Verb Phrase Ellipsis (VPE) is an anaphoric construction in which a verb phrase has been elided. It occurs frequently in dialogue and informal conversational settings, but despite its evident impact on event coreference resolution and extraction, there has been relatively little work on computational methods for identifying and resolving VPE. Here, we present a novel approach to detecting and resolving VPE by using supervised discriminative machine learning techniques trained on features extracted from an automatically parsed, publicly available dataset. Our approach yields state-of-the-art results for VPE detection by improving F1 score by over 11\%; additionally, we explore an approach to antecedent identification that uses the Margin-Infused-Relaxed-Algorithm, which shows promising results.