  A preference order or ranking aggregated from pairwise comparison data is
commonly understood as a strict total order. However, in real-world scenarios,
some items are intrinsically ambiguous in comparisons, which may very well be
an inherent uncertainty of the data. In this case, the conventional total order
ranking can not capture such uncertainty with mere global ranking or utility
scores. In this paper, we are specifically interested in the recent surge in
crowdsourcing applications to predict partial but more accurate (i.e., making
less incorrect statements) orders rather than complete ones. To do so, we
propose a novel framework to learn some probabilistic models of partial orders
as a \emph{margin-based Maximum Likelihood Estimate} (MLE) method. We prove
that the induced MLE is a joint convex optimization problem with respect to all
the parameters, including the global ranking scores and margin parameter.
Moreover, three kinds of generalized linear models are studied, including the
basic uniform model, Bradley-Terry model, and Thurstone-Mosteller model,
equipped with some theoretical analysis on FDR and Power control for the
proposed methods. The validity of these models are supported by experiments
with both simulated and real-world datasets, which shows that the proposed
models exhibit improvements compared with traditional state-of-the-art
algorithms.
