相关论文: Asymptotic Properties of Lasso+mLS and Lasso+Ridge…

The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…

Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some…

The least trimmed squares (LTS) estimator is a renowned robust alternative to the classic least squares estimator and is popular in location, regression, machine learning, and AI literature. Many studies exist on LTS, including its…

This paper presents a comprehensive exploration of the theoretical properties inherent in the Adaptive Lasso and the Transfer Lasso. The Adaptive Lasso, a well-established method, employs regularization divided by initial estimators and is…

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression…

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge…

The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO…

The fused lasso is an important method for signal processing when the hidden signals are sparse and blocky. It is often used in combination with the squared loss function. However, the squared loss is not suitable for heavy tail error…

Data driven soft sensor design has recently gained immense popularity, due to advances in sensory devices, and a growing interest in data mining. While partial least squares (PLS) is traditionally used in the process literature for…

The Lasso is one of the most ubiquitous methods for variable selection in high-dimensional linear regression and has been studied extensively under different regimes. In a particular asymptotic setup entailing $n/p\to \text{constant}$, an…

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…

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…