Learning with coefficient-based regularization and a""1 -penalty

被引：18

作者：

Guo, Zheng-Chu ^{[1
]}

Shi, Lei ^{[2
]}

机构：

[1] Univ Exeter, Coll Engn Math & Phys Sci, Exeter EX4 4QF, Devon, England

[2] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2013年 / 39卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Learning theory; Coefficient-based regularization and l(1)-penalty; Unbounded sampling processes; Concentration estimate for error analysis; KERNEL BANACH-SPACES; L(1) NORM; REGRESSION; SELECTION; RATES;

D O I：

10.1007/s10444-012-9288-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The least-square regression problem is considered by coefficient-based regularization schemes with a""(1) -penalty. The learning algorithm is analyzed with samples drawn from unbounded sampling processes. The purpose of this paper is to present an elaborate concentration estimate for the algorithms by means of a novel stepping stone technique. The learning rates derived from our analysis can be achieved in a more general setting. Our refined analysis will lead to satisfactory learning rates even for non-smooth kernels.

引用

页码：493 / 510

页数：18

共 26 条

[1]

[Anonymous], T AM MATH SOC, DOI DOI 10.2307/1990404

[2] PROBABILITY-INEQUALITIES FOR SUM OF INDEPENDENT RANDOM-VARIABLES [J].

BENNETT, G .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1962, 57 (297) :33-&

[3] Sparsity and incoherence in compressive sampling [J].

Candes, Emmanuel ;

Romberg, Justin .

INVERSE PROBLEMS, 2007, 23 (03) :969-985

[4]

Conway J. B., 2000, COURSE OPERATOR THEO

[5]

Cucker F, 2007, C MO AP C M, P1, DOI 10.1017/CBO9780511618796

[6] Model selection for regularized least-squares algorithm in learning theory [J].

De Vito, E ;

Caponnetto, A ;

Rosasco, L .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2005, 5 (01) :59-85

[7] Concentration estimates for learning with unbounded sampling [J].

Guo, Zheng-Chu ;

Zhou, Ding-Xuan .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2013, 38 (01) :207-223

[8]

Lin H.-T., 2003, Neural Computation, P1

[9] Gabor-based kernel PCA with fractional power polynomial models for face recognition [J].

Liu, CJ .

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2004, 26 (05) :572-581

[10] REGULARIZATION IN KERNEL LEARNING [J].

Mendelson, Shahar ;

Neeman, Joseph .

ANNALS OF STATISTICS, 2010, 38 (01) :526-565

← 1 2 3 →