This work would not be possible without the guidance and support of my advisors, Prof. Joydeep Ghosh and Prof. Sriram Vishwanath. I am profoundly grateful to both of them for their mentorship, advice, encouragement, and the opportunity to pursue various research areas. I've learned many skills from them: researching, writing, mentoring, teaching, and many other aspects related to both the academic and real world. I am extremely fortunate to have been their graduate student. I would also like to

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... thank the members of my thesis committee: Prof. Sujay Sangahvi, Prof. Jimeng Sun, and Prof. Haris Vikalo, for their comments, suggestions, and conversations about research. In particular, I am indebted to Prof. Jimeng Sun for steering me towards tensor factorization models for healthcare data. Some of the key ideas of this dissertation were a product of our collaboration, and without him, I may not have pursued this avenue of research. I want to express my gratitude to the excellent collaborators I've had the privilege to work with including Cheng Lee, Sanmi Koyejo, Natalia Arzeno, Suriya Gunesekar, Ioannis Mitliagkas, and Jette Henderson. In addition, I want to thank the past and current members of IDEAL and LINC for the happy memories. Even though I have not listed all of you here, I am grateful to have shared the company.