Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Felix Otto,Cédric Villani +1 more
TLDR
In this paper, it was shown that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587-600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities.About:
This article is published in Journal of Functional Analysis.The article was published on 2000-06-01 and is currently open access. It has received 1080 citations till now. The article focuses on the topics: Sobolev inequality & Interpolation inequality.read more
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A unified performance analysis of likelihood-informed subspace methods
Tiangang Cui,Xin T. Tong +1 more
TL;DR: The likelihood-informed subspace (LIS) method as discussed by the authors identifies an intrinsic low-dimensional linear subspace where the target distribution differs the most from some tractable reference distribution, and then the original high-dimensional target distribution is approximated through various forms of ridge approximations of the likelihood function.
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Convergence of the Riemannian Langevin Algorithm
TL;DR: In this article , the Riemannian Langevin algorithm for the problem of sampling from a distribution with density ν with respect to the natural measure on a manifold with metric g was studied.
How good is your Gaussian approximation of the posterior? Finite-sample computable error bounds for a variety of useful divergences
TL;DR: This work provides the first closed-form, finite-sample bounds for the quality of the Laplace approximation that do not require log concavity of the posterior or an exponential-family likelihood.
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Faster high-accuracy log-concave sampling via algorithmic warm starts
Jason M. Altschuler,Sinho Chewi +1 more
TL;DR: In this paper , the authors improved the complexity of sampling from a strongly log-concave and log-smooth distribution to high accuracy by using differential privacy techniques based on R\'enyi divergences with Orlicz-Wasserstein shifts.
Large deviation and variational approaches to generalized gradient flows
TL;DR: A submitted manuscript is the author's version of the article upon submission and before peer-review as discussed by the authors, and the final published version features the final layout of the paper including the volume, issue and page numbers.
References
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Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
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Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
TL;DR: In this paper, it was shown that for every vector-valued function u Lp(X, p; Rd) there is a unique polar factorization u = V$.s, where $ is a convex function defined on R and s is a measure-preserving mapping from (x, p) into (Q, I. I), provided that u is nondegenerate.
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The geometry of dissipative evolution equations: the porous medium equation
TL;DR: In this paper, the authors show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural, and they use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
Book
Topological methods in hydrodynamics
Vladimir I. Arnold,Boris Khesin +1 more
TL;DR: A group theoretical approach to hydrodynamics is proposed in this article, where the authors consider the hydrodynamic geometry of diffeomorphism groups and the principle of least action implies that the motion of a fluid is described by geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy.
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The variational formulation of the Fokker-Planck equation
TL;DR: The Fokker-Planck equation as mentioned in this paper describes the evolution of the probability density for a stochastic process associated with an Ito Stochastic Differential Equation.