Related papers: Efficient Mixed-Norm Regularization: Algorithms an…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

In this paper we consider the problem of grouped variable selection in high-dimensional regression using $\ell_1-\ell_q$ regularization ($1\leq q \leq \infty$), which can be viewed as a natural generalization of the $\ell_1-\ell_2$…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…

In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this…

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…

In this paper, the recursive least squares (RLS) algorithm is considered in the sparse system identification setting. The cost function of RLS algorithm is regularized by a $p$-norm-like ($0 \leq p \leq 1$) constraint of the estimated…

Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…

Sparse learning is an important topic in many areas such as machine learning, statistical estimation, signal processing, etc. Recently, there emerges a growing interest on structured sparse learning. In this paper we focus on the…

Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and…

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1…

High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…

We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic…

The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…

In this work we propose and analyze a novel approach for group sparse recovery. It is based on regularized least squares with an $\ell^0(\ell^2)$ penalty, which penalizes the number of nonzero groups. One distinct feature of the approach is…

This paper considers solving the unconstrained $\ell_q$-norm ($0\leq q<1$) regularized least squares ($\ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via…

We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…

The elastic net penalty is frequently employed in high-dimensional statistics for parameter regression and variable selection. It is particularly beneficial compared to lasso when the number of predictors greatly surpasses the number of…