Uncertainty in Artificial Intelligence
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Markov Determinantal Point Processes
Raja Affandi, Alex Kulesza, Emily Fox
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to a user's interests while covering a variety of topics. Suppose, however, that we are asked to sequentially select multiple diverse sets of items, for example, displaying new headlines day-by-day. We might want these sets to be diverse not just individually but also through time, offering headlines today that are unlike the ones shown yesterday. In this paper, we construct a Markov DPP (M-DPP) that models a sequence of random sets {Yt}. The proposed M-DPP defines a stationary process that maintains DPP margins. Crucially, the induced union process Zt = Yt u Yt-1 is also marginally DPP-distributed. Jointly, these properties imply that the sequence of random sets are encouraged to be diverse both at a given time step as well as across time steps. We describe an exact, efficient sampling procedure, and a method for incrementally learning a quality measure over items in the base set Y based on external preferences. We apply the M-DPP to the task of sequentially displaying diverse and relevant news articles to a user with topic preferences.
Pages: 26-35
PS Link:
PDF Link: /papers/12/p26-affandi.pdf
AUTHOR = "Raja Affandi and Alex Kulesza and Emily Fox",
TITLE = "Markov Determinantal Point Processes",
BOOKTITLE = "Proceedings of the Twenty-Eighth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-12)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2012",
PAGES = "26--35"

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