Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Large-scale sparse logistic regression
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Trading Accuracy for Sparsity in Optimization Problems with Sparsity Constraints
SIAM Journal on Optimization
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Sparse Recovery With Orthogonal Matching Pursuit Under RIP
IEEE Transactions on Information Theory
User-Friendly Tail Bounds for Sums of Random Matrices
Foundations of Computational Mathematics
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Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and Compressed Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of sparse estimation in linear models where the fidelity of the estimate is measured by the squared error. In contrast, relatively less effort has been made in the study of sparsity-constrained optimization in cases where nonlinear models are involved or the cost function is not quadratic. In this paper we propose a greedy algorithm, Gradient Support Pursuit (GraSP), to approximate sparse minima of cost functions of arbitrary form. Should a cost function have a Stable Restricted Hessian (SRH) or a Stable Restricted Linearization (SRL), both of which are introduced in this paper, our algorithm is guaranteed to produce a sparse vector within a bounded distance from the true sparse optimum. Our approach generalizes known results for quadratic cost functions that arise in sparse linear regression and Compressed Sensing. We also evaluate the performance of GraSP through numerical simulations on synthetic and real data, where the algorithm is employed for sparse logistic regression with and without l2-regularization.