Page 1 |
Save page Remove page | Previous | 1 of 134 | Next |
|
small (250x250 max)
medium (500x500 max)
Large (1000x1000 max)
Extra Large
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
|
SPARSENESS IN FUNCTIONAL DATA ANALYSIS
by
Xinghao Qiao
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
August 2015
Copyright 2015 Xinghao Qiao
Object Description
| Title | Sparseness in functional data analysis |
| Author | Qiao, Xinghao |
| Author email | qiaoxinghao@gmail.com;qiaoxinghao@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Business Administration |
| School | Marshal School of Business |
| Date defended/completed | 2015-06-19 |
| Date submitted | 2015-07-29 |
| Date approved | 2015-07-31 |
| Restricted until | 2015-07-31 |
| Date published | 2015-07-31 |
| Advisor (committee chair) | James, Gareth |
| Advisor (committee member) |
Radchenko, Peter Tong, Xin Goldstein, Larry |
| Abstract | Functional Data Analysis (FDA), a branch of statistics that analyzes data providing information about functions measured over some domain, has recently attracted more attention. In my thesis, I present a brief overview of FDA and consider three different settings in FDA where sparseness can play an important role. ❧ The first setting considers sparseness in the functions. Classical FDA requires a large number of regularly spaced measurements per subject. I consider the situation involving sparse, irregularly observed and noisy data. I propose a new functional errors-in-variable approach, Sparse Index Model Functional Formulation (SIMFE), which uses a functional index model formulation to handle sparsely sampled functional predictors. SIMFE enjoys several advantages over traditional methods. First, it implements a non-linear regression and uses a supervised approach to estimate the lower dimensional space that the predictors should be projected. Second, SIMFE can be applied to both scalar and functional responses with multiple predictors. Finally, SIMFES uses a mixed effect model to deal with sparsely sampled functional data. ❧ The other two settings focus on sparseness arising from high dimensional functional data, where the number of functional variables, p, exceeds the number of observations, n. One example considers extending Gaussian graphical model, which depicts the conditional dependence structure among p multivariate Gaussian variables, to the functional domain. Fitting high dimensional graphical model pose several challenges, thus I need assume sparseness in the edges, where the edges only connect a subset of nodes i.e. only some pairs of random variables are conditional dependent. I propose a functional graphical model (FGM) describing the conditional dependence structure among p random functions. Then I develop a fglasso criterion, which estimates FGM by imposing block sparsity in the precision matrix, via a group lasso penalty. I show the successful graph recovery with a high probability. ❧ The other example concerns screening features for ultra-high dimensional functional data. To make the problem feasible I assume extreme sparseness in the predictor space, i.e. most of the functional predictors are not contributing to the response. I propose several model-free independence screening procedures to rank the importance of functional predictors. I compare different active sets of predictors that these approaches aim to select and establish the corresponding sure screening properties when the number of predictors diverges at an exponential rate with the number of observations. ❧ In each setting, I illustrate the sample performance of my proposed method through a series of simulations and a real world data example. |
| Keyword | functional regression; sparsely sampled functional data; high dimensional functional data; graphical models; features screening |
| Language | English |
| Format (imt) | application/pdf |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Qiao, Xinghao |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-QiaoXingha-3771.pdf |
| Archival file | Volume4/etd-QiaoXingha-3771.pdf |
Description
| Title | Page 1 |
| Repository email | cisadmin@lib.usc.edu |
| Full text | SPARSENESS IN FUNCTIONAL DATA ANALYSIS by Xinghao Qiao A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) August 2015 Copyright 2015 Xinghao Qiao |
