Related papers: Correlated Feature Selection with Extended Exclusi…

The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…

Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…

We propose a method for finding alternate features missing in the Lasso optimal solution. In ordinary Lasso problem, one global optimum is obtained and the resulting features are interpreted as task-relevant features. However, this can…

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…

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…

The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is…

The sparse-group lasso performs both variable and group selection, simultaneously using the strengths of the lasso and group lasso. It has found widespread use in genetics, a field that regularly involves the analysis of high-dimensional…

Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding…

In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…

We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…

The Lasso has been widely used as a method for variable selection, valued for its simplicity and empirical performance. However, Lasso's selection stability deteriorates in the presence of correlated predictors. Several approaches have been…

We propose a general family of algorithms for regression estimation with quadratic loss. Our algorithms are able to select relevant functions into a large dictionary. We prove that a lot of algorithms that have already been studied for this…

In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…

Along with the desire to address more complex problems, feature selection methods have gained in importance. Feature selection methods can be classified into wrapper method, filter method, and embedded method. Being a powerful embedded…

We consider the problems of estimation and selection of parameters endowed with a known group structure, when the groups are assumed to be sign-coherent, that is, gathering either nonnegative, nonpositive or null parameters. To tackle this…

The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…

We propose a novel approach, Sequential Lasso, for feature selection in linear regression models with ultra-high dimensional feature spaces. We investigate in this article the asymptotic properties of Sequential Lasso and establish its…

The high dimensional nature of genomics data complicates feature selection, in particular in low sample size studies - not uncommon in clinical prediction settings. It is widely recognized that complementary data on the features, `co-data',…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…