Non-negative matrix factorization and topic models
Abstract/Contents
- Abstract
- Matrix factorization algorithms provide a powerful tool for data analysis and statistical inference. As an important class of these algorithms, nonnegative matrix factorization (NMF) suggests expressing a collection of data points as convex combinations of a small set of 'archetypes' with nonnegative entries. As a result, NMF enables us to extract the latent structure and underlying 'pure components' in a broad range of applications from chemometrics to image processing and topic modeling. In this thesis, we study the NMF problem from two different perspectives: 1. We consider the NMF problem under a deterministic model and propose a new estimator that robustly recovers the factors under a more general settings than the state-of-the-art estimators, with theoretical guarantees. 2. We analyze the NMF problem in a Bayesian setting under which the data is generated using an LDA model. We show negative results about variational inference in this problem, showing that it is not 'stable'. In particular, we show that in a certain region for signal-to-noise ratio, in which the underlying signal cannot be recovered, the variational method is randomly biased and outputs a non-trivial solution. This output, of course, is uncorrelated with the underlying truth. We also suggest a possible correction to remedy this issue.
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 | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Hakim Javadi, Hamidreza |
|---|---|
| Degree supervisor | Montanari, Andrea |
| Thesis advisor | Montanari, Andrea |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Weissman, Tsachy |
| Degree committee member | Boyd, Stephen P |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Weissman, Tsachy |
| Associated with | Stanford University, Department of Electrical Engineering. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Hamidreza Hakim Javadi. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Hamidreza Hakim Javadi
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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