ERA

Download the full-sized PDF of Fitting Sparse Hierarchical Models: Applications to Factorial DesignsDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R33X83T7H

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

Fitting Sparse Hierarchical Models: Applications to Factorial Designs Open Access

Descriptions

Other title
Subject/Keyword
degrees of freedom
group lasso
regularization
hierarchy
factorial designs
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Nabipoor Sanjebad, Majid
Supervisor and department
Ivan Mizera
Examining committee member and department
Thomas Hillen, Department of Mathematical and Statistical Sciences, University of Alberta
Ivan Mizera, Department of Mathematical and Statistical Sciences, University of Alberta
Douglas Wiens, Department of Mathematical and Statistical Sciences, University of Alberta
Linglong Kong, Department of Mathematical and Statistical Sciences,University of Alberta
Syed Ejaz Ahmed, Department of Mathematics & Statistics, Brock University
Department
Department of Mathematical and Statistical Sciences
Specialization
Statistics
Date accepted
2016-09-28T11:19:48Z
Graduation date
2016-06:Fall 2016
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
We study penalized fitting strategies aimed at sparse model selection of models satisfying certain hierarchical restrictions, in linear models arising from factorial experiments. After discussing various merits of existing approaches, we propose a modification and generalization of the approach of Bien, Taylor and Tibshirani, capable of handling also models with factors with possibly more than two levels. The approach is based on the modified constraint used in conjunction with the group LASSO. The effect of the modified constraint on the selection of main effects and pair interactions is explored. We characterize the solution for both quadratic and logistic loss and give an unbiased Stein-type estimate for the degrees of freedom, the quantity required as the key component for the selection among competing models in regularization. We compare the derived estimates of the degrees of freedom with the existing ones from the literature.\\ \\We also study properties of certain alternative approaches: for the so-called standardized group LASSO of Simon and Tibshirani, we show first that it remains unchanged under the transformation of Zhao et al., aimed at unifying group weights, and then we characterize the solution of the newly standardized group LASSO. Based on this characterization, we again derive the unbiased estimate of the degrees of freedom. We establish such an estimate of the degrees of freedom also for the overlapped group LASSO of Obozinski et al.\\ \\We after show that the derived estimates of the degrees of freedom converge, when the tuning parameter converges to zero, to the (true) degrees of freedom of the corresponding constrained least-squares estimator. We investigate certain particular properties of sparse fitting procedures in factorial designs. We establish the connection, for balanced designs, between penalized estimation and traditional constrained least-squares estimators. We also propose methods of selecting the regularization parameter selection based on AIC and BIC. Finally, we show how replications in factorial designs affect the selection process of standardized group LASSO.
Language
English
DOI
doi:10.7939/R33X83T7H
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2016-09-28T17:19:48.792+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 1140329
Last modified: 2016:11:16 15:20:21-07:00
Filename: Nabipoor Sanjebad_Majid_201609_PhD.pdf
Original checksum: d2c48fdc5be8ced0e3697da4f232a8b2
Well formed: true
Valid: true
Status message: Too many fonts to report; some fonts omitted. Total fonts = 1420
File title: Introduction
Page count: 124
Activity of users you follow
User Activity Date