We are excited to announce that our paper “Bayesian nonparametric model for arbitrary cubic partitioning” has been accepted to ACML2021 as a long oral presentation.
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. 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, 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.
A pre-print and a python implementation will be coming soon.