Topics in optimization and learning
Abstract/Contents
- Abstract
- Optimization algorithms that learn from data have been around for a long time. Nevertheless, the ever-changing nature of computational resources, the development of modern theoretical tools, and the availability of new kinds of data keep us wondering what is possible in this field. This work gives us a fresh look at three classical problems: point-set registration, multi-resolution analysis, and tensor factorization. First, we explore how the least unsquared loss ensures exact recovery of the optimal rotation between two point clouds under gross corruption. We also show a phase transition of the probability of exact recovery when the least unsquared loss is optimized over convex sets containing the special orthogonal group. Second, we present a neural network architecture inspired in the non-standard wavelet form, called BCR-net. The BCR-net uses significantly fewer parameters than standard neural networks and shows promising behavior compressing non-linear integral operators. Lastly, we discuss the implications of defining a factorization-preserving algebra to evaluate functions over high-dimensional tensors. We focus on what makes tensors in tensor ring form challenging to work with, and we give insights on how to overcome these challenges.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Orozco Bohorquez, Cindy Catherine |
|---|---|
| Degree supervisor | Ying, Lexing |
| Thesis advisor | Ying, Lexing |
| Thesis advisor | Darve, Eric |
| Thesis advisor | Gerritsen, Margot (Margot G.) |
| Degree committee member | Darve, Eric |
| Degree committee member | Gerritsen, Margot (Margot G.) |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Cindy Catherine Orozco Bohorquez. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/qn148ph7611 |
Access conditions
- Copyright
- © 2021 by Cindy Catherine Orozco Bohorquez
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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