We study the problem of ranking from crowdsourced pairwise comparisons. Answers to pairwise tasks are known to be affected by the position of items on the screen, however, previous models for aggregation of pairwise comparisons do not focus on modeling such kind of biases. We introduce a new aggregation model factorBT for pairwise comparisons, which accounts for certain factors of pairwise tasks that are known to be irrelevant to the result of comparisons but may affect workers' answers due to perceptual reasons. By modeling biases that influence workers, factorBT is able to reduce the effect of biased pairwise comparisons on the resulted ranking. Our empirical studies on real-world data sets showed that factorBT produces more accurate ranking from crowdsourced pairwise comparisons than previously established models.
It was observed long ago that results of pairwise comparisons are affected by position bias @cite_5 . focused on filtering out workers having position bias rather than on aggregating pairwise comparisons. For this reason, their approach to optimization process is not traditional, and we do not see an easy extension of this process to account for multiple factors of bias. Secondly, in their method, all labels from biased workers are discarded and therefore we waste some unbiased labels produced by workers, who are biased only when they are confused or tired. Both of these shortcomings are covered by our work.
@cite_5
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Given a set V of n elements we wish to linearly order them given pairwise preference labels which may be non-transitive (due to irrationality or arbitrary noise). The goal is to linearly order the elements while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The number of disagreements (loss) and the query complexity (number of pairwise preference labels). Our algorithm adaptively queries at most O(e-6n log5 n) preference labels for a regret of e times the optimal loss. As a function of n, this is asymptotically better than standard (non-adaptive) learning bounds achievable for the same problem. Our main result takes us a step closer toward settling an open problem posed by learning-to-rank (from pairwise information) theoreticians and practitioners: What is a provably correct way to sample preference labels? To further show the power and practicality of our solution, we analyze a typical test case in which a large margin linear relaxation is used for efficiently solving the simpler learning problems in our decomposition. We study the problem of label ranking, a machine learning task that consists of inducing a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations (preferences) from suitable training data, using a natural extension of so-called pairwise classification. A ranking is then derived from a set of such relations by means of a ranking procedure. In this paper, we first elaborate on a key advantage of such a decomposition, namely the fact that it allows the learner to adapt to different loss functions without re-training, by using different ranking procedures on the same predicted order relations. In this regard, we distinguish between two types of errors, called, respectively, ranking error and position error. Focusing on the position error, which has received less attention so far, we then propose a ranking procedure called ranking through iterated choice as well as an efficient pairwise implementation thereof. Apart from a theoretical justification of this procedure, we offer empirical evidence in favor of its superior performance as a risk minimizer for the position error. Given a set V of n elements we wish to linearly order them using pairwise preference labels which may be non-transitive (due to irrationality or arbitrary noise). The goal is to linearly order the elements while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The number of disagreements (loss) and the query complexity (number of pairwise preference labels). Our algorithm adaptively queries at most O(n poly(log n, e-1)) preference labels for a regret of e times the optimal loss. This is strictly better, and often significantly better than what non-adaptive sampling could achieve. Our main result helps settle an open problem posed by learning-to-rank (from pairwise information) theoreticians and practitioners: What is a provably correct way to sample preference labels? The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining ranking, finding 'scores' for each object (e.g. player's rating) is of interest to understanding the intensity of the preferences. In this paper, we propose a novel iterative rank aggregation algorithm for discovering scores for objects from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with edges present between two objects if they are compared; the scores turn out to be the stationary probability of this random walk. The algorithm is model independent. To establish the efficacy of our method, however, we consider the popular Bradley-Terry-Luce (BTL) model in which each object has an associated score which determines the probabilistic outcomes of pairwise comparisons between objects. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. This, in essence, leads to order-optimal dependence on the number of samples required to learn the scores well by our algorithm. Indeed, the experimental evaluation shows that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms a recently proposed algorithm by Ammar and Shah [1].