Inferring Sparse Preference Lists from Partial Information
Name
stsy.2019.0060.pdf
Description
Published version
Size
903.38 KB
Format
Adobe PDF
Checksum (MD5)
ac11f8ef10acb744d97b2006a271157c
Author(s)
Farias, Vivek
Jagabathula, Srikanth
Shah, Devavrat
Date Issued
2020
Journal
Stochastic Systems
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Version
Final published version
Abstract
© 2020 The Author(s). Probability distributions over rankings are crucial for the modeling and design of a wide range of practical systems. In this work, we pursue a nonparametric approach that seeks to learn a distribution over rankings (aka the ranking model) that is consistent with the observed data and has the sparsest possible support (i.e., the smallest number of rankings with nonzero probability mass). We focus on first-order marginal data, which comprise information on the probability that item i is ranked at position j, for all possible item and position pairs. The observed data may be noisy. Finding the sparsest approximation requires brute force search in the worst case. To address this issue, we restrict our search to, what we dub, the signature family, and show that the sparsest model within the signature family can be found computationally efficiently compared with the brute force approach. We then establish that the signature family provides good approximations to popular ranking model classes, such as the multinomial logit and the exponential family classes, with support size that is small relative to the dimension of the observed data. We test our methods on two data sets: the ranked election data set from the American Psychological Association and the preference ordering data on 10 different sushi varieties.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/STSY.2019.0060
