Spectral Methods for Data Science: A Statistical Perspective
نویسندگان
چکیده
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In nutshell, spectral refer to collection of algorithms built upon the eigenvalues (resp. singular values) eigenvectors vectors) some properly designed matrices constructed A diverse array applications been found in machine learning, data science, signal processing. Due their simplicity effectiveness, are not only used stand-alone estimator, but also frequently employed initialize other more sophisticated improve performance. While studies can be traced back classical matrix perturbation theory moments, past decade has witnessed tremendous theoretical advances demystifying efficacy through lens statistical modeling, with aid non-asymptotic random theory. This monograph aims present systematic, comprehensive, accessible introduction modern perspective, highlighting algorithmic implications large-scale applications. particular, our exposition gravitates around several central questions that span various applications: how characterize sample efficiency reaching target level accuracy, assess stability face noise, missing data, adversarial corruptions? addition conventional $\ell_2$ analysis, we systematic $\ell_{\infty}$ $\ell_{2,\infty}$ eigenspace subspaces, which recently become available owing powerful "leave-one-out" analysis framework.
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ژورنال
عنوان ژورنال: Foundations and trends in machine learning
سال: 2021
ISSN: ['1935-8245', '1935-8237']
DOI: https://doi.org/10.1561/2200000079