Related papers: The Geometry and Well-Posedness of Sparse Regulari…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…

In this work, we address three non-convex optimization problems associated with the training of shallow neural networks (NNs) for exact and approximate representation, as well as for regression tasks. Through a mean-field approach, we…

We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…

We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

Spectrahedra are affine sections of the cone of positive semidefinite matrices which form a rich class of convex bodies that properly contains that of polyhedra. While the class of polyhedra is closed under linear projections, the class of…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…

We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…