arXiv research

Sparse group Lasso optimizes sparse and grouped parameters in high-dimensional data.

In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance group sparsity. Sparse-Group Lasso has recently been introduced in the context of l…

A new estimator learns sparse linear models with context-dependent coefficients.

DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…

Bayesian Lasso Sparse model provides sparse estimates in linear and nonlinear regression.

Proposes an algorithm for infinite-dimensional sparse learning in system identification.

A two-phase algorithm identifies the best arm in sparse linear bandits with fixed budget.

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 usual group Lasso penalty on a set of latent variables. A detailed analysis of th…

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is …

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 used to investigate the performance of the multinomial sparse group lasso classifi…

New bounds for Lasso and Group Lasso in high dimensions derived.

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In th…

In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping variables and then pursuing model fitting is widely accepted. When the dimension is…

c-lasso is a Python tool for robust and sparse regression with linear constraints.

Improves Group Lasso for categorical data by reducing dimensionality and selecting models.

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the indivi…

New theorem for generalized group sparsity improves consistency and convergence rates.

Improved online Lasso reduces regret in sparse linear contextual bandits.

The paper tackles automatic interpretation of manifold coordinates.

The Lasso is suboptimal in sparse linear regression due to design matrix constraints.

Lasso performs poorly with correlated covariates, but a rescaled approach fixes this.

New method corrects selection bias in post-selective inference for Group LASSO.

New guarantees for Group LASSO in sparse convex optimization.

Study improves carbon price forecasting using quantile regression and feature selection.

New research shows how preconditioning can solve sparse linear regression problems efficiently.

SNAM improves NAM's accuracy and feature selection via group sparsity.

The paper examines how to protect LASSO-based feature selection from adversarial attacks.

Robust Lasso-Zero handles missing covariates and sparse corruptions.

Paper introduces machine learning for time series data, improving nowcasting accuracy.

In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the $\ell_1$- and $\ell_2$-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…

Thresholded Lasso bandit minimizes regret in sparse linear bandits.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…

Study high-dimensional Granger causality tests for VIX and financial news.

A new method solves large-scale sparse group square-root Lasso problems efficiently.

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal $\ell_{1,\infty}$-penalized recursive least squares (R…

Genome-wide association studies (GWA studies or GWAS) investigate the relationships between genetic variants such as single-nucleotide polymorphisms (SNPs) and individual traits. Recently, incorporating biological priors together with machine learning methods in GWA studies has attracted increasing attention. However, …

Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.

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 schemes. As proposed in Yuan and Lin [J. R. Statist. Soc. B, 68 (2006), 49-67], the gr…

In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\ell_…

Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group effects upon variable selection. To this end, we first propose group-sparse SVD model…

The paper improves machine learning for heavy-tailed panel data.

Paper develops a new estimator for high-dimensional panel data with common shocks.

A new method solves sparse regularization problems efficiently and robustly.

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its variants which have been shown to converge under nonconvex context recently. We show th…

L2-Boosting fails to recover sparse parameters in high-dimensional models.

In this paper, we consider the joint task of simultaneously optimizing (i) the weights of a deep neural network, (ii) the number of neurons for each hidden layer, and (iii) the subset of active input features (i.e., feature selection). While these problems are generally dealt with separately, we present a simple regula…

New theoretical framework improves error rates for sparse learning with convex regularization.