Related papers: Least angle and $\ell_1$ penalized regression: A r…
Bayesian penalized regression techniques, such as the Bayesian lasso and the Bayesian horseshoe estimator, have recently received a significant amount of attention in the statistics literature. However, software implementing…
Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic…
Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…
In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm…
We consider a two-stage estimation method for linear regression. First, it uses the lasso in Tibshirani (1996) to screen variables and, second, re-estimates the coefficients using the least-squares boosting method in Friedman (2001) on…
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
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…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…
Variable (feature, gene, model, which we use interchangeably) selections for regression with high-dimensional BIGDATA have found many applications in bioinformatics, computational biology, image processing, and engineering. One appealing…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
Linear least squares regression is subject to bias due to an omitted variable, a mismeasured regressor, or simultaneity. A simple test to detect the bias is proposed and explored in simulation and in real data sets.
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…