The Mondrian Process

We describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over kd-tree data structures. Mondrian processes are multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generalizations of the stickbreaking process described by Sethuraman (1994), recovering the Dirichlet process in one dimension. After introducing the Aldous-Hoover representation for jointly and separately exchangeable arrays, we show how the process can be used as a nonparametric prior distribution in Bayesian models of relational data.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Daniel M. Roy, Yee Whye Teh
• Keywords: Information Technology, Kd-tree Data Structures, Mondrian Processes, Multidimensional Generalizations, NIPS 2008