EMPRR : A High - dimensional EM - Based Piecewise Regression Algorithm

We propose a novel general piecewise surface regression model that allows for arbitrary functions to be used in each piece, and arbitrary boundary surfaces between pieces. We also give an EM-based algorithm for this model, EMPRR, that scales to high dimensions. We compare EMPRR's performance with those of model trees and functional trees, two regression tree learning methods, on synthetic piecewise data and benchmark data sets. Our results show that EMPRR outperforms the other two methods on the synthetic data sets and performs competitively on the benchmark data sets while generating accurate and much more compact models. ii Acknowledgements I would like to thank my advisor Prof. Stephen Scott first of all for making me a computer scientist. He took a risk of hiring a student with biotechnology background as a research assistant in computer science and I hope I have justified his decision in the past two and a half years. He has been more a friend to me than an advisor, making sure that things are fine for me during my stay in Lincoln. I would also like to thank him for his invaluable guidance throughout my research and when I was writing research papers and this thesis. Finally, I am grateful to him, for his reference played a major role in my job offers. being on my committee and for their valuable input on my work and this report. Thanks are due to Dr. Deogun and Prof. Byrav Ramamurthy for providing me references in my job search. I also thank Dr. João Gama for providing the implementation of functional trees and helpful instructions on running the implementation, and Prof. Tapabrata Maiti for his helpful discussions during the early development of this work. I thank my friends and acquaintances in Lincoln, who made my stay a very pleasant one. I thank my parents for bringing me to this world and making me what I am today. I thank God Almighty for his blessings throughout my life, through the good and bad times.