TRADING ACCURACY FOR SPARSITY IN OPTIMIZATION PROBLEMS WITH SPARSITY CONSTRAINTS

被引：89

作者：

Shalev-Shwartz, Shai ^{[1
]}

Srebro, Nathan ^{[2
]}

Zhang, Tong ^{[3
]}

机构：

[1] Hebrew Univ Jerusalem, Sch Comp Sci & Engn, Jerusalem, Israel

[2] Toyota Technol Inst, Chicago, IL 60637 USA

[3] Rutgers State Univ, Dept Stat, New Brunswick, NJ 08901 USA

来源：

SIAM JOURNAL ON OPTIMIZATION | 2010年 / 20卷 / 06期

关键词：

sparsity; linear prediction; GREEDY APPROXIMATION; CONVERGENCE; REGRESSION; SELECTION; SYSTEMS; LASSO; WOLFE;

D O I：

10.1137/090759574

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the problem of minimizing the expected loss of a linear predictor while constraining its sparsity, i.e., bounding the number of features used by the predictor. While the resulting optimization problem is generally NP-hard, several approximation algorithms are considered. We analyze the performance of these algorithms, focusing on the characterization of the trade-off between accuracy and sparsity of the learned predictor in different scenarios.

引用

页码：2807 / 2832

页数：26

共 50 条

[41] Structural properties of affine sparsity constraints
Hongbo Dong
Miju Ahn
Jong-Shi Pang
Mathematical Programming, 2019, 176 : 95 - 135
[42] Recognizing underlying sparsity in optimization
Sunyoung Kim
Masakazu Kojima
Philippe Toint
Mathematical Programming, 2009, 119 : 273 - 303
[43] Recognizing underlying sparsity in optimization
Kim, Sunyoung
Kojima, Masakazu
Toint, Philippe
MATHEMATICAL PROGRAMMING, 2009, 119 (02) : 273 - 303
[44] On Solutions of Sparsity Constrained Optimization
Pan L.-L.
Xiu N.-H.
Zhou S.-L.
Journal of the Operations Research Society of China, 2015, 3 (4) : 421 - 439
[45] Improvement of Submodular Maximization Problems With Routing Constraints via Submodularity and Fourier Sparsity
Lin, Pao-Te
Tseng, Kuo-Shih
IEEE ROBOTICS AND AUTOMATION LETTERS, 2023, 8 (04) : 1927 - 1934
[46] Adaptive Iterative Hard Thresholding for Least Absolute Deviation Problems with Sparsity Constraints
Li, Song
Liu, Dekai
Shen, Yi
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2023, 29 (01)
[47] COLLAGE-BASED INVERSE PROBLEMS FOR IFSM WITH ENTROPY MAXIMIZATION AND SPARSITY CONSTRAINTS
Kunze, Herb
La Torre, Davide
Vrscay, Edward
IMAGE ANALYSIS & STEREOLOGY, 2013, 32 (03): : 183 - 188
[48] Adaptive Iterative Hard Thresholding for Least Absolute Deviation Problems with Sparsity Constraints
Song Li
Dekai Liu
Yi Shen
Journal of Fourier Analysis and Applications, 2023, 29
[49] Accelerated projected steepest descent method for nonlinear inverse problems with sparsity constraints
Teschke, Gerd
Borries, Claudia
INVERSE PROBLEMS, 2010, 26 (02)
[50] A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints
Voronin, Sergey
Woerdeman, Hugo J.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2013, 35 (01) : 151 - 164

← 1 2 3 4 5 →