Data for which the number of predictors exponentially exceeds the number of observations is becoming increasingly prevalent in fields such as bioinformatics, medical imaging, computer vision, And social network analysis. One of the leading questions statisticians must answer when confronted with such “big data” is how to reduce a set of exponentially many predictors down to a set of a mere few predictors which have a truly causative effect on the response being modelled. This process is often referred to as feature screening. In this work we propose three new methods for feature screening. The first method we propose (TC-SIS) is specifically intended for use with data having both categorical response and predictors. The second method we propose (JCIS) is meant for feature screening for interactions between predictors. JCIS is rare among interaction screening methods in that it does not require first finding a set of causative main effects before screening for interactive effects. Our final method (GenCorr) is intended for use with data having a multivariate response. GenCorr is the only method for multivariate screening which can screen for both causative main effects and causative interactions. Each of these aforementioned methods will be shown to possess both theoretical robustness as well as empirical agility.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8342 |
| Date | 01 August 2018 |
| Creators | Reese, Randall D. |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
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