English
Related papers

Related papers: Lasso Estimation of an Interval-Valued Multiple Re…

200 papers

The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…

Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…

Statistics Theory · Mathematics 2022-03-30 Zheng Tracy Ke , Longlin Wang

We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We…

Machine Learning · Computer Science 2012-06-22 Elad Hazan , Tomer Koren

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…

Computation · Statistics 2015-09-29 Rahul Mazumder , Arkopal Choudhury , Garud Iyengar , Bodhisattva Sen

The purpose of the present paper is to investigate on a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding…

Statistics Theory · Mathematics 2020-07-06 Alessia Caponera , Claudio Durastanti , Anna Vidotto

The use of prior information in the linear regression is well known to provide more efficient estimators of regression coefficients. The methods of non-stochastic restricted regression estimation proposed by Theil and Goldberger (1961) are…

Applications · Statistics 2017-10-12 Yetkin Tuaç , Olcay Arslan

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

Machine Learning · Statistics 2013-02-28 Aleksandr Y. Aravkin , James V. Burke , Alessandro Chiuso , Gianluigi Pillonetto

We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…

Machine Learning · Computer Science 2009-01-22 Francis Bach

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

Methodology · Statistics 2019-07-22 Guo Yu , Jacob Bien

The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, including the change-points, and automatic variable…

Statistics Theory · Mathematics 2012-04-19 Gabriela Ciuperca

Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually…

Applications · Statistics 2022-10-31 Tingting Huang

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

Optimization and Control · Mathematics 2019-03-13 Zengde Deng , Anthony Man-Cho So

Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…

Statistics Theory · Mathematics 2014-10-31 James Sharpnack , Mladen Kolar

The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…

Methodology · Statistics 2023-11-21 Anant Mathur , Sarat Moka , Zdravko Botev

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…

Econometrics · Economics 2024-01-17 Ziwei Mei , Zhentao Shi

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double…

Statistics Theory · Mathematics 2008-05-09 Yuval Nardi , Alessandro Rinaldo

Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context…

Statistics Theory · Mathematics 2016-11-09 Arnak S. Dalalyan , Mohamed Hebiri , Johannes Lederer

A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the…

Machine Learning · Statistics 2021-09-24 Shuaiwen Wang , Haolei Weng , Arian Maleki

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…

Applications · Statistics 2025-02-03 Andreas Alfons , Christophe Croux , Sarah Gelper

When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…

Machine Learning · Statistics 2020-06-12 Huamei Huang , Yujing Gao , Huiming Zhang , Bo Li