Throughout machine learning and data mining, we often make predictions about single entities, such as which TV show someone will watch on Netflix, which ad someone will click on a search engine, or what new friendship will form on a social network. This talk will instead consider three tasks related to predicting sets of entities. The first involves modeling human repetition behavior at the individual level, including, for example, the sets of recipients on emails sent by individuals and the sets of tags that users apply to questions on stack overflow. The second is a model for set selection through the lens of discrete choice theory, where an individual selects a subset from a given slate of alternatives, such as which items to buy at a grocery store. And the third develops new algorithms for predicting new multi-way interactions not yet observed in complex systems, such as new combinations of substances in drug development and the formation of new social groups.