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 offer 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 multi-document summarization task, achieving state-of-the-art results

Enumeration of Extractive Oracle Summaries

To analyze the limitations and the future directions of the extractive summarization paradigm, this paper proposes an Integer Linear Programming (ILP) formulation to obtain extractive oracle summaries in terms of ROUGE-N. We also propose an algorithm that enumerates all of the oracle summaries for a set of reference summaries to exploit F-measures that evaluate which system summaries contain how many sentences that are extracted as an oracle summary. Our experimental results obtained from Document Understanding Conference (DUC) corpora demonstrated the following: (1) room still exists to improve the performance of extractive summarization; (2) the F-measures derived from the enumerated oracle summaries have significantly stronger correlations with human judgment than those derived from single oracle summaries.Comment: 12 page