Related papers: GEP-MSCRA for computing the group zero-norm regula…

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA),…

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…

We propose a unified class of calibration weighting methods based on weighted generalized entropy to handle missing at random (MAR) data with improved stability and efficiency. The proposed generalized entropy calibration (GEC) formulates…

Sorted L-One Penalized Estimation (SLOPE) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation…

Sorted L-One Penalized Estimation is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when…

The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…

Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where…

Stochastic MPECs have found increasing relevance for modeling a broad range of settings in engineering and statistics. Yet, there seem to be no efficient first/zeroth-order schemes equipped with non-asymptotic rate guarantees for resolving…

We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…

The generalized orthogonal Procrustes problem (GOPP) plays a fundamental role in several scientific disciplines including statistics, imaging science and computer vision. Despite its tremendous practical importance, it is generally an…

Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…

By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…

This two-part work considers the minimum means square error (MMSE) estimation problem for a high dimensional multi-layer generalized linear model (ML-GLM), which resembles a feed-forward fully connected deep learning network in that each of…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…