Statistical and computational problems in low-rank matrix estimation
Abstract/Contents
- Abstract
- This dissertation explores several problems in the realm of low-rank matrix estimation. A primary focus is on understanding the statistical and computational limitations. From a practical perspective, understanding such limitations not only provides practitioners with guidance on algorithm selection, but also in some cases spurs the development of cutting-edge methodologies which improve on the state of the art. Within this theme, this dissertation explores and partially answers the following two questions: (1) Given a large-scale low-rank matrix corrupted by random noise, how much information can we accurately infer from the limited observations? (2) How do restrictions on computational resources affect information retrieval? A secondary focus of this dissertation is on developing algorithms that sample from the posterior in the context of low-rank matrix estimation. A standard machinery to fulfill this task is based on Markov Chain Monte Carlo (MCMC) algorithms. However, rigorous guarantees are often difficult to obtain for MCMC algorithms of common use. This dissertation contributes to this line of work from an alternative perspective: We propose an alternative class of efficient algorithms based on diffusion processes that come with rigorous guarantee. This dissertation is organized as follows: We describe the problem in Chapter 1. Chapter 2 studies low-rank matrix estimation from an information-theoretic perspective, and Chapter 3-4 analyzes the effects of limited computational resource. In Chapter 5, we design a sampling algorithm that works well with the low-rank model. Standalone versions of each chapter can be found in [154, 50, 151].
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Wu, Yuchen |
|---|---|
| Degree supervisor | Montanari, Andrea |
| Thesis advisor | Montanari, Andrea |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Schramm, Tselil |
| Degree committee member | Johnstone, Iain |
| Degree committee member | Schramm, Tselil |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Yuchen Wu. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/dq353dk0293 |
Access conditions
- Copyright
- © 2023 by Yuchen Wu
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