Rectangular Tiling Process

Masahiro Nakano, Katsuhiko Ishiguro, Akisato Kimura, Takeshi Yamada, Naonori Ueda
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):361-369, 2014.

Abstract

This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first two, including the product of Chinese restaurant processes and the Mondrian process. However, existing models for arbitrary partitioning are too complicated to permit the analysis of the statistical behaviors of models, which places very severe capability limits on relational data analysis. In this paper, we propose a new probabilistic model of arbitrary partitioning called the rectangular tiling process (RTP). Our model has a sound mathematical base in projective systems and infinite extension of conditional probabilities, and is capable of representing partitions of infinite elements as found in ordinary Bayesian nonparametric models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-nakano14, title = {Rectangular Tiling Process}, author = {Nakano, Masahiro and Ishiguro, Katsuhiko and Kimura, Akisato and Yamada, Takeshi and Ueda, Naonori}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {361--369}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/nakano14.pdf}, url = {https://proceedings.mlr.press/v32/nakano14.html}, abstract = {This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first two, including the product of Chinese restaurant processes and the Mondrian process. However, existing models for arbitrary partitioning are too complicated to permit the analysis of the statistical behaviors of models, which places very severe capability limits on relational data analysis. In this paper, we propose a new probabilistic model of arbitrary partitioning called the rectangular tiling process (RTP). Our model has a sound mathematical base in projective systems and infinite extension of conditional probabilities, and is capable of representing partitions of infinite elements as found in ordinary Bayesian nonparametric models.} }
Endnote
%0 Conference Paper %T Rectangular Tiling Process %A Masahiro Nakano %A Katsuhiko Ishiguro %A Akisato Kimura %A Takeshi Yamada %A Naonori Ueda %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-nakano14 %I PMLR %P 361--369 %U https://proceedings.mlr.press/v32/nakano14.html %V 32 %N 2 %X This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first two, including the product of Chinese restaurant processes and the Mondrian process. However, existing models for arbitrary partitioning are too complicated to permit the analysis of the statistical behaviors of models, which places very severe capability limits on relational data analysis. In this paper, we propose a new probabilistic model of arbitrary partitioning called the rectangular tiling process (RTP). Our model has a sound mathematical base in projective systems and infinite extension of conditional probabilities, and is capable of representing partitions of infinite elements as found in ordinary Bayesian nonparametric models.
RIS
TY - CPAPER TI - Rectangular Tiling Process AU - Masahiro Nakano AU - Katsuhiko Ishiguro AU - Akisato Kimura AU - Takeshi Yamada AU - Naonori Ueda BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-nakano14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 361 EP - 369 L1 - http://proceedings.mlr.press/v32/nakano14.pdf UR - https://proceedings.mlr.press/v32/nakano14.html AB - This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first two, including the product of Chinese restaurant processes and the Mondrian process. However, existing models for arbitrary partitioning are too complicated to permit the analysis of the statistical behaviors of models, which places very severe capability limits on relational data analysis. In this paper, we propose a new probabilistic model of arbitrary partitioning called the rectangular tiling process (RTP). Our model has a sound mathematical base in projective systems and infinite extension of conditional probabilities, and is capable of representing partitions of infinite elements as found in ordinary Bayesian nonparametric models. ER -
APA
Nakano, M., Ishiguro, K., Kimura, A., Yamada, T. & Ueda, N.. (2014). Rectangular Tiling Process. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):361-369 Available from https://proceedings.mlr.press/v32/nakano14.html.

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