相关论文: Uniform multi-penalty regularization for linear il…

A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…

Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…

A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a…

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…

Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the…

In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…

In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Combining multiple modalities carrying complementary information through multimodal learning (MML) has shown considerable benefits for diagnosing multiple pathologies. However, the robustness of multimodal models to missing modalities is…

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties.…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…