Related papers: Grouped Variable Selection with Discrete Optimizat…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
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…
We study the proximal gradient descent (PGD) method for $\ell^{0}$ sparse approximation problem as well as its accelerated optimization with randomized algorithms in this paper. We first offer theoretical analysis of PGD showing the bounded…
We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…
In this paper, we consider an $\ell_{0}$-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a…
This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…
Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…
In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…