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Statistical Explorations of Determin...

Hoyt, Christopher Richard,

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Statistical Explorations of Deterministic Functions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Statistical Explorations of Deterministic Functions // Christopher Richard Hoyt.
Author:	Hoyt, Christopher Richard,
Description:	1 electronic resource (143 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
Contained By:	Dissertations Abstracts International85-04B.
Subject:	Decomposition. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30615117
ISBN:	9798380484169

Statistical Explorations of Deterministic Functions /
Hoyt, Christopher Richard,

Statistical Explorations of Deterministic Functions /Christopher Richard Hoyt. - 1 electronic resource (143 pages)

Source: Dissertations Abstracts International, Volume: 85-04, Section: B.

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.

English

ISBN: 9798380484169Subjects--Topical Terms:

3561186
Decomposition.

Statistical Explorations of Deterministic Functions /
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245 1 0 $a Statistical Explorations of Deterministic Functions / $c Christopher Richard Hoyt.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 1 electronic resource (143 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
500 $a Advisors: Owen, Art; Candes, Emmanuel; Friedman, Jerome Committee members: Bent, Stacey F.
502 $b Ph.D. $c Stanford University $d 2023.
520 $a 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.
546 $a English
590 $a School code: 0212
650 4 $a Decomposition. $3 3561186
650 4 $a Mathematical functions. $3 3564295
650 4 $a Applied mathematics. $3 2122814
650 4 $a Histograms. $3 3683681
650 4 $a Neural networks. $3 677449
650 4 $a Trucks. $3 573590
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710 2 $a Stanford University. $e degree granting institution. $3 3765820
720 1 $a Owen, Art $e degree supervisor.
720 1 $a Candes, Emmanuel $e degree supervisor.
720 1 $a Friedman, Jerome $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-04B.
790 $a 0212
791 $a Ph.D.
792 $a 2023
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30615117