Incremental Tree-Based Inference with Dependent Normalized Random Measures

Juho Lee, Seungjin Choi
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:558-566, 2014.

Abstract

Normalized random measures (NRMs) form a broad class of discrete random measures that are used as priors for Bayesian nonparametric models. Dependent normalized random measures (DNRMs) introduce dependencies in a set of NRMs, to facilitate the handling of data where the assumption of exchangeability is violated. Various methods have been developed to construct DNRMs; of particular interest is mixed normalized random measures (MNRMs), where DNRM is represented as a mixture of underlying shared normalized random measures. Emphasis in existing works is placed on the construction methods of DNRMs, but there is a little work on efficient inference for DNRMs. In this paper, we present a tree-based inference method for MNRM mixture models, extending Bayesian hierarchical clustering (BHC) which was originally developed as a deterministic approximate inference for Dirichlet process mixture (DPM) models. We also present an incremental inference for MNRM mixture models, building a tree incrementally in the sense that the tree structure is partially updated whenever a new data point comes in. The tree, when constructed in such a way, allows us to efficiently perform tree-consistent MAP inference in MRNM mixture models, determining a most probable tree-consistent partition, as well as to compute a marginal likelihood approximately. Numerical experiments on both synthetic and real-world datasets demonstrate the usefulness of our algorithm, compared to MCMC methods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v33-lee14, title = {{Incremental Tree-Based Inference with Dependent Normalized Random Measures}}, author = {Juho Lee and Seungjin Choi}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {558--566}, year = {2014}, editor = {Samuel Kaski and Jukka Corander}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/lee14.pdf}, url = {http://proceedings.mlr.press/v33/lee14.html}, abstract = {Normalized random measures (NRMs) form a broad class of discrete random measures that are used as priors for Bayesian nonparametric models. Dependent normalized random measures (DNRMs) introduce dependencies in a set of NRMs, to facilitate the handling of data where the assumption of exchangeability is violated. Various methods have been developed to construct DNRMs; of particular interest is mixed normalized random measures (MNRMs), where DNRM is represented as a mixture of underlying shared normalized random measures. Emphasis in existing works is placed on the construction methods of DNRMs, but there is a little work on efficient inference for DNRMs. In this paper, we present a tree-based inference method for MNRM mixture models, extending Bayesian hierarchical clustering (BHC) which was originally developed as a deterministic approximate inference for Dirichlet process mixture (DPM) models. We also present an incremental inference for MNRM mixture models, building a tree incrementally in the sense that the tree structure is partially updated whenever a new data point comes in. The tree, when constructed in such a way, allows us to efficiently perform tree-consistent MAP inference in MRNM mixture models, determining a most probable tree-consistent partition, as well as to compute a marginal likelihood approximately. Numerical experiments on both synthetic and real-world datasets demonstrate the usefulness of our algorithm, compared to MCMC methods.} }
Endnote
%0 Conference Paper %T Incremental Tree-Based Inference with Dependent Normalized Random Measures %A Juho Lee %A Seungjin Choi %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-lee14 %I PMLR %P 558--566 %U http://proceedings.mlr.press/v33/lee14.html %V 33 %X Normalized random measures (NRMs) form a broad class of discrete random measures that are used as priors for Bayesian nonparametric models. Dependent normalized random measures (DNRMs) introduce dependencies in a set of NRMs, to facilitate the handling of data where the assumption of exchangeability is violated. Various methods have been developed to construct DNRMs; of particular interest is mixed normalized random measures (MNRMs), where DNRM is represented as a mixture of underlying shared normalized random measures. Emphasis in existing works is placed on the construction methods of DNRMs, but there is a little work on efficient inference for DNRMs. In this paper, we present a tree-based inference method for MNRM mixture models, extending Bayesian hierarchical clustering (BHC) which was originally developed as a deterministic approximate inference for Dirichlet process mixture (DPM) models. We also present an incremental inference for MNRM mixture models, building a tree incrementally in the sense that the tree structure is partially updated whenever a new data point comes in. The tree, when constructed in such a way, allows us to efficiently perform tree-consistent MAP inference in MRNM mixture models, determining a most probable tree-consistent partition, as well as to compute a marginal likelihood approximately. Numerical experiments on both synthetic and real-world datasets demonstrate the usefulness of our algorithm, compared to MCMC methods.
RIS
TY - CPAPER TI - Incremental Tree-Based Inference with Dependent Normalized Random Measures AU - Juho Lee AU - Seungjin Choi BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-lee14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 558 EP - 566 L1 - http://proceedings.mlr.press/v33/lee14.pdf UR - http://proceedings.mlr.press/v33/lee14.html AB - Normalized random measures (NRMs) form a broad class of discrete random measures that are used as priors for Bayesian nonparametric models. Dependent normalized random measures (DNRMs) introduce dependencies in a set of NRMs, to facilitate the handling of data where the assumption of exchangeability is violated. Various methods have been developed to construct DNRMs; of particular interest is mixed normalized random measures (MNRMs), where DNRM is represented as a mixture of underlying shared normalized random measures. Emphasis in existing works is placed on the construction methods of DNRMs, but there is a little work on efficient inference for DNRMs. In this paper, we present a tree-based inference method for MNRM mixture models, extending Bayesian hierarchical clustering (BHC) which was originally developed as a deterministic approximate inference for Dirichlet process mixture (DPM) models. We also present an incremental inference for MNRM mixture models, building a tree incrementally in the sense that the tree structure is partially updated whenever a new data point comes in. The tree, when constructed in such a way, allows us to efficiently perform tree-consistent MAP inference in MRNM mixture models, determining a most probable tree-consistent partition, as well as to compute a marginal likelihood approximately. Numerical experiments on both synthetic and real-world datasets demonstrate the usefulness of our algorithm, compared to MCMC methods. ER -
APA
Lee, J. & Choi, S.. (2014). Incremental Tree-Based Inference with Dependent Normalized Random Measures. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:558-566 Available from http://proceedings.mlr.press/v33/lee14.html.

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