Submodular Optimization and Machine Learning: Theoretical Results, Unifying and Scalable Algorithms, and Applications

Abstract

In this dissertation, we explore a class of unifying and scalable algorithms for a number of submodular optimization problems, and connect them to several machine learning applications. These optimization problems include, 1. Constrained and Unconstrained Submodular Minimization, 2. Constrained and Unconstrained Submodular Maximization, 3. Difference of Submodular Optimization 4. Submodular Optimization subject to Submodular Constraints The main focus of this thesis, is to study these problems theoretically, in the light of the machine learning problems where they naturally occur. We provide scalable, practical and unifying algorithms for all the above optimization problems, which retain good theoretical guarantees, and investigate the underlying hardness of these optimization problems. We also study natural subclasses of submodular functions, along with theoretical constructs, which help connect theory to practice by providing tighter worst case guarantees. While the focus of this thesis is mainly theoretical, we also empirically demonstrate the applicability of these techniques on several synthetic and real world problems.