Related papers: Penalized Orthogonal-Components Regression for Lar…

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

Longitudinal and high-dimensional measurements have become increasingly common in biomedical research. However, methods to predict survival outcomes using covariates that are both longitudinal and high-dimensional are currently missing. In…

This paper investigates the property of the penalized estimating equations when both the mean and association structures are modelled. To select variables for the mean and association structures sequentially, we propose a hierarchical…

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…

Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression…

Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose…

We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…

Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Matrix factorization methods are extensively employed to understand complex data. In this paper, we introduce the cross-product penalized component analysis (XCAN), a sparse matrix factorization based on the optimization of a loss function…

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both…

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…