An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling

Zhihua Zhang, Dakan Wang, Edward Chang
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1416-1424, 2012.

Abstract

We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (wDDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this wDDP to Bayesian multivariate-response regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-zhang12c, title = {An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling}, author = {Zhang, Zhihua and Wang, Dakan and Chang, Edward}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {1416--1424}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/zhang12c/zhang12c.pdf}, url = {https://proceedings.mlr.press/v22/zhang12c.html}, abstract = {We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (wDDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this wDDP to Bayesian multivariate-response regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction.} }
Endnote
%0 Conference Paper %T An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling %A Zhihua Zhang %A Dakan Wang %A Edward Chang %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-zhang12c %I PMLR %P 1416--1424 %U https://proceedings.mlr.press/v22/zhang12c.html %V 22 %X We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (wDDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this wDDP to Bayesian multivariate-response regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction.
RIS
TY - CPAPER TI - An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling AU - Zhihua Zhang AU - Dakan Wang AU - Edward Chang BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-zhang12c PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 1416 EP - 1424 L1 - http://proceedings.mlr.press/v22/zhang12c/zhang12c.pdf UR - https://proceedings.mlr.press/v22/zhang12c.html AB - We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (wDDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this wDDP to Bayesian multivariate-response regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction. ER -
APA
Zhang, Z., Wang, D. & Chang, E.. (2012). An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:1416-1424 Available from https://proceedings.mlr.press/v22/zhang12c.html.

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