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

Chen, Yuxin ; Chi, Yuejie ; Fan, Jianqing ; Ma, Cong

9781680838961: Spectral Methods for Data Science: A Statistical Perspective (Foundations and Trends(r) in Machine Learning)

Softcover

ISBN 10: 1680838962 ISBN 13: 9781680838961

Publisher: Now Publishers, 2021

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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.

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