On collapsed representation of hierarchical Completely Random Measures

Gaurav Pandey, Ambedkar Dukkipati
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1605-1613, 2016.

Abstract

The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-pandey16, title = {On collapsed representation of hierarchical Completely Random Measures}, author = {Pandey, Gaurav and Dukkipati, Ambedkar}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1605--1613}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/pandey16.pdf}, url = {https://proceedings.mlr.press/v48/pandey16.html}, abstract = {The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP.} }
Endnote
%0 Conference Paper %T On collapsed representation of hierarchical Completely Random Measures %A Gaurav Pandey %A Ambedkar Dukkipati %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-pandey16 %I PMLR %P 1605--1613 %U https://proceedings.mlr.press/v48/pandey16.html %V 48 %X The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP.
RIS
TY - CPAPER TI - On collapsed representation of hierarchical Completely Random Measures AU - Gaurav Pandey AU - Ambedkar Dukkipati BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-pandey16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1605 EP - 1613 L1 - http://proceedings.mlr.press/v48/pandey16.pdf UR - https://proceedings.mlr.press/v48/pandey16.html AB - The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP. ER -
APA
Pandey, G. & Dukkipati, A.. (2016). On collapsed representation of hierarchical Completely Random Measures. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1605-1613 Available from https://proceedings.mlr.press/v48/pandey16.html.

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