A Systematic and Empirical Introduction to Spectral Methods

Home

Discover

Bookmarks

Keep Up With Latest Trending Papers. Computer Science, AI and Machine Learning and more.Subscribe

Added to collectionTop 100 Trending AI & Computer Science Papers

Stats Machine Learning

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.

Authors

Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma

◐ Recommended Follows

◐ Latest Activity