Related papers: A Stable Lasso
Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set keeps good statistical properties of the original estimator under standard assumptions, and guarantees valid average…
In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended…
Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Recently, considerable interest has focused on variable selection methods in regression situations where the number of predictors, $p$, is large relative to the number of observations, $n$. Two commonly applied variable selection approaches…
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a…
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…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been…
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…
Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the…
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…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…
Estimating a prediction function is a fundamental component of many data analyses. The super learner ensemble, a particular implementation of stacking, has desirable theoretical properties and has been used successfully in many…
In many high dimensional classification or regression problems set in a biological context, the complete identification of the set of informative features is often as important as predictive accuracy, since this can provide mechanistic…
The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso…
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…