Screen LibrarySpectral methods for data science : a statistical perspective /
This monograph presents a systematic, yet accessible introduction to spectral methods from a modern statistical perspective. It is essential reading for all students, researchers and practitioners working in Data Science.
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| Main Authors: | |
|---|---|
| Group Author: | ; ; |
| Published: |
Now Publishers,
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| Publisher Address: | Hanover, MA : |
| Publication Dates: | [2021] |
| Literature type: | Book |
| Language: | English |
| Series: |
Foundations and Trends in Machine Learning,
volume 14, issue 5 |
| Subjects: | |
| Summary: |
This monograph presents a systematic, yet accessible introduction to spectral methods from a modern statistical perspective. It is essential reading for all students, researchers and practitioners working in Data Science. |
| Carrier Form: | 246 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 211-246). |
| ISBN: | 9781680838961 |
| Index Number: | QA320 |
| CLC: | O177.7 |
| Call Number: | O177.7/C518 |
| Contents: |
Intro -- Introduction -- Motivating applications -- A modern statistical perspective -- Organization -- What is not here and complementary readings -- Notation -- Classical spectral analysis: 2 perturbation theory -- Preliminaries: Basics of matrix analysis -- Preliminaries: Distance and angles between subspaces -- Perturbation theory for eigenspaces -- Perturbation theory for singular subspaces -- Eigenvector perturbation for probability transition matrices -- Appendix: Proofs of auxiliary lemmas in Section 2.2 -- Notes -- Applications of 2 perturbation theory to data science Preliminaries: Matrix tail bounds -- Low-rank matrix denoising -- Principal component analysis and factor models -- Graph clustering and community recovery -- Clustering in Gaussian mixture models -- Ranking from pairwise comparisons -- Phase retrieval and solving quadratic systems of equations -- Matrix completion -- Tensor completion -- Notes -- Fine-grained analysis: and 2, perturbation theory -- Leave-one-out analysis: An illustrative example -- 2, eigenspace perturbation under independent noise -- 2, singular subspace perturbation under independent noise Application: Entrywise guarantees for matrix completion -- Application: Exact community recovery -- Distributional theory and uncertainty quantification -- Application: Confidence intervals for matrix completion -- Appendix A: Proof of Theorem 4.2 -- Appendix B: Proof of Corollary 4.3 -- Appendix C: Proof of Theorem 4.4 -- Appendix D: Proof of Theorem 4.10 -- Appendix E: Proof of Theorem 4.11 -- Notes -- Concluding remarks and open problems -- Acknowledgements -- References |