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University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2016 Variable selection via penalized regression and the genetic algorithm using information complexity, with applications for high-dimensional -omics data Tyler J. Massaro University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Applied Statistics Commons, Biostatistics Commons, and the Multivariate Analysis Commons Recommended Citation Massaro, Tyler J., "Variable selection via penalized regression and the genetic algorithm using information complexity, with applications for high-dimensional -omics data. " PhD diss., University of Tennessee, 2016. https://trace.tennessee.edu/utk_graddiss/3944 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Tyler J. Massaro entitled "Variable selection via penalized regression and the genetic algorithm using information complexity, with applications for high-dimensional -omics data." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Mathematics. Hamparsum Bozdogan, Major Professor We have read this dissertation and recommend its acceptance: Vasileios Maroulas, Xiaobeng Feng, Haileab Hilafu, Michael Vose Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Variable selection via penalized regression and the genetic algorithm using information complexity, with applications for high-dimensional -omics data A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Tyler J. Massaro August 2016 Copyright c 2016, by Tyler J. Massaro All Rights Reserved ii DEDICATION Isaac Newton famously wrote in a letter to Robert Hooke, \If I have seen further, it is by standing on the shoulders of Giants." If I have seen anything, it is first and foremost because my parents realized I needed a pair of glasses. Once properly bespectacled, they hoisted me onto their shoulders to get a better view of the wide and confusing world around us. They've been supporting me ever since. I will never be convinced that anyone else has had parents (or even just 2 people) more invested in his or her success than me. I said it to them after my defense, and I will write it here for anyone reading to see: Bill and Terrie Massaro were with me in every equation, every figure, every table, every page of this thing. This is as much their work as it is mine. For this reason a dedication is unnecessary but I dedicate it to both of you anyway. To my partner in crime and sister, Marina. I will have no greater friend and no more constructive critic. You play each part beautifully, and I needed both this past year. You helped Sarah and I build a bright future for ourselves, and I will do everything I can to make yours even brighter than it already is. To Sarah, my girlfriend of 2 years, my personal hair and fashion authority, she of an endless and tireless patience. You, too, were here with me through all of the late nights, through my doubts and my struggles, seated next to me on the roller coaster ride that this turned into. The ride isn't over (sorry, did I not mention that before?), but I feel better knowing that you've strapped yourself in here with me. And to your family: you guys took me in and embraced me as your own. If it weren't for my parents and my sister, you cheered harder for me than anyone else has. iii Getting a Ph.D. never has to take a village, but in my case it did. There is a sizable part of Baldwinsville, NY that has waited for this almost as long as I or my parents or my sister have. I could fill a small stadium (Pelcher-Arcaro?) with people{old friends of mine, friends and co-workers of my parents and sister, family{who have reached out these past few weeks to cheer me on. I dedicate this to all of you, to the BCSFD, and to the OCFIU. To my school friends back home in Syracuse, in Rochester, in Knoxville, and abroad or elsewhere. You have all been like family; like brothers. It means everything to me that I can laugh or cry; be frustrated or selfish or down or anxious; get excited and all worked up about sports, TV, or movie drama; throw a frisbee, kick a soccer ball, crush a softball or a kickball or a wiffleball or a volleyball; engage in a deep discussion; make art or music; provide video game lessons; have a drink or too many; share a meal; be a friend with all of you. Finally, to my family. This includes my parents and my sister, but it also includes everyone else. Everyone who is here supporting me, and especially everyone we had to lay to rest along the way. Giants, each of them, hoisting us onto their shoulders. I've been down here in Knoxville, and all of you were back home holding down the fort. That was the hardest part of these past 5 years. I can't wait to come home and see you again soon. iv ACKNOWLEDGEMENTS I would like to start by thanking Dr. Bozdogan for his steady guidance throughout the past year and a half. My decision to completely alter the course of my previous dissertation research was an extremely difficult one. If nothing else, the contents of this dissertation are proof that that decision{reached over many nights of coffee down at Golden Roast{was indisputably the correct one. This dissertation is not the only piece of evidence. I look also at how well-prepared I feel for life after Knoxville. Dr. B, you have given me a gift, one that has and will continue to open doors for me as I continue growing as a statistical researcher. To my committee, Dr.'s Maroulas, Feng, Hilafu, and Vose, I also wish to express my most sincere gratitude. At some point in the last year I've brought questions to each of you, and I've had each one answered. I honestly couldn't have asked for anything more though I know I did. Dr. Maroulas, I would like to especially thank you for taking as much time as you did to chat with me, work with me, and help Sarah and I get set up in Durham next year. Your counsel has been equally important to my growth as a researcher. To the staff in the Mathematics Department and in the BAS Department{thank you. So much. None of this is actually possible without you. Pam, my days are always brighter when I see that your door is open, although why you have continued to let me into your office is a mystery since 9 times out of 10 it just means more paperwork, emails, or phonecalls for you. To Dr. Lenhart, who, from the very beginning, was instrumental in bringing me to Knoxville. Between getting me to land on my feet as a graduate student, helping me study abroad 2 (nearly 3) different times in some of the most exotic places on the planet, sharing your knowledge of v optimal control theory, and teaching me how to effectively function as a member on a research team, I just want to say thank you. To Dr. Gray: I cannot begin to thank you enough for all of the work you put into writing letters for me last fall, for your constant willingness to answer any questions I send your way, and your genuine interest in seeing me achieve success. To Dr. Spring: I eagerly look forward to our continued collaboration with one another. The passion that you have for your work is infectious and it is tangible. To you and your family, I want to thank you for helping make my trip to Melbourne a delightful, memorable, and productive one. To Dr.'s Esham, Haddad, Hartvigsen, Leary, and Spicka, I would like to thank you for being among the first to show me that any of this was possible. To all of the students that I have had in class, here at UTK and at Geneseo. You make teaching way too much fun. To so many of my classmates, too many to name here but I will give it my best shot: Eddie, Nate, Ernest, Andrew, Marina, Murat, Ben, Darrin, Kelly, John, Brian, Peter, Will, R´eka, Jason, Steve. I have found our discussions so incredibly beneficial, and, in some cases necessary to the advancement of the research contained here. Your willingness to let me share this research with you or simply listen while I bounced ideas around ended up being a crucial part of the process. vi And I add my own love to the history of people who have loved beautiful things, and looked out for them, and pulled them from the fire, and sought them when they were lost, and tried to preserve them and save them while passing them along literally from hand to hand, singing out brilliantly from the wreck of time to the next generation of lovers, and the next. |Donna Tartt, The Goldfinch vii ABSTRACT This dissertation is a collection of examples, algorithms, and techniques for researchers interested in selecting influential variables from statistical regression models.

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