Metadata Dependent Mondrian Processes

Yi Wang, Bin Li, Yang Wang, Fang Chen
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1339-1347, 2015.

Abstract

Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-wangd15, title = {Metadata Dependent Mondrian Processes}, author = {Wang, Yi and Li, Bin and Wang, Yang and Chen, Fang}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1339--1347}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/wangd15.pdf}, url = {https://proceedings.mlr.press/v37/wangd15.html}, abstract = {Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.} }
Endnote
%0 Conference Paper %T Metadata Dependent Mondrian Processes %A Yi Wang %A Bin Li %A Yang Wang %A Fang Chen %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-wangd15 %I PMLR %P 1339--1347 %U https://proceedings.mlr.press/v37/wangd15.html %V 37 %X Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.
RIS
TY - CPAPER TI - Metadata Dependent Mondrian Processes AU - Yi Wang AU - Bin Li AU - Yang Wang AU - Fang Chen BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-wangd15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1339 EP - 1347 L1 - http://proceedings.mlr.press/v37/wangd15.pdf UR - https://proceedings.mlr.press/v37/wangd15.html AB - Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure. ER -
APA
Wang, Y., Li, B., Wang, Y. & Chen, F.. (2015). Metadata Dependent Mondrian Processes. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1339-1347 Available from https://proceedings.mlr.press/v37/wangd15.html.

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