Related papers: A theory of shape regularity for local regression …

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

By applying some theorems of Levy and Mordukhovich (Math Program 99: 311--327, 2004) and other related results, we estimate the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric…

We give a sharp lower bound on the number of matchings of a given size in a bipartite graph. When specialized to regular bipartite graphs, our results imply Friedland's Lower Matching Conjecture and Schrijver's theorem proven by Gurvits and…

Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…

Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes…

We obtain some sharp estimates for the $p$-torsion of convex planar domains in terms of their area, perimeter, and inradius. The approach we adopt relies on the use of web functions (i.e. functions depending only on the distance from the…

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…

Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…

Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…

This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a…

We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…

These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order…

Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

In this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning $C^1$-extremals at which the second variation is strictly positive. The results are presented in the quasiconvex setting, in accordance…