Bayesian nonparametric model for arbitrary cubic partitioning

Masahiro Nakano (NTT communication science laboratories)*; Yasuhiro Fujiwara (NTT Communication Science Laboratories); Akisato Kimura (NTT Communication Science Laboratories); Takeshi Yamada (NTT Communication Science Laboratories); Naonori Ueda (NTT Communication Science Labs.)

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Abstract

In this paper, we propose a continuous-time Markov process for cubic partitioning models of three-dimensional (3D) arrays and its application to Bayesian nonparametric relational data analysis of 3D array data. Relational data analysis is a topic that has been actively studied in the field of Bayesian nonparametrics, and in particular, models for analyzing 3D arrays have attracted much attention in recent years. In particular, the cubic partitioning model is very popular due to its practical usefulness, and various models such as the infinite relational model and the Mondrian process have been proposed. However, these conventional models have the disadvantage that they are limited to a certain class of cubic partitions, and there is a need for a model that can represent a broader class of arbitrary cubic partitions, which has long been an open issue in this field. In this study, we propose a stochastic process that can represent arbitrary cubic partitions of 3D arrays as a continuous-time Markov process. Furthermore, by combining it with the Aldous-Hoover-Kallenberg representation theorem, we construct an infinitely exchangeable 3D relational model and apply it to real data to show its application to relational data analysis. Experiments show that the proposed model improves the prediction performance by expanding the class of representable cubic partitioning.