  In this work, we leverage a generative data model considering comparison
noise to develop a fast, precise, and informative ranking algorithm from
pairwise comparisons that produces a measure of confidence on each comparison.
The problem of ranking a large number of items from noisy and sparse pairwise
comparison data arises in diverse applications, like ranking players in online
games, document retrieval or ranking human perceptions. Although different
algorithms are available, we need fast, large-scale algorithms whose accuracy
degrades gracefully when the number of comparisons is too small. Fitting our
proposed model entails solving a non-convex optimization problem, which we
tightly approximate by a sum of quasi-convex functions and a regularization
term. Resorting to an iterative reweighted minimization and the Primal-Dual
Hybrid Gradient method, we obtain PD-Rank, achieving a Kendall tau 0.1 higher
than all comparing methods, even for 10\% of wrong comparisons in simulated
data matching our data model, and leading in accuracy if data is generated
according to the Bradley-Terry model, in both cases faster by one order of
magnitude, in seconds. In real data, PD-Rank requires less computational time
to achieve the same Kendall tau than active learning methods.
