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This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
Motivated by the problem of tuning hyperparameters in machine learning, we present a new approach for gradually and adaptively optimizing an unknown function using estimated gradients. We validate the empirical performance of the proposed…
In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…
The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. In this paper we focus on gamma models having a linear predictor without intercept. For a specific…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients.…
This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975) 57-70].…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-dimensional matching problem asks whether there is a disjoint collection of the hyperedges which…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…