Related papers: Model Selection with Low Complexity Priors

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\left(Y_i-f(X_i)\right)^2+\lambda \Psi(f)\right) \end{equation*} when $\Psi$…

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…

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…

This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1),…

Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…

Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional…

The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…