Vaccination rates are decreasing in many areas of the world, and outbreaks of preventable diseases tend to follow in areas with particular low rates. Much research has been devoted to improving our understanding of the motivations behind vaccination decisions and the effects of various types of information offered to skeptics, no large-scale study of the structure of online vaccination discourse have been conducted. Here, we offer an approach to quantitatively study the vaccine discourse in an online system, exemplified by Twitter. We use train a deep neural network to predict tweet vaccine sentiments, surpassing state-of-the-art performance, attaining two-class accuracy of $90.4\%$, and a three-class F1 of $0.762$. We identify profiles which consistently produce strongly anti- and pro-vaccine content. We find that strongly anti-vaccine profiles primarily post links to Youtube, and commercial sites that make money on selling alternative health products, representing a conflict of interest. We also visualize the network of repeated mutual interactions of actors in the vaccine discourse and find that it is highly stratified, with an assortativity coefficient of $r = .813$.