Learning Determinantal Point Processes

The increasing availability of both interesting data and processing capacity has led to widespread interest in machine learning techniques that deal with complex, structured output spaces in fields like image processing, computational biology, and natural language processing. By making multiple interrelated decisions at once, these methods can achieve far better performance than is possible treating each decision in isolation. However, accounting for the complexity of the output space is also a significant computational burden that must be balanced against the modeling advantages. Graphical models, for example, offer efficient approximations when considering only local, positive interactions. The popularity of graphical models attests to the fact that these restrictions can be a good fit in some cases, but there are also many other interesting tasks for which we need new models with new assumptions. In this thesis we show how determinantal point processes (DPPs) can be used as probabilistic models for binary structured problems characterized by global, negative interactions. Samples from a DPP correspond to subsets of a fixed ground set, for instance, the documents in a corpus or possible locations of objects in an image, and their defining characteristic is a tendency to be diverse. Thus, DPPs can be used to choose diverse sets of high-quality search results, to build informative summaries by selecting diverse sentences from documents, or to model non-overlapping human poses in images or video. DPPs arise in quantum physics and random matrix theory from a number of interesting theoretical constructions, but we show how they can also be used to model real-world data; we develop new extensions, algorithms, and theoretical results that make modeling and learning with DPPs efficient and practical. Throughout, we demonstrate experimentally that the techniques we introduce allow DPPs to be used for performing real-world tasks like document summarization, multiple human pose estimation, search diversification, and the threading of large document collections.