相关论文: Estimating the reach of a manifold via its convexi…

Point cloud completion seeks to recover geometrically consistent shapes from partial or sparse 3D observations. Although recent methods have achieved reasonable global shape reconstruction, they often rely on Euclidean proximity and…

This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…

We prove the weak and the strong convergence of the trajectories of the continuous gradient projection method under some mild assumptions on the objective function and the step size function. Moreover, we estimate the decay rate to…

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC…

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of…

In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…

Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…

A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…

In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…

We draw elliptic regularity results for 4-manifolds with an elliptic system, without Sobolev constant control. Direct use of analysis is circumvented; the results come mainly through geometric and topological arguments. In contrast to our…

We give a proof of the Donnelly-Fefferman growth bound of Laplace-Beltrami eigenfunctions which is probably the easiest and the most elementary one. Our proof also gives new quantitative geometric estimates in terms of curvature bounds…

Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact…

The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…

The volume function V(t) of a compact set S\in R^d is just the Lebesgue measure of the set of points within a distance to S not larger than t. According to some classical results in geometric measure theory, the volume function turns out to…