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Conference Paper: Fast Algorithm for Generalized Multinomial Models with Ranking Data
Title | Fast Algorithm for Generalized Multinomial Models with Ranking Data |
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Authors | |
Issue Date | 2019 |
Publisher | PMLR. The Journal's web site is located at http://proceedings.mlr.press/ |
Citation | The 36th International Conference on Machine Learning (ICML 2019), Long Beach, CA, USA, 10-15 June 2019. In Proceedings of Machine Learning Research (PMLR), 2019, v. 97, p. 2445-2453 How to Cite? |
Abstract | We develop a framework of generalized multinomial models, which includes both the popular Plackett–Luce model and Bradley–Terry model as special cases. From a theoretical perspective, we prove that the maximum likelihood estimator (MLE) under generalized multinomial models corresponds to the stationary distribution of an inhomogeneous Markov chain uniquely. Based on this property, we propose an iterative algorithm that is easy to implement and interpret, and is guaranteed to converge. Numerical experiments on synthetic data and real data demonstrate the advantages of our Markov chain based algorithm over existing ones. Our algorithm converges to the MLE with fewer iterations and at a faster convergence rate. The new algorithm is readily applicable to problems such as page ranking or sports ranking data. |
Persistent Identifier | http://hdl.handle.net/10722/279401 |
ISSN |
DC Field | Value | Language |
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dc.contributor.author | Gu, J | - |
dc.contributor.author | Yin, G | - |
dc.date.accessioned | 2019-11-01T07:16:39Z | - |
dc.date.available | 2019-11-01T07:16:39Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | The 36th International Conference on Machine Learning (ICML 2019), Long Beach, CA, USA, 10-15 June 2019. In Proceedings of Machine Learning Research (PMLR), 2019, v. 97, p. 2445-2453 | - |
dc.identifier.issn | 2640-3498 | - |
dc.identifier.uri | http://hdl.handle.net/10722/279401 | - |
dc.description.abstract | We develop a framework of generalized multinomial models, which includes both the popular Plackett–Luce model and Bradley–Terry model as special cases. From a theoretical perspective, we prove that the maximum likelihood estimator (MLE) under generalized multinomial models corresponds to the stationary distribution of an inhomogeneous Markov chain uniquely. Based on this property, we propose an iterative algorithm that is easy to implement and interpret, and is guaranteed to converge. Numerical experiments on synthetic data and real data demonstrate the advantages of our Markov chain based algorithm over existing ones. Our algorithm converges to the MLE with fewer iterations and at a faster convergence rate. The new algorithm is readily applicable to problems such as page ranking or sports ranking data. | - |
dc.language | eng | - |
dc.publisher | PMLR. The Journal's web site is located at http://proceedings.mlr.press/ | - |
dc.relation.ispartof | Proceedings of Machine Learning Research (PMLR) | - |
dc.relation.ispartof | Proceedings of the 36th International Conference on Machine Learning (PMLR) | - |
dc.title | Fast Algorithm for Generalized Multinomial Models with Ranking Data | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Yin, G: gyin@hku.hk | - |
dc.identifier.authority | Yin, G=rp00831 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.hkuros | 308614 | - |
dc.identifier.volume | 97 | - |
dc.identifier.spage | 2445 | - |
dc.identifier.epage | 2453 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 2640-3498 | - |