Learning Mixtures of Plackett-Luce Models
Zhibing Zhao, Peter Piech, Lirong Xia
Abstract
In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any k≥2, the mixture of k Plackett-Luce models for no more than 2k-1 alternatives is non-identifiable and this bound is tight for k=2. For generic identifiability, we prove that the mixture of k Plackett-Luce models over m alternatives is \em generically identifiable if k≤⌊\frac m-2 2⌋!. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley & Murphy (2008), while achieving competitive statistical efficiency.
BibTeX
@InProceedings{pmlr-v48-zhaob16,
title = {Learning Mixtures of Plackett-Luce Models},
author = {Zhao, Zhibing and Piech, Peter and Xia, Lirong},
booktitle = {Proceedings of The 33rd International Conference on Machine Learning},
pages = {2906--2914},
year = {2016},
editor = {Balcan, Maria Florina and Weinberger, Kilian Q.},
volume = {48},
series = {Proceedings of Machine Learning Research},
address = {New York, New York, USA},
month = {20--22 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v48/zhaob16.pdf},
url = {https://proceedings.mlr.press/v48/zhaob16.html},
abstract = {In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any k≥2, the mixture of k Plackett-Luce models for no more than 2k-1 alternatives is non-identifiable and this bound is tight for k=2. For generic identifiability, we prove that the mixture of k Plackett-Luce models over m alternatives is \em generically identifiable if k≤⌊\frac m-2 2⌋!. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley & Murphy (2008), while achieving competitive statistical efficiency.}
}