Related papers: Sparse Linear Regression with Constraints: A Flexi…

Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…

This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

Many problems in classification involve huge numbers of irrelevant features. Model selection reveals the crucial features, reduces the dimensionality of feature space, and improves model interpretation. In the support vector machine…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

Sparse tensor decomposition and completion are common in numerous applications, ranging from machine learning to computational quantum chemistry. Typically, the main bottleneck in optimization of these models are contractions of a single…

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…

In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the…

Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of…

Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…

In a linear transformation model, there exists an unknown monotone nonlinear transformation function such that the transformed response variable and the predictor variables satisfy a linear regression model. In this paper, we present CENet,…

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…

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…