Related papers: Iterative regularization for convex regularizers
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…
Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised learning. Model consistency consists then in selecting the…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…
In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
In this paper, we analyse the recovery properties of nonconvex regularized $M$-estimators, under the assumption that the true parameter is of soft sparsity. In the statistical aspect, we establish the recovery bound for any stationary point…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…
The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…