nips nips2010 nips2010-51 nips2010-51-reference knowledge-graph by maker-knowledge-mining

51 nips-2010-Construction of Dependent Dirichlet Processes based on Poisson Processes


Source: pdf

Author: Dahua Lin, Eric Grimson, John W. Fisher

Abstract: We present a novel method for constructing dependent Dirichlet processes. The approach exploits the intrinsic relationship between Dirichlet and Poisson processes in order to create a Markov chain of Dirichlet processes suitable for use as a prior over evolving mixture models. The method allows for the creation, removal, and location variation of component models over time while maintaining the property that the random measures are marginally DP distributed. Additionally, we derive a Gibbs sampling algorithm for model inference and test it on both synthetic and real data. Empirical results demonstrate that the approach is effective in estimating dynamically varying mixture models. 1


reference text

[1] A. Ahmed and E. Xing. Dynamic Non-Parametric Mixture Models and The Recurrent Chinese Restaurant Process : with Applications to Evolutionary Clustering. In Proc. of SDM’08, 2008.

[2] F. R. Bach and M. I. Jordan. Learning spectral clustering. In Proc. of NIPS’03, 2003.

[3] J. Boyd-Graber and D. M. Blei. Syntactic Topic Models. In Proc. of NIPS’08, 2008.

[4] F. Caron, M. Davy, and A. Doucet. Generalized Polya Urn for Time-varying Dirichlet Process Mixtures. In Proc. of UAI’07, number 6, 2007.

[5] Y. Chung and D. B. Dunson. The local Dirichlet Process. Annals of the Inst. of Stat. Math., (October 2007), January 2009.

[6] D. B. Dunson. Bayesian Dynamic Modeling of Latent Trait Distributions. Biostatistics, 7(4), October 2006.

[7] J. E. Griffin and M. F. J. Steel. Order-Based Dependent Dirichlet Processes. Journal of the American Statistical Association, 101(473):179–194, March 2006.

[8] J. E. Griffin and M. F. J. Steel. Time-Dependent Stick-Breaking Processes. Technical report, 2009.

[9] J. F. C. Kingman. Poisson Processes. Oxford University Press, 1993.

[10] J. J. Kivinen, E. B. Sudderth, and M. I. Jordan. Learning Multiscale Representations of Natural Scenes Using Dirichlet Processes. In Proc. of ICCV’07, 2007.

[11] D. Lin, E. Grimson, and J. Fisher. Learning Visual Flows: A Lie Algebraic Approach. In Proc. of CVPR’09, 2009.

[12] S. N. MacEachern. Dependent Nonparametric Processes. In Proceedings of the Section on Bayesian Statistical Science, 1999.

[13] M. Meila. Comparing clusterings - An Axiomatic View. In Proc. of ICML’05, 2005.

[14] P. Muller, F. Quintana, and G. Rosner. A Method for Combining Inference across Related Nonparametric Bayesian Models. J. R. Statist. Soc. B, 66(3):735–749, August 2004.

[15] R. M. Neal. Markov Chain Sampling Methods for Dirichlet Process Mixture Models. Journal of computational and graphical statistics, 9(2):249–265, 2000.

[16] V. Rao and Y. W. Teh. Spatial Normalized Gamma Processes. In Proc. of NIPS’09, 2009.

[17] C. E. Rasmussen. The Infinite Gaussian Mixture Model. In Proc. of NIPS’00, 2000.

[18] L. Ren, D. B. Dunson, and L. Carin. The Dynamic Hierarchical Dirichlet Process. In Proc. of ICML’08, New York, New York, USA, 2008. ACM Press.

[19] J. Sethuraman. A Constructive Definition of Dirichlet Priors. Statistica Sinica, 4(2):639–650, 1994.

[20] K.-a. Sohn and E. Xing. Hidden Markov Dirichlet process: modeling genetic recombination in open ancestral space. In Proc. of NIPS’07, 2007.

[21] N. Srebro and S. Roweis. Time-Varying Topic Models using Dependent Dirichlet Processes, 2005.

[22] Y. W. Teh. Dirichlet Process, 2007.

[23] Y. W. Teh, M. I. Jordan, M. J. Beal, and D. M. Blei. Hierarchical Dirichlet Processes. Journal of the American Statistical Association, 101(476):1566–1581, 2006.

[24] X. Zhu and J. Lafferty. Time-Sensitive Dirichlet Process Mixture Models, 2005. 9