Statistical explorations of deterministic functions
Abstract/Contents
- Abstract
- In this thesis, we discuss several ways that statistical approaches can be used to investigate black box functions. In the first part of the thesis, we consider the mean dimension, a statistical property of functions concerning how important the interactions between the inputs matter. We show that the mean dimension for some functions, like Gaussian radial basis functions or ridge functions, can vary widely while other functions, like multiquadric radial basis functions, converge to one under weak conditions. In the second part of the talk, we consider probing neural networks, an strategy in which we examine the intermediate outputs as a way to learn more about the mechanics of the overall network. By using tSNE and a class-specific analogue of principle components, we can visualize the progression of how the classifications are made. Further examination are made with tours, an visualization technique that animates interpolations between pairs of projections.
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 | Hoyt, Christopher Richard |
|---|---|
| Degree supervisor | Owen, Art B |
| Thesis advisor | Owen, Art B |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Friedman, J. H. (Jerome H.) |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Friedman, J. H. (Jerome H.) |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Christopher Hoyt. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/wz600gk2481 |
Access conditions
- Copyright
- © 2023 by Christopher Richard Hoyt
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...