Related papers: Anti-concentration inequalities for log-concave va…
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…
In our recent work we found a surprising breakdown of symmetry conservation: using standard numerical discretization with very high precision the computed numerical solutions corresponding to very nice initial data may converge to…
The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…
In this article, we prove some total variation inequalities for maximal functions. Our results deal with two possible generalizations of the results contained in Aldaz and P\'erez L\'azaro's work, one of whose considers a variable…
Lie scale invariance is used to reduce the incompressible Navier-Stokes equations to non-linear ordinary equations. This yields a formulation in terms of logarithmic spirals as independent variables. We give the equations when the spirals…
This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…
We study and develop multilevel methods for the numerical approximation of a log-concave probability $\pi$ on $\mathbb{R}^d$, based on (over-damped) Langevin diffusion. In the continuity of \cite{art:egeapanloup2021multilevel} concentrated…
We consider the Frank-Wolfe algorithm for solving variational inequalities over compact, convex sets under a monotone $C^1$ operator and vanishing, nonsummable step sizes. We introduce a continuous-time interpolation of the discrete…
We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk…
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…
We show that a mixture of Beta distributions has log-concave density whenever the mixing weights are themselves log-concave. Some economic and statistical applications are provided in the last section.
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these…
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…
In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under some "curvature" assumptions. Our notion of curvature coincides with the usual $\Gamma_2$ curvature of Bakry and Emery in the…