Related papers: Uniform multi-penalty regularization for linear il…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization…

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

Bilinear pooling achieves great success in fine-grained visual recognition (FGVC). Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features, but some problems, e.g.,…

The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose…

In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees.…

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where…

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to…