Related papers: Minimax lower bounds for function estimation on gr…
We study classification problems using binary estimators where the decision boundary is described by horizon functions and where the data distribution satisfies a geometric margin condition. A key novelty of our work is the derivation of…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
In this work we consider the problem of estimating function-on-scalar regression models when the functions are observed over multi-dimensional or manifold domains and with potentially multivariate output. We establish the minimax rates of…
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total…
We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate "Riemannian" metric to uniformize the geometry of the graph. In many interesting cases, the existence of…
We obtain sharp oracle inequalities for the empirical risk minimization procedure in the regression model under the assumption that the target Y and the model F are subgaussian. The bound we obtain is sharp in the minimax sense if F is…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
We develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. The extension we compute is the absolutely…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…
In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a…
In this paper, we are interested in learning the underlying graph structure behind training data. Solving this basic problem is essential to carry out any graph signal processing or machine learning task. To realize this, we assume that the…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of \emph{patchworks} to describe the possible…
We prove local and global upper estimates for the infimum of the mean curvature, the scalar curvature and the norm of the shape operator of graphs in a warped product space. Using these estimates, we obtain some results on pseudo-hyperbolic…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…