Mirrored langevin dynamics
We consider the problem of sampling from constrained distributions, which has posed
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …
Universality of langevin diffusion for private optimization, with applications to sampling from rashomon sets
A Ganesh, A Thakurta… - The Thirty Sixth Annual …, 2023 - proceedings.mlr.press
In this paper we provide an algorithmic framework based on Langevin diffusion (LD) and its
corresponding discretizations that allow us to simultaneously obtain: i) An algorithm for …
corresponding discretizations that allow us to simultaneously obtain: i) An algorithm for …
How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences
The Laplace approximation is a popular method for providing posterior mean and variance
estimates. But can we trust these estimates for practical use? One might consider using rate …
estimates. But can we trust these estimates for practical use? One might consider using rate …
[HTML][HTML] On the stability of Brunn–Minkowski type inequalities
A Colesanti, GV Livshyts, A Marsiglietti - Journal of Functional Analysis, 2017 - Elsevier
On the stability of Brunn–Minkowski type inequalities - ScienceDirect Skip to main contentSkip
to article Elsevier logo Journals & Books Search RegisterSign in View PDF Download full …
to article Elsevier logo Journals & Books Search RegisterSign in View PDF Download full …
Stein kernels and moment maps
M Fathi - The Annals of Probability, 2019 - JSTOR
We describe a construction of Stein kernels using moment maps, which are solutions to a
variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds …
variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds …
The Brownian transport map
D Mikulincer, Y Shenfeld - Probability Theory and Related Fields, 2024 - Springer
Contraction properties of transport maps between probability measures play an important
role in the theory of functional inequalities. The actual construction of such maps, however …
role in the theory of functional inequalities. The actual construction of such maps, however …
Brascamp–Lieb-type inequalities on weighted Riemannian manifolds with boundary
AV Kolesnikov, E Milman - The Journal of Geometric Analysis, 2017 - Springer
It is known that by dualizing the Bochner–Lichnerowicz–Weitzenböck formula, one obtains
Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy …
Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy …
On the local version of the Log-Brunn–Minkowski conjecture and some new related geometric inequalities
AV Kolesnikov, GV Livshyts - … Mathematics Research Notices, 2022 - academic.oup.com
We prove that for any semi-norm on and any symmetric convex body in (1) and characterize
the equality cases of this new inequality. The above would also follow from the Log-Brunn …
the equality cases of this new inequality. The above would also follow from the Log-Brunn …
On the Gardner-Zvavitch conjecture: symmetry in inequalities of Brunn-Minkowski type
AV Kolesnikov, GV Livshyts - Advances in Mathematics, 2021 - Elsevier
In this paper, we study the conjecture of Gardner and Zvavitch from [22], which suggests that
the standard Gaussian measure γ enjoys 1 n-concavity with respect to the Minkowski …
the standard Gaussian measure γ enjoys 1 n-concavity with respect to the Minkowski …
On a conjectural symmetric version of Ehrhard's inequality
G Livshyts - Transactions of the American Mathematical Society, 2024 - ams.org
We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex
symmetric sets with respect to the Gaussian measure. Namely, letting $ J_ {k-1}(s)=\int^ s_0 …
symmetric sets with respect to the Gaussian measure. Namely, letting $ J_ {k-1}(s)=\int^ s_0 …