A greedy approach to sparse canonical correlation analysis

SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit D…

Sparse Polynomial Chaos Expansions via Compressed Sensing and D-optimal Design

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this sparsity in order to reduce computational costs. A class of greedy compressed sensing algorithms use least squares minimization to approximate PC coefficients. This least squares problem lends itself to the theory of optimal design of experiments (ODE). Our work focuses on selecting an experimental design that improves the accuracy of sparse PC approximations for …

贪婪稀疏约束优化

Greedy Sparsity-Constrained Optimization

提出一种贪婪算法GraSP，用于近似任意形式代价函数的稀疏最小值，并在代价函数满足稳定受限Hessian或稳定受限线性化时保证收敛到真稀疏最优解的有界距离内。

通过贪心条件选择实现稠密核矩阵的稀疏逆 Cholesky 分解

Sparse inverse Cholesky factorization of dense kernel matrices by greedy conditional selection

本文提出以条件互信息贪心选择构造稠密核矩阵稀疏逆 Cholesky 因子的模式，降低复杂度并在分解、GP 回归和预条件中优于 k-近邻。