Related papers: Simultaneous sparse estimation of canonical vector…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP…

Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major…

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing…

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…

Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one…

Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation…

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…

This paper deals with the grouped variable selection problem. A widely used strategy is to augment the negative log-likelihood function with a sparsity-promoting penalty. Existing methods include the group Lasso, group SCAD, and group MCP.…

This article considers the problem of multi-group classification in the setting where the number of variables $p$ is larger than the number of observations $n$. Several methods have been proposed in the literature that address this problem,…

In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…

Canonical Correlation Analysis (CCA) is a widespread technique for discovering linear relationships between two sets of variables $X \in \mathbb{R}^{n \times p}$ and $Y \in \mathbb{R}^{n \times q}$. In high dimensions however, standard…