{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-mondrian-process-for-machine-learning","title":"The Mondrian Process for Machine Learning","arxiv_id":"1507.05181","date":"2015-07-18","proceeding":null,"authors":["Matej Balog","Yee Whye Teh"],"abstract":"This report is concerned with the Mondrian process and its applications in\nmachine learning. The Mondrian process is a guillotine-partition-valued\nstochastic process that possesses an elegant self-consistency property. The\nfirst part of the report uses simple concepts from applied probability to\ndefine the Mondrian process and explore its properties.\n  The Mondrian process has been used as the main building block of a clever\nonline random forest classification algorithm that turns out to be equivalent\nto its batch counterpart. We outline a slight adaptation of this algorithm to\nregression, as the remainder of the report uses regression as a case study of\nhow Mondrian processes can be utilized in machine learning. In particular, the\nMondrian process will be used to construct a fast approximation to the\ncomputationally expensive kernel ridge regression problem with a Laplace\nkernel.\n  The complexity of random guillotine partitions generated by a Mondrian\nprocess and hence the complexity of the resulting regression models is\ncontrolled by a lifetime hyperparameter. It turns out that these models can be\nefficiently trained and evaluated for all lifetimes in a given range at once,\nwithout needing to retrain them from scratch for each lifetime value. This\nleads to an efficient procedure for determining the right model complexity for\na dataset at hand.\n  The limitation of having a single lifetime hyperparameter will motivate the\nfinal Mondrian grid model, in which each input dimension is endowed with its\nown lifetime parameter. In this model we preserve the property that its\nhyperparameters can be tweaked without needing to retrain the modified model\nfrom scratch.","url_abs":"http://arxiv.org/abs/1507.05181v1","url_pdf":"http://arxiv.org/pdf/1507.05181v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-mondrian-process-for-machine-learning","repo_url":"https://github.com/harveydevereux/Mondrian","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}