Related papers: Learning Sparse Classifiers: Continuous and Mixed …

Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…

Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…

Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

We propose a new sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the $\ell_0$-norm with…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…

In this paper, a novel framework of sparse kernel learning for Support Vector Data Description (SVDD) based anomaly detection is presented. In this work, optimal sparse feature selection for anomaly detection is first modeled as a Mixed…

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…

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

We propose an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…