Statistical explorations of deterministic functions

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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.


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


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


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.

Access conditions

© 2023 by Christopher Richard Hoyt
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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