Related papers: Sparse model from optimal nonuniform embedding of …
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
We investigate the application of a framework for sparse model identification of differential equations from timeseries data in the context of compartmental models in epidemiology. Such frameworks often seek a sparse representation from a…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
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…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
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…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
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…
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…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
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…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a…