9,932 research outputs found
A Margin-based MLE for Crowdsourced Partial Ranking
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.Comment: 9 pages, Accepted by ACM Multimedia 2018 as a full pape
Minimax-optimal Inference from Partial Rankings
This paper studies the problem of inferring a global preference based on the
partial rankings provided by many users over different subsets of items
according to the Plackett-Luce model. A question of particular interest is how
to optimally assign items to users for ranking and how many item assignments
are needed to achieve a target estimation error. For a given assignment of
items to users, we first derive an oracle lower bound of the estimation error
that holds even for the more general Thurstone models. Then we show that the
Cram\'er-Rao lower bound and our upper bounds inversely depend on the spectral
gap of the Laplacian of an appropriately defined comparison graph. When the
system is allowed to choose the item assignment, we propose a random assignment
scheme. Our oracle lower bound and upper bounds imply that it is
minimax-optimal up to a logarithmic factor among all assignment schemes and the
lower bound can be achieved by the maximum likelihood estimator as well as
popular rank-breaking schemes that decompose partial rankings into pairwise
comparisons. The numerical experiments corroborate our theoretical findings.Comment: 16 pages, 2 figure
Just Sort It! A Simple and Effective Approach to Active Preference Learning
We address the problem of learning a ranking by using adaptively chosen
pairwise comparisons. Our goal is to recover the ranking accurately but to
sample the comparisons sparingly. If all comparison outcomes are consistent
with the ranking, the optimal solution is to use an efficient sorting
algorithm, such as Quicksort. But how do sorting algorithms behave if some
comparison outcomes are inconsistent with the ranking? We give favorable
guarantees for Quicksort for the popular Bradley-Terry model, under natural
assumptions on the parameters. Furthermore, we empirically demonstrate that
sorting algorithms lead to a very simple and effective active learning
strategy: repeatedly sort the items. This strategy performs as well as
state-of-the-art methods (and much better than random sampling) at a minuscule
fraction of the computational cost.Comment: Accepted at ICML 201
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