Related papers: Element-wise uniqueness, prior knowledge, and data…

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

In this paper we revisit one of the classical problems of compressed sensing. Namely, we consider linear under-determined systems with sparse solutions. A substantial success in mathematical characterization of an $\ell_1$ optimization…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of…

Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Pre-trained language models have been successful on text classification tasks, but are prone to learning spurious correlations from biased datasets, and are thus vulnerable when making inferences in a new domain. Prior work reveals such…

This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…

In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…

Unsupervised and self-supervised learning approaches have become a crucial tool to learn representations for downstream prediction tasks. While these approaches are widely used in practice and achieve impressive empirical gains, their…