Related papers: Regularization and the small-ball method I: sparse…
Sparse alpha-norm regularization has many data-rich applications in Marketing and Economics. Alpha-norm, in contrast to lasso and ridge regularization, jumps to a sparse solution. This feature is attractive for ultra high-dimensional…
We study Regularized Empirical Risk Minimizers (RERM) and minmax Median-Of-Means (MOM) estimators where the regularization function $\phi(\cdot)$ is an even convex function. We obtain bounds on the $L_2$-estimation error and the excess risk…
We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…
In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
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…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined,…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
The problem of minimization of the least squares functional with a smooth, lower semi-continuous, convex regularizer $J(\cdot)$ is considered to be solved. Over some compact and convex subset $\Omega$ of the Hilbert space $\mathcal{H},$ the…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization…
Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an…
Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…