相关论文: Optimal designs for Lasso and Dantzig selector usi…

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d.…

We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS), which includes Linkages and Frameworks. Each representation corresponds to a choice of Cayley parameters and yields a…

This paper studies the problem of accurately recovering a sparse vector $\beta^{\star}$ from highly corrupted linear measurements $y = X \beta^{\star} + e^{\star} + w$ where $e^{\star}$ is a sparse error vector whose nonzero entries may be…

The Dantzig selector for the proportional hazards model proposed by D.R. Cox is studied in a high-dimensional and sparse setting. We prove the $l_q$ consistency for all $q \geq 1$ of some estimators based on the compatibility factor, the…

Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…

We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order…

We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…

In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to…

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…

This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…

In linear regression with fixed design, we propose two procedures that aggregate a data-driven collection of supports. The collection is a subset of the $2^p$ possible supports and both its cardinality and its elements can depend on the…

We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…

We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…

In our recent work \cite{StojnicCSetam09} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved that if the number of equations in the system is…

We show that the $A$-optimal design optimization problem over $m$ design points in $\mathbb{R}^n$ is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over $n\times m$ real matrices. This observation…