A Systematic and Empirical Introduction to Spectral Methods
Spectral Methods for Data Science: A Statistical Perspective
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data.
This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications.
Our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions.
In addition to conventional perturbation analysis, we present a systematic and perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful"leave-one-out"analysis framework.