Blei · 2014
Cited alongside, same era.
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
Accelerating Langevin sampling with birth-death
Yulong Lu, Jianfeng Lu, and James Nolen · 2019
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Computational optimal transport: with applications to data science
Gabriel Peyré and Marco Cuturi · 2019
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The randomized midpoint method for log-concave sampling
Ruoqi Shen and Yin Tat Lee · 2019
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Rapid convergence of the unadjusted Langevin algorithm: isoperimetry suffices
Santosh Vempala and Andre Wibisono · 2019
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Frequentist consistency of variational Bayes
Yixin Wang and David M. Blei · 2019
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Concentration of tempered posteriors and of their variational approximations
Pierre Alquier and James Ridgway · 2020
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Giovanni A. Bonaschi, José A. Carrillo, Marco Di Francesco, and Mark A. Peletier · 2015
Cited alongside, same era.
Optimal transport for applied mathematicians , volume 87 of Progress in Nonlinear Differential Equations and their Applications
Filippo Santambrogio · 2015
Cited alongside, same era.
On the properties of variational approximations of Gibbs posteriors
Pierre Alquier, James Ridgway, and Nicolas Chopin · 2016
Cited alongside, same era.
A blob method for the aggregation equation
Katy Craig and Andrea L. Bertozzi · 2016
Cited alongside, same era.
Optimal transport in competition with reaction: the Hellinger–Kantorovich distance and geodesic curves
Matthias Liero, Alexander Mielke, and Giuseppe Savaré · 2016
Cited alongside, same era.
Stein variational gradient descent: a general purpose Bayesian inference algorithm
Qiang Liu and Dilin Wang · 2016
Cited alongside, same era.
Information geometry , volume 64 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]
Nihat Ay, Jürgen Jost, Hông Vân Lê, and Lorenz Schwachhöfer · 2017
Cited alongside, same era.
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Fast mixing of Metropolized Hamiltonian Monte Carlo: benefits of multi-step gradients
Yuansi Chen, Raaz Dwivedi, Martin J. Wainwright, and Bin Yu · 2020
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SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, and Philippe Rigollet · 2020
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Gradient descent algorithms for Bures–Wasserstein barycenters
Sinho Chewi, Tyler Maunu, Philippe Rigollet, and Austin J. Stromme · 2020
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On sampling from a log-concave density using kinetic Langevin diffusions
Arnak S. Dalalyan and Lionel Riou-Durand · 2020
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A Wasserstein-type distance in the space of Gaussian mixture models
Julie Delon and Agnès Desolneux · 2020
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Provable smoothness guarantees for black-box variational inference
Justin Domke · 2020
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Analysis of Langevin Monte Carlo from Poincaré to log-Sobolev
Sinho Chewi, Murat A. Erdogdu, Mufan B. Li, Ruoqi Shen, and Matthew Zhang · 2021
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Mixture weights optimisation for alpha-divergence variational inference
Kamélia Daudel and Randal Douc · 2021
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Infinite-dimensional gradient-based descent for alpha-divergence minimisation
Kamélia Daudel, Randal Douc, and François Portier · 2021
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Flexible and efficient inference with particles for the variational Gaussian approximation
Théo Galy-Fajou, Valerio Perrone, and Manfred Opper · 2021
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The limited-memory recursive variational Gaussian approximation (L-RVGA)
Marc Lambert, Silvère Bonnabel, and Francis Bach · 2021
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Structured logconcave sampling with a restricted Gaussian oracle
Yin Tat Lee, Ruoqi Shen, and Kevin Tian · 2021
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Is there an analog of Nesterov acceleration for gradient-based MCMC?
Yi-An Ma, Niladri S. Chatterji, Xiang Cheng, Nicolas Flammarion, Peter L. Bartlett, and Michael I. Jordan · 2021
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A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling
Katy Craig, Karthik Elamvazhuthi, Matt Haberland, and Olga Turanova · 2022
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Efficient derivative-free Bayesian inference for large-scale inverse problems
Daniel Z. Huang, Jiaoyang Huang, Sebastian Reich, and Andrew M. Stuart · 2022
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Mohammad Emtiyaz Khan and Rue Håvard · 2022
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An optimization-centric view on Bayes’ rule: reviewing and generalizing variational inference
Jeremias Knoblauch, Jack Jewson, and Theodoros Damoulas · 2022
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The continuous-discrete variational Kalman filter (CD-VKF)
Marc Lambert, Silvère Bonnabel, and Francis Bach · 2022
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Minimax mixing time of the Metropolis-adjusted Langevin algorithm for log-concave sampling
Keru Wu, Scott Schmidler, and Yuansi Chen · 2022
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The computational asymptotics of Gaussian variational inference and the Laplace approximation
Zuheng Xu and Trevor Campbell · 2022
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Averaging on the Bures–Wasserstein manifold: dimension-free convergence of gradient descent
Jason Altschuler, Sinho Chewi, Patrik Gerber, and Austin J. Stromme · 2023
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