Nonparametric Relational Models with Superrectangulation

Masahiro Nakano, Ryo Nishikimi, Yasuhiro Fujiwara, Akisato Kimura, Takeshi Yamada, Naonori Ueda
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:8921-8937, 2022.

Abstract

This paper addresses the question, ”What is the smallest object that contains all rectangular partitions with n or fewer blocks?” and shows its application to relational data analysis using a new strategy we call super Bayes as an alternative to Bayesian nonparametric (BNP) methods. Conventionally, standard BNP methods have combined the Aldous-Hoover-Kallenberg representation with parsimonious stochastic processes on rectangular partitioning to construct BNP relational models. As a result, conventional methods face the great difficulty of searching for a parsimonious random rectangular partition that fits the observed data well in Bayesian inference. As a way to essentially avoid such a problem, we propose a strategy to combine an extremely redundant rectangular partition as a deterministic (non-probabilistic) object. Specifically, we introduce a special kind of rectangular partitioning, which we call superrectangulation, that contains all possible rectangular partitions. Delightfully, this strategy completely eliminates the difficult task of searching around for random rectangular partitions, since the superrectangulation is deterministically fixed in inference. Experiments on predictive performance in relational data analysis show that the super Bayesian model provides a more stable analysis than the existing BNP models, which are less likely to be trapped in bad local optima.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-nakano22a, title = { Nonparametric Relational Models with Superrectangulation }, author = {Nakano, Masahiro and Nishikimi, Ryo and Fujiwara, Yasuhiro and Kimura, Akisato and Yamada, Takeshi and Ueda, Naonori}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {8921--8937}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/nakano22a/nakano22a.pdf}, url = {https://proceedings.mlr.press/v151/nakano22a.html}, abstract = { This paper addresses the question, ”What is the smallest object that contains all rectangular partitions with n or fewer blocks?” and shows its application to relational data analysis using a new strategy we call super Bayes as an alternative to Bayesian nonparametric (BNP) methods. Conventionally, standard BNP methods have combined the Aldous-Hoover-Kallenberg representation with parsimonious stochastic processes on rectangular partitioning to construct BNP relational models. As a result, conventional methods face the great difficulty of searching for a parsimonious random rectangular partition that fits the observed data well in Bayesian inference. As a way to essentially avoid such a problem, we propose a strategy to combine an extremely redundant rectangular partition as a deterministic (non-probabilistic) object. Specifically, we introduce a special kind of rectangular partitioning, which we call superrectangulation, that contains all possible rectangular partitions. Delightfully, this strategy completely eliminates the difficult task of searching around for random rectangular partitions, since the superrectangulation is deterministically fixed in inference. Experiments on predictive performance in relational data analysis show that the super Bayesian model provides a more stable analysis than the existing BNP models, which are less likely to be trapped in bad local optima. } }
Endnote
%0 Conference Paper %T Nonparametric Relational Models with Superrectangulation %A Masahiro Nakano %A Ryo Nishikimi %A Yasuhiro Fujiwara %A Akisato Kimura %A Takeshi Yamada %A Naonori Ueda %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-nakano22a %I PMLR %P 8921--8937 %U https://proceedings.mlr.press/v151/nakano22a.html %V 151 %X This paper addresses the question, ”What is the smallest object that contains all rectangular partitions with n or fewer blocks?” and shows its application to relational data analysis using a new strategy we call super Bayes as an alternative to Bayesian nonparametric (BNP) methods. Conventionally, standard BNP methods have combined the Aldous-Hoover-Kallenberg representation with parsimonious stochastic processes on rectangular partitioning to construct BNP relational models. As a result, conventional methods face the great difficulty of searching for a parsimonious random rectangular partition that fits the observed data well in Bayesian inference. As a way to essentially avoid such a problem, we propose a strategy to combine an extremely redundant rectangular partition as a deterministic (non-probabilistic) object. Specifically, we introduce a special kind of rectangular partitioning, which we call superrectangulation, that contains all possible rectangular partitions. Delightfully, this strategy completely eliminates the difficult task of searching around for random rectangular partitions, since the superrectangulation is deterministically fixed in inference. Experiments on predictive performance in relational data analysis show that the super Bayesian model provides a more stable analysis than the existing BNP models, which are less likely to be trapped in bad local optima.
APA
Nakano, M., Nishikimi, R., Fujiwara, Y., Kimura, A., Yamada, T. & Ueda, N.. (2022). Nonparametric Relational Models with Superrectangulation . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:8921-8937 Available from https://proceedings.mlr.press/v151/nakano22a.html.

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