Article

Dirichlet process mixtures of generalized mallows models

Authors:

Marina Meilă and

Harr ChenAuthors Info & Claims

UAI'10: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence

July 2010

Pages 358 - 367

Published: 08 July 2010 Publication History

Abstract

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters by taking advantage of approximations to the conditional posteriors. We empirically demonstrate (1) the effectiveness of this approximation for improving convergence, (2) the benefits of the Dirichlet process model over alternative clustering techniques for ranked data, and (3) the applicability of the approach to exploring large real-world ranking datasets.

References

[1]

C. E. Antoniak. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann Stat, 2(6):1152-1174, 1974.

[2]

D. M. Blei and M. I. Jordan. Variational inference for Dirichlet process mixtures. Bayes Anal, 1(1):121-144, 2006.

[3]

L. M. Busse, P. Orbanz, and J. Bühmann. Cluster analysis of heterogeneous rank data. In Proceedings of ICML, 2007.

[4]

M. A. Fligner and J. S. Verducci. Distance based ranking models. J Roy Stat Soc B Met, 48(3):359-369, 1986.

[5]

M. A. Fligner and J. S. Verducci. Multistage ranking models. J Am Stat Assoc, 83(403):892-901, 1988.

[6]

K. Goldberg, T. Roeder, D. Gupta, and C. Perkins. Eigen-taste: A constant time collaborative filtering algorithm. Inform Retrieval, 4(2):133-151, 2001.

[7]

I. C. Gormley and T. B. Murphy. Analysis of Irish third-level college applications data. J Roy Stat Soc A Sta, 169(2):361-379, 2006.

[8]

I. C. Gormley and T. B. Murphy. Exploring voting blocs within the Irish electorate: a mixture modeling approach. J Am Stat Assoc, 103(483):1014-1027, 2008a.

[9]

I. C. Gormley and T. B. Murphy. A mixture of experts model for rank data with applications in election studies. Ann Appl Stat, 2(4):1452-1477, 2008b.

[10]

J. Guiver and E. Snelson. Bayesian estimation for Plackett-Luce ranking models. In Proceedings of ICML, 2009.

[11]

S. Jain and R. M. Neal. Splitting and merging components of a nonconjugate Dirichlet process mixture model. Bayes Anal, 2(3):445-472, 2007.

[12]

G. Lebanon and Y. Mao. Non-parametric modeling of partially ranked data. J Mach Learn Res, 9:2401-2429, 2008.

[13]

P. Liang, S. Petrov, M. I. Jordan, and D. Klein. The infinite PCFG using hierarchical Dirichlet processes. In Proceedings of EMNLP, 2007.

[14]

M. Meilă. Comparing clusterings—an information based distance. J Multivariate Anal, 98:873-895, 2007.

[15]

M. Meilă and L. Bao. Estimation and clustering with infinite rankings. In Proceedings of UAI, 2008.

[16]

M. Meilă, K. Phadnis, A. Patterson, and J. Bilmes. Consensus ranking under the exponential model. In Proceedings of UAI, 2007.

[17]

R. M. Neal. Markov chain sampling methods for Dirichlet process mixture models. J Comput Graph Stat, 9(2):249-265, 2000.

[18]

R. M. Neal. Slice sampling. Ann Stat, 31(3):705-767, 2003.

[19]

C. E. Rasmussen, B. J. de la Cruz, Z. Ghahramani, and D. L. Wild. Modeling and visualizing uncertainty in gene expression clusters using Dirichlet process mixtures. IEEE/ACM T Comput Bi, 6(4):615-628, 2009.

[20]

E. B. Sudderth, A. Torralba, W. T. Freeman, and A. S. Willsky. Describing visual scenes using transformed dirichlet processes. In Advances in NIPS, 2005.

[21]

Y. W. Teh, M. I. Jordan, M. J. Beal, and D. M. Blei. Hierarchical Dirichlet processes. J Am Stat Assoc, 101(476):1566-1581, 2006.

Cited By

Yu PGu JXu H(2019)Analysis of ranking dataWIREs Computational Statistics10.1002/wics.148311:6Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1002/wics.1483
Vitelli VSørensen ØCrispino MFrigessi AArjas E(2017)Probabilistic preference learning with the mallows rank modelThe Journal of Machine Learning Research10.5555/3122009.324201518:1(5796-5844)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.5555/3122009.3242015
Doucette JCohen RLarson KWinikoff MDas SDurfee E(2017)A Restricted Markov Tree Model for Inference and Generation in Social Choice with Incomplete PreferencesProceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems10.5555/3091125.3091251(893-901)Online publication date: 8-May-2017
https://dl.acm.org/doi/10.5555/3091125.3091251
Show More Cited By

Index Terms

Dirichlet process mixtures of generalized mallows models
1. Computing methodologies
  1. Machine learning

Index terms have been assigned to the content through auto-classification.

Recommendations

Variational learning for Dirichlet process mixtures of Dirichlet distributions and applications

In this paper, we propose a Bayesian nonparametric approach for modeling and selection based on a mixture of Dirichlet processes with Dirichlet distributions, which can also be seen as an infinite Dirichlet mixture model. The proposed model uses a stick-...
Read More
Nonparametric localized feature selection via a dirichlet process mixture of generalized dirichlet distributions
ICONIP'12: Proceedings of the 19th international conference on Neural Information Processing - Volume Part III

In this paper, we propose a novel Bayesian nonparametric statistical approach of simultaneous clustering and localized feature selection for unsupervised learning. The proposed model is based on a mixture of Dirichlet processes with generalized ...
Read More
Partially collapsed parallel Gibbs sampler for Dirichlet process mixture models

Proposed representation for DP is ideally suited for distributed computing.Proposed sampler offers advantages in terms of both scalability and run-time.Proposed sampler outperforms existing parallel samplers for Dirichlet process mixtures in terms of ...
Read More

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

UAI'10: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence

July 2010

751 pages

ISBN:9780974903965

Editors:
Peter Grunwald
Advanced Systems Research, CWI, Amsterdam, Netherlands
,
Peter Spirtes
Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA

Publisher

AUAI Press

Arlington, Virginia, United States

Publication History

Published: 08 July 2010

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Yu PGu JXu H(2019)Analysis of ranking dataWIREs Computational Statistics10.1002/wics.148311:6Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1002/wics.1483
Vitelli VSørensen ØCrispino MFrigessi AArjas E(2017)Probabilistic preference learning with the mallows rank modelThe Journal of Machine Learning Research10.5555/3122009.324201518:1(5796-5844)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.5555/3122009.3242015
Doucette JCohen RLarson KWinikoff MDas SDurfee E(2017)A Restricted Markov Tree Model for Inference and Generation in Social Choice with Incomplete PreferencesProceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems10.5555/3091125.3091251(893-901)Online publication date: 8-May-2017
https://dl.acm.org/doi/10.5555/3091125.3091251
Lu TTang PProcaccia ABoutilier C(2012)Bayesian vote manipulationProceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence10.5555/3020652.3020710(543-553)Online publication date: 14-Aug-2012
https://dl.acm.org/doi/10.5555/3020652.3020710

View Options

View options

Media

Figures

Other

Tables

View Table of Contents