{"paper":{"title":"The Binary Space Partitioning-Tree Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Bin Li, Scott Anthony Sisson, Xuhui Fan","submitted_at":"2019-03-22T03:38:00Z","abstract_excerpt":"The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the Mondrian process. The BSP-Tree process is an almost surely right continuous Markov jump process that allows uniformly distributed oblique cuts in a two-dimensional convex polygon. The BSP-Tree process can also be extended using a non-uniform probability measure to generate direction differentiated c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09343","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}