Learning Determinantal Point Processes

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs other tractable algorithms for exact inference, including computing marginal probabilities and sampling; however, an important open question has been how to learn a DPP from labeled training data. In this paper we propose a natural feature-based parameterization of conditional DPPs, and show how it leads to a convex and efficient learning formulation. We analyze the relationship between our model and binary Markov random fields with repulsive potentials, which are qualitatively similar but computationally intractable. Finally, we apply our approach to the task of extractive summarization, where the goal is to choose a small subset of sentences conveying the most important information from a set of documents. In this task there is a fundamental tradeoff between sentences that are highly relevant to the collection as a whole, and sentences that are diverse and not repetitive. Our parameterization allows us to naturally balance these two characteristics. We evaluate our system on data from the DUC 2003/04 multidocument summarization task, achieving state-of-the-art results. Disciplines Computer Sciences Comments Learning Determinantal Point Processes, A. Kulesza, and B. Taskar. Conference on Uncertainty in Artificial Intelligence (UAI), Barcelona, Spain, July 2011. Authors retain the right to post a pre-print version of the journal article on Internet web sites including electronic pre-print servers, and to retain indefinitely such version on such servers or sites. The right to post a revised personal version of the text of the final journal article (to reflect changes made in the peer review process) on the author's personal or institutional web site or server, incorporating the complete citation and with a link to the Digital Object Identifier (DOI) of the article This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/542 Learning Determinantal Point Processes Alex Kulesza Dept. of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104 [email protected] Ben Taskar Dept. of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104 [email protected]