Related papers: The Sparse Solution to $\mathcal{KS}$-Tensor Compl…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…
In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
Sparse linear regression is the well-studied inference problem where one is given a design matrix $\mathbf{A} \in \mathbb{R}^{M\times N}$ and a response vector $\mathbf{b} \in \mathbb{R}^M$, and the goal is to find a solution $\mathbf{x}…
Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…
Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…
In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…
The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has…
This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…