Conference Paper

Collaborate with strangers to find own preferences

DOI: 10.1007/s00224-007-9016-7 Conference: SPAA 2005: Proceedings of the 17th Annual ACM Symposium on Parallelism in Algorithms and Architectures, July 18-20, 2005, Las Vegas, Nevada, USA
Source: DBLP


Abstract We consider a model with n players and m objects. Each player has an unknown,grade for each object, modeled by a “preference vector” of length m. A player can learn his grade for an object by probing that object, but performing a probe incurs cost. The goal of the players is to learn their own evaluations of objects with minimal cost, by adopting the results of probes performed by other players. To facilitate communication, we assume that players collaborate by posting their grades for objects on a shared billboard: reading from the billboard is free. We consider players whose preference vectors are popular, i.e., players whose preferences are common to many other players. We present distributed and sequential algorithms to solve the problem with logarithmic cost overhead. Submitted as a regular presentation. Please consider as a brief announcement as well.

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Available from: Zvi Lotker, Dec 15, 2013
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    • "Recently, it has been shown that the problem of finding a good object for each user can be solved by very simple combinatorial algorithms without any restriction on the preference vectors [4]: for any set P of users with a common object they all like, only O(m + n log |P |) probes are required overall until all users in P will find a good object (w.h.p.). The result closest to our work is [3], where algorithms are given for the case where many users have identical preference vectors (see Section 3.1). We note that when the preference matrix is arbitrary, the case where user preferences may be concentrated in sets of positive diameter is much harder than dealing with sets of diameter 0. "
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    ABSTRACT: We consider a model of recommendation systems, where each member from a given set of players has a binary preference to each element in a given set of objects: in- tuitively, each player either likes or dislikes each object. However, the players do not know their preferences. To nd his preference of an object, a player may probe it, but each probe incurs unit cost. The goal of the play- ers is to learn their complete preference vector (approx- imately) while incurring minimal cost. This is possible if many players have similar preference vectors: such a set of players with similar \taste" may split the cost of probing all objects among them, and share the results of their probes by posting them on a public billboard. The problem is that players do not know a priori whose taste is close to theirs. In this paper we present a distributed randomized peer-to-peer algorithm in which each player outputs a vector which is close to the best possible ap-
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    • "In [4] it was shown that in this model, a user sharing its preference with at least α fraction of the users (D = 0 in our terms), can find a product he likes in O m n log n/α tries. Later, in the same model Awerbuch et al. [2] reconstruct the users preference for all objects with similar probe complexity and show this is a lower bound. "
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    ABSTRACT: We consider the interactive model of recommender systems, in which users are asked about just a few of their preferences, and in return the system outputs an approximation of all their preferences. The measure of performance is the probe complexity of the algorithm, defined to be the maximal number of answers any user should provide (probe complexity typically depends inversely on the number of users with similar preferences and on the quality of the desired approximation). Previous interactive recommendation algorithms assume that user preferences are binary, meaning that each object is either "liked" or "disliked" by each user. In this paper we consider the general case in which users may have a more refined scale of preference, namely more than two possible grades. We show how to reduce the non-binary case to the binary one, proving the following results. For discrete grades with s possible values, we give a simple deterministic reduction that preserves the approximation properties of the binary algorithm at the cost of increasing probe complexity by factor s. Our main result is for the general case, where we assume that user grades are arbitrary real numbers. For this case we present an algorithm that preserves the approximation properties of the binary algorithm while incurring only polylogarithmic overhead.
    Preview · Conference Paper · Jan 2011
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    • "Other theoretical work on recommendation systems. There have been many other theoretical efforts on recommendation systems [2] [4] [7] [8] [9] [10] [27] [39]. They largely deal with finding good objects out of a fixed set of objects, while our model involves multiple rounds where each round has its own set of objects. "
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    ABSTRACT: Recommendation systems can be attacked in various ways, and the ultimate attack form is reached with a sybil attack, where the attacker creates a potentially unlimited number of sybil identities to vote. Defending against sybil attacks is often quite challenging, and the nature of recommendation systems makes it even harder. This paper presents DSybil, a novel defense for diminishing the influence of sybil identities in recommendation systems. DSybil provides strong provable guarantees that hold even under the worst-case attack and are optimal. DSybil can defend against an unlimited number of sybil identities over time. DSybil achieves its strong guarantees by i) exploiting the heavy-tail distribution of the typical voting behavior of the honest identities, and ii) carefully identifying whether the system is already getting "enough help" from the (weighted) voters already taken into account or whether more "help" is needed. Our evaluation shows that DSybil would continue to provide high-quality recommendations even when a million- node botnet uses an optimal strategy to launch a sybil attack.
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