Aggregating Incomplete and Noisy Rankings
This work addresses a fundamental issue in ranking aggregation for applications like recommendation systems, offering theoretical guarantees for handling incomplete and noisy data, though it is incremental in building on prior models.
The paper tackles the problem of learning a true ordering from incomplete and noisy rankings by introducing the selective Mallows model, which generalizes classical ranking models, and provides asymptotically tight sample complexity bounds for learning the complete ranking and top-k alternatives, along with an efficient maximum likelihood computation method.
We consider the problem of learning the true ordering of a set of alternatives from largely incomplete and noisy rankings. We introduce a natural generalization of both the classical Mallows model of ranking distributions and the extensively studied model of noisy pairwise comparisons. Our selective Mallows model outputs a noisy ranking on any given subset of alternatives, based on an underlying Mallows distribution. Assuming a sequence of subsets where each pair of alternatives appears frequently enough, we obtain strong asymptotically tight upper and lower bounds on the sample complexity of learning the underlying complete ranking and the (identities and the) ranking of the top-k alternatives from selective Mallows rankings. Moreover, building on the work of (Braverman and Mossel, 2009), we show how to efficiently compute the maximum likelihood complete ranking from selective Mallows rankings.