40 research outputs found
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Random Utility Theory for Social Choice
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, for which fast inference methods for maximum likelihood estimators are available. This paper develops conditions on general random utility models that enable fast inference within a Bayesian framework through MC-EM, providing concave loglikelihood functions and bounded sets of global maxima solutions. Results on both real-world and simulated data provide support for the scalability of the approach and capability for model selection among general random utility models including Plackett-Luce.Engineering and Applied Science
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
Generalized Random Utility Models with Multiple Types
We propose a model for demand estimation in multi-agent, differentiated product settings and present an estimation algorithm that uses reversible jump MCMC techniques to classify agents' types. Our model extends the popular setup in Berry, Levinsohn and Pakes (1995) to allow for the data-driven classification of agents' types using agent-level data. We focus on applications involving data on agents' ranking over alternatives, and present theoretical conditions that establish the identifiability of the model and uni-modality of the likelihood/posterior. Results on both real and simulated data provide support for the scalability of our approach.EconomicsEngineering and Applied SciencesMathematic
Generalized Method-of-Moments for Rank Aggregation
In this paper we propose a class of efficient Generalized Method-of-Moments(GMM) algorithms for computing parameters of the Plackett-Luce model, where the data consists of full rankings over alternatives. Our technique is based on breaking the full rankings into pairwise comparisons, and then computing parameters that satisfy a set of generalized moment conditions. We identify conditions for the output of GMM to be unique, and identify a general class of consistent and inconsistent breakings. We then show by theory and experiments that our algorithms run significantly faster than the classical Minorize-Maximization (MM) algorithm, while achieving competitive statistical efficiency.Engineering and Applied SciencesStatistic
Hybrid-MST: A hybrid active sampling strategy for pairwise preference aggregation
In this paper we present a hybrid active sampling strategy for pairwise
preference aggregation, which aims at recovering the underlying rating of the
test candidates from sparse and noisy pairwise labelling. Our method employs
Bayesian optimization framework and Bradley-Terry model to construct the
utility function, then to obtain the Expected Information Gain (EIG) of each
pair. For computational efficiency, Gaussian-Hermite quadrature is used for
estimation of EIG. In this work, a hybrid active sampling strategy is proposed,
either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST)
sampling in each trial, which is determined by the test budget. The proposed
method has been validated on both simulated and real-world datasets, where it
shows higher preference aggregation ability than the state-of-the-art methods