Concepts de base
Revealing the explicit representer theorem for sparse learning solutions in RKBS.
Résumé
This article delves into the concept of sparsity in machine learning solutions within reproducing kernel Banach spaces (RKBS). It explores the explicit representer theorem for solutions in RKBS, focusing on the minimum norm interpolation (MNI) and regularization problems. The study establishes conditions for sparse kernel representations, emphasizing the role of the regularization parameter in promoting sparsity. Specific RKBSs, like sequence space ℓ1(N) and measure space, are identified to have sparse representer theorems. The content is structured as follows:
- Introduction to RKBS and sparse learning methods.
- Representer theorems for MNI and regularization problems.
- Sparse representer theorem establishment process.
- Sparse kernel representations and conditions for sparsity.
- Specific RKBSs with sparse representer theorems.
- Application of sparse techniques in neural networks.
- Organizational structure in sections and appendices.
Stats
목표는 RKBS에서 희소 학습 솔루션의 명시적 표현 이론을 밝히는 것입니다.
RKBS에서 최소 노름 보간(MNI) 및 정규화 문제에 대한 대표 이론을 수립합니다.
희소 커널 표현을 위한 조건 설정 및 희소성 촉진을 위한 정규화 매개변수의 역할 강조합니다.
특정 RKBS(예: 시퀀스 공간 ℓ1(N) 및 측정 공간)이 희소 대표 이론을 갖는 것을 확인합니다.
Citations
"Sparsity of a learning solution is a desirable feature in machine learning."
"Certain RKBSs are appropriate hypothesis spaces for sparse learning methods."