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Collaborative filtering with low regret

Author(s)
Voloch, Luis F
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Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Advisor
Devavrat Shah.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
Collaborative filtering (CF) is a widely used technique in recommendation systems where recommendations are provided in a content-agnostic manner, and there are two main paradigms in neighborhood-based CF: the user-user paradigm and the item-item paradigm. To recommend to a user in the user-user paradigm, one first looks for similar users, and then recommends items liked by those similar users. In the item-item paradigm, in contrast, items similar to those liked by the user are found and subsequently recommended. Much empirical evidence exists for the success of the item-item paradigm (Linden et aL, 2003; Koren and Bell, 2011), and in this thesis, motivated to understand reasons behind this, we study its theoretical performance and prove guarantees. We work under a generic model where the population of items is represented by a distribution over [-1, +1 ]N , with a binary string of length N associated with each item to represent which of the N users likes (+1) or dislikes (-1) the item. As the first main result, we show that a simple algorithm following item-item paradigm achieves a regret (which captures the number of poor recommendations over T time steps) that is sublinear and scales as ... , where d is the doubling dimension of the item space. As the second main result we show that the cold-start time (which is the first time after which quality recommendations can be given) of this algorithm is ... , where v is the typical fraction of items that users like. This thesis advances the state of the art on many fronts. First, our cold-start bound differs from that of Brester et al. (2014) for user-user paradigm, where the cold-start time increases with number of items. Second, our regret bound is similar to those obtained in multi-armed bandits (surveyed in Bubeck and Cesa-Bianchi (2012)) when the arms belong to general spaces (Kleinberg et aL, 2013; Bubeck et aL, 2011). This is despite the notable differences that in our setting: (a) recommending the same item twice to a given user is not allowed, unlike in bandits where arms can be pulled twice; and (b) the distance function for the underlying metric space is not known in our setting. Finally, our mixture assumptions differ from earlier works, cf. (Kleinberg and Sandler, 2004; Dabeer, 2013; Bresler et al., 2014), that assume "gap" between mixture components. We circumvent gap conditions by instead using the doubling dimension of the item space.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 69-72).
 
Date issued
2015
URI
http://hdl.handle.net/1721.1/99837
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Publisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science.

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