Spectral Methods for Data Science : A Statistical Perspective (Foundations and Trends® in Machine Learning)

Chen, Yuxin/ Chi, Yuejie/ Fan, Jianqing

now publishers Inc（2021/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 254 p.
• 言語 ENG
• 商品コード 9781680838961

Full Description

In contemporary science and engineering applications, the volume of available data is growing at an enormous rate. Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. A diverse array of applications have been found in machine learning, imaging science, financial and econometric modeling, and signal processing.This monograph presents a systematic, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. The authors provide a unified and comprehensive treatment that establishes the theoretical underpinnings for spectral methods, particularly through a statistical lens.Building on years of research experience in the field, the authors present a powerful framework, called leave-one-out analysis, that proves effective and versatile for delivering fine-grained performance guarantees for a variety of problems. This book is essential reading for all students, researchers and practitioners working in Data Science.

Contents

Introduction
2. Classical spectral analysis: ℓ2 perturbation theory
3. Applications of ℓ2 perturbation theory to data science
4. Fine-grained analysis: ℓ∞ and ℓ2,∞ perturbation theory
5. Concluding remarks and open problems
Acknowledgements
References