相关论文: CR-Lasso: Robust cellwise regularized sparse regre…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Cellwise outliers are likely to occur together with casewise outliers in modern data sets with relatively large dimension. Recent work has shown that traditional robust regression methods may fail for data sets in this paradigm. The…

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…

This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…

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…

We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology, initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly…

Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…

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…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…

We propose the Lasso Weighted $k$-means ($LW$-$k$-means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features ($p$) can be much larger compared to the number of observations…

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…

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods such as compressed sensing. In statistical learning, a class of methods known as structured sparsity…

Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…