Related papers: Sparse systems and algorithmic equidimensional dec…
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…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
In this paper we study sums of powers of affine functions in (mostly) one variable. Although quite simple, this model is a generalization of two well-studied models: Waring decomposition and sparsest shift. For these three models there are…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored. Such objects are ubiquitous in exact computing, and so naturally we would like to have efficient algorithms to handle them. However, with this compact…
We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…
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…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers.…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Let n denote the number of variables and m the number of equations in a sparse polynomial system over the binary field. We study the inconsistency probability of randomly generated sparse polynomial systems over the binary field, where each…
We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that their difference probably has at most half the number of terms of…
Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…
We consider the problem of identifying the sparse principal component of a rank-deficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate index-sets (that is, sets of indices to the nonzero…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…