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We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…

Distributed sensors in the internet-of-things (IoT) generate vast amounts of sparse data. Analyzing this high-dimensional data and identifying relevant predictors pose substantial challenges, especially when data is preferred to remain on…

We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…

In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty…

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$…

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…

In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

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…