Bayesian optimization of partition layouts for Mondrian processes

Wang Yi, Bin Li, Xuhui Fan, Wang Yang, Fang Chen

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review


The Mondrian process (MP) produces hierarchical partitions on a product space as a kd-tree, which can be served as a flexible yet parsimonious partition prior for relational modeling. Due to the recursive generation of partitions and varying dimensionality of the partition state space, the inference procedure for the MP relational modeling is extremely difficult. The prevalent inference method reversible-jump MCMC for this problem requires a number of unnecessary retrospective steps to transit from one partition state to a very similar one and it is prone to fall into a local optimum. In this paper, we attempt to circumvent these drawbacks by proposing an alternative method for inferring the MP partition structure. Based on the observation that similar cutting rate measures on the partition space lead to similar partition layouts, we propose to impose a nonhomogeneous cutting rate measure on the partition space to control the layouts of the generated partitions - the original MCMC sampling problem is thus transformed into a Bayesian global optimization problem. The empirical tests demonstrate that Bayesian optimization is able to find better partition structures than MCMC sampling with the same number of partition structure proposals.

Original languageEnglish
Title of host publicationProceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence
EditorsSubbarao Kambhampati
Place of PublicationCalifornia
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages7
ISBN (Electronic)9781577357704, 9781577357711
Publication statusPublished - 2016
Externally publishedYes
Event25th International Joint Conference on Artificial Intelligence, IJCAI 2016 - New York, United States
Duration: 9 Jul 201615 Jul 2016


Conference25th International Joint Conference on Artificial Intelligence, IJCAI 2016
Country/TerritoryUnited States
CityNew York


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