Abstract
In this chapter, we address the situation where agents need to learn from one another by exchanging learned knowledge. We employ hierarchical Bayesian modelling, which provides a powerful and principled solution. We point out some shortcomings of parametric hierarchical Bayesian modelling and thus focus on a nonparametric approach. Nonparametric hierarchical Bayesian modelling has its roots in Bayesian statistics and, in the form of Dirichlet process mixture modelling, was recently introduced into the machine learning community. In this chapter, we hope to provide an accessible introduction to this particular branch of statistics. We present the standard sampling-based learning algorithms and introduce a particular EM learning approach that leads to efficient and plausible solutions. We illustrate the effectiveness of our approach in context of a recommendation engine where our approach allows the principled combination of content-based and collaborative filtering.
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References
Antoniak, C.E.: Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems. Annals of Statistics 2, 1152–1174 (1974)
Bakker, B., Heskes, T.: Task Clustering and Gating for Bayesian Multitask Learning. Journal of Machine Learning Research 4 (2003)
Beal, M.J., Ghahramani, Z., Rasmussen, C.E.: The Infinite Hidden Markov Model. Advances in Neural Information Processing Systems 14 (2002)
Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet Allocation. Journal of Machine Learning Research 3 (2003)
Blei, D.M., Jordan, M.I., Ng, A.Y.: Hierarchical Bayesian Modelling for Applications in Information Retrieval. Bayesian Statistics 7. Oxford University Press, Oxford (2003)
Blei, D.M., Jordan, M.I.: Variational methods for the Dirichlet process. To appear in Proceedings of the 21st International Conference on Machine Learning (2004)
Breese, J.S., Heckerman, D., Kadie, C.: Empirical Analysis of Predictive Algorithms for Collaborative Filtering. In: Proceedings of the 14th Conference on Uncertainty in Artificial Intelligence (1998)
Cadez, I., Smyth, P.: Probabilistic Clustering using Hierarchical Models. TR No 99-16, Dept. of Information and Computer Science. University of California, Irvine (1999)
Escobar, M. D.: Estimating the Means of Several Normal Populations by Nonparametric Estimation of the Distribution of the Means. Unpublished PhD dissertation, Yale University (1988)
Escobar, M.D., West, M.: Computing Bayesian Nonparametric Hierarchical Models. In: Dey, D., Müller, P., Sinha, D. (eds.) Practical Nonparametric and Semiparametric Bayesian Statistics. Springer, Heidelberg (1998)
Ferguson, T.S.: A Bayesian Analysis of some Nonparametric Problems. Annals of Statistics 1, 209–230 (1973)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. CRC Press, Boca Raton (2003)
Gilks, W.R., Richardson, S., Spiegelhalter, D.J.: Markov Chain Monte Carlo in Practice. CRC Press, Boca Raton (1995)
Gosh, J.K., Ramamoorthi, R.V.: Bayesian Nonparametrics. Springer Series in Statistics (2002)
Heckerman, D.: A Tutorial on Learning with Bayesian Networks. Technical report MSR-TR-95-06 of Microsoft Research (1995)
Heskes, T.: Empirical Bayes for Learning to Learn. In: Proc. 17th International Conf. on Machine Learning, pp. 367–374. Morgan Kaufmann, San Francisco (2000)
Holmen, J., Tresp, V., Simula, O.: A Self-Organizing Map for Clustering Probabilistic Models. In: Proceedings of the Ninth International Conference on Artificial Neural Networks (ICANN 1999), vol. 2 (1999)
Ishwaran, H., James, L.F.: Gibbs Sampling Methods for Stick-Breaking Priors. Journal of the American Statistical Association 96(453) (2001)
MacEachern, S. M.: Estimating Normal Means with Conjugate Style Dirichlet Process Prior. Technical report No. 487, Department of Statistics, The Ohio State University (1992)
Neal, R, M.: Bayesian Mixture Modeling by Monte Carlo Simulation. Technical Teport No. DCR-TR-91-2, Department of Computer Science, University of Toronto (1991)
Neal, R, M.: Markov Chain Sampling Methdos for Dirichlet Process Mixture Models. Technical report No. 9815, Department of Statistics, University of Toronto (1998)
Platt, J.C.: Probabilities for SV machines. In: Advances in Large Margin Classifiers. MIT Press, Cambridge (1999)
Rasmussen, C.E.: The Infinite Gaussian Mixture Model. Advances in Neural Information Processing Systems 12 (2000)
Rasmussen, C.E., Ghahramani, Z.: Infinite Mixtures of Gaussian Process Experts. Advances in Neural Information Processing Systems 14 (2002)
Rocchio, J.J.: Relevance Feedback in Information Retrieval. In: The SMART Retrieval System: Experiments in Automatic Document Processing. Prentice Hall, Englewood Cliffs (1971)
Sethuraman, J.: A Constructive definition of Dirichlet Priors. Statistica Sinica 4 (1994)
Teh, Y.W., Jordan, M. I., Beal, M. J., Blei, D. M.: Hierarchical Dirichlet Proceses. Technical Report 653, UC Berkeley Statistics (2004)
Tomlinson, G., Escobar, M.: Analysis of Densities. Talk given at the Joint Statistical Meeting (2003)
Yu, K., Schwaighofer, A., Tresp, V., Ma, W.-Y., Zhang, H.: Collaborative Ensemble Learning: Combining Collaborative and Content-Based Information Filtering via Hierarchical Bayes. In: Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence (UAI), vol. 19 (2003)
Yu, K., Tresp, V., Yu, S.: A Nonparametric Bayesian Framework for Information Filtering. In: The Proceedings of the 27th Annual International ACM SIGIR Conference (2004)
Yu, K., Yu, S., Tresp, V.: Dirichlet Enhanced Latent Semantic Analysis. In: The Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics (2005)
West, M., Müller, P., Escobar, M.D.: Hierarchical Priors and Mixture Models, with Application in Regression and Density Estimation. In: Lindley, D.V., Smith, A.F.M., Freeman, P. (eds.) Aspects of Uncertainty: A Tribute, pp. 363–386. Wiley, New York (1994)
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Tresp, V., Yu, K. (2005). An Introduction to Nonparametric Hierarchical Bayesian Modelling with a Focus on Multi-agent Learning. In: Murray-Smith, R., Shorten, R. (eds) Switching and Learning in Feedback Systems. Lecture Notes in Computer Science, vol 3355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30560-6_13
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DOI: https://doi.org/10.1007/978-3-540-30560-6_13
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