相关论文: 2DNMR data inversion using locally adapted multi-p…

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

The atomic norm provides a generalization of the $\ell_1$-norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This…

The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…

The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks. Inspired by the well-known Tammes problem, we propose a novel diversity regularization method to address this issue,…

The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

Mean-variance optimization (MVO) is known to be sensitive to estimation error in its inputs. Norm penalization of MVO programs is a regularization technique that can mitigate the adverse effects of estimation error. We augment the standard…

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…

We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving…

Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while…

This work proposes an efficient batch algorithm for feature selection in reinforcement learning (RL) with theoretical convergence guarantees. To mitigate the estimation bias inherent in conventional regularization schemes, the first…

In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such…

Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or…

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…

Nonnegative Matrix Factorization (NMF), first proposed in 1994 for data analysis, has received successively much attention in a great variety of contexts such as data mining, text clustering, computer vision, bioinformatics, etc. In this…