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Bayesian inference problems require sampling or approximating high-dimensional probability distributions.
Accelerating Langevin sampling with birth-death
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Using perturbed underdamped Langevin dynamics to efficiently sample from probability distributions
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Fluctuations and irreversible process. ii. systems with kinetic energy
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Convex analysis , volume 28
R. T. Rockafellar · 1970
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Methods of modern mathematical physics , volume 1
Michael Reed, Barry Simon, Barry Simon, and Barry Simon · 1972
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A polyalgorithm for the numerical solution of ordinary differential equations
G. D. Byrne and A. C. Hindmarsh · 1975
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Introductory functional analysis with applications , volume 1
E. Kreyszig · 1978
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Recurrence and invariant measures for degenerate diffusions
W. Kliemann · 1987
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Stability of Markovian processes iii: Foster–Lyapunov criteria for continuous-time processes
S. P. Meyn and R. L. Tweedie · 1993
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Exponential convergence of Langevin distributions and their discrete approximations
G. O. Roberts, R. L. Tweedie, et al · 1996
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A convexity principle for interacting gases
R. J. McCann · 1997
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The variational formulation of the Fokker–Planck equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
F. Otto · 1998
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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
F. Otto and C. Villani · 2000
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The geometry of dissipative evolution equations: the porous medium equation
F. Otto · 2001
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Scattered data approximation , volume 17
H. Wendland · 2004
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Fourier analysis in convex geometry
A. Koldobsky · 2005
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On learning vector-valued functions
C. A. Micchelli and M. Pontil · 2005
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Beyond equilibrium thermodynamics
H. C. Öttinger · 2005
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Eulerian calculus for the contraction in the Wasserstein distance
F. Otto and M. Westdickenberg · 2005
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Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem
C. Carmeli, E. De Vito, and A. Toigo · 2006
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Riemannian manifolds: an introduction to curvature , volume 176
J. M. Lee · 2006
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Meshfree approximation methods with MATLAB , volume 6
G. E. Fasshauer · 2007
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Gradient flows: in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
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Eulerian calculus for the displacement convexity in the Wasserstein distance
S. Daneri and G. Savaré · 2008
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Some geometric calculations on Wasserstein space
J. Lott · 2008
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Support vector machines
I. Steinwart and A. Christmann · 2008
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An optimization problem for mass transportation with congested dynamics
G. Buttazzo, C. Jimenez, and E. Oudet · 2009
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A new class of transport distances between measures
J. Dolbeault, B. Nazaret, and G. Savaré · 2009
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Kernel choice and classifiability for RKHS embeddings of probability distributions
K. Fukumizu, A. Gretton, G. R. Lanckriet, B. Schölkopf, and B. K. Sriperumbudur · 2009
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Optimal transport , volume 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
C. Villani · 2009
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Nonlinear mobility continuity equations and generalized displacement convexity
J. A. Carrillo, S. Lisini, G. Savaré, and D. Slepčev · 2010
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Hilbert space embeddings and metrics on probability measures
B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. G. Lanckriet · 2010
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Stochastic stability of differential equations , volume 66
R Khasminskii · 2011
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A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
Probabilistic Theory of Mean Field Games with Applications I-II
R. Carmona and F. Delarue · 2018
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A Stein variational Newton method
G. Detommaso, T. Cui, Y. Marzouk, A. Spantini, and R. Scheichl · 2018
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Stochastic gradient MCMC with repulsive forces
V. Gallego and D. R. Insua · 2018
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Natural gradient via optimal transport
W. Li and G. Montúfar · 2018
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Riemannian Stein variational gradient descent for Bayesian inference
C. Liu and J. Zhu · 2018
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Stein variational gradient descent as moment matching
Q. Liu and D. Wang · 2018
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A. Mielke · 2011
Cited alongside, same era.
Universality, characteristic kernels and RKHS embedding of measures
B. K. Sriperumbudur, K. Fukumizu, and G. R. G. Lanckriet · 2011
Cited alongside, same era.
Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction
S. Arnrich, A. Mielke, M. A. Peletier, G. Savaré, and M. Veneroni · 2012
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A survey on dynamical transport distances
L. Brasco · 2012
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Second Order Analysis on ( 𝒫 2 ( M ) , W 2 ) (\mathcal{P}_{2}(M),W_{2})
N. Gigli · 2012
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A user’s guide to optimal transport
L. Ambrosio and N. Gigli · 2013
Cited alongside, same era.
Analysis and geometry of Markov diffusion operators , volume 348
D. Bakry, I. Gentil, and M. Ledoux · 2013
Cited alongside, same era.
Sobolev GAN
Y. Mroueh, C.-L. Li, T. Sercu, A. Raj, and Y. Cheng · 2018
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Kernel embedding of maps for sequential Bayesian inference: the variational mapping particle filter
M. Pulido and P. J. van Leeuwen · 2018
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Towards more theoretically-grounded sampling for deep learning
J. Zhang, R. Zhang, and C. Chen · 2018
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Message passing Stein variational gradient descent
J. Zhuo, C. Liu, J. Shi, J. Zhu, N. Chen, and B. Zhang · 2018
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Maximum mean discrepancy gradient flow
M. Arbel, A. Korba, A. Salim, and A. Gretton · 2019
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Greedy inference with layers of lazy maps
D. Bigoni, O. Zahm, A. Spantini, and Y. Marzouk · 2019
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Projected Stein variational Newton: A fast and scalable Bayesian inference method in high dimensions
P. Chen, K. Wu, J. Chen, T. O’Leary-Roseberry, and O. Ghattas · 2019
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G. Detommaso, H. Hoitzing, T. Cui, and A. Alamir · 2019
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Deep generative learning via variational gradient flow
Y. Gao, Y. Jiao, Y. Wang, Y. Wang, C. Yang, and S. Zhang · 2019
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Diffusion hypercontractivity via generalized density manifold
W. Li · 2019
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Understanding and accelerating particle-based variational inference
C. Liu, J. Zhuo, P. Cheng, R. Zhang, and J. Zhu · 2019
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Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
A. Liutkus, U. Simsekli, S. Majewski, A. Durmus, and F.-R. Stöter · 2019
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Sobolev descent
Y. Mroueh, T. Sercu, and A. Raj · 2019
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Constructing sampling schemes via coupling: Markov semigroups and optimal transport
N. Nüsken and G. A. Pavliotis · 2019
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N. Nüsken and S Reich · 2019
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Discrete gradients for computational Bayesian inference
S. Pathiraja and S. Reich · 2019
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A stochastic version of Stein variational gradient descent for efficient sampling
L. Li, Y. Li, J.-G. Liu, Z. Liu, and J. Lu · 2020
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Ricci curvature for parametric statistics via optimal transport
W. Li and G. Montúfar · 2020
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Information Newton’s flow: second-order optimization method in probability space
Y. Wang and W. Li · 2020
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Stochastic particle-optimization sampling and the non-asymptotic convergence theory
J. Zhang, R. Zhang, L. Carin, and C. Chen · 2020
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An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
Alessio Figalli and Federico Glaudo · 2021
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Hessian metric via transport information geometry
W. Li · 2021
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Stein variational gradient descent: many-particle and long-time asymptotics
N. Nüsken and D. R. Renger · 2021
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Fokker–Planck particle systems for Bayesian inference: Computational approaches
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