Composite Marginal Likelihood Methods for Random Utility Models

Zhibing Zhao, Lirong Xia
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5922-5931, 2018.

Abstract

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computation efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-zhao18d, title = {Composite Marginal Likelihood Methods for Random Utility Models}, author = {Zhao, Zhibing and Xia, Lirong}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {5922--5931}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/zhao18d/zhao18d.pdf}, url = {https://proceedings.mlr.press/v80/zhao18d.html}, abstract = {We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computation efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.} }
Endnote
%0 Conference Paper %T Composite Marginal Likelihood Methods for Random Utility Models %A Zhibing Zhao %A Lirong Xia %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-zhao18d %I PMLR %P 5922--5931 %U https://proceedings.mlr.press/v80/zhao18d.html %V 80 %X We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computation efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.
APA
Zhao, Z. & Xia, L.. (2018). Composite Marginal Likelihood Methods for Random Utility Models. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:5922-5931 Available from https://proceedings.mlr.press/v80/zhao18d.html.

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