{"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/bayesian-multi-scale-modeling-of-factor","title":"Bayesian Multi-scale Modeling of Factor Matrix without using Partition Tree","arxiv_id":"2002.09606","date":"2020-02-22","proceeding":null,"authors":["Maoran Xu","Leo L. Duan"],"abstract":"The multi-scale factor models are particularly appealing for analyzing matrix- or tensor-valued data, due to their adaptiveness to local geometry and intuitive interpretation. However, the reliance on the binary tree for recursive partitioning creates high complexity in the parameter space, making it extremely challenging to quantify its uncertainty. In this article, we discover an alternative way to generate multi-scale matrix using simple matrix operation: starting from a random matrix with each column having two unique values, its Cholesky whitening transform obeys a recursive partitioning structure. This allows us to consider a generative distribution with large prior support on common multi-scale factor models, and efficient posterior computation via Hamiltonian Monte Carlo. We demonstrate its potential in a multi-scale factor model to find broader regions of interest for human brain connectivity.","url_abs":"http://arxiv.org/abs/2002.09606v2","url_pdf":"http://arxiv.org/pdf/2002.09606v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"bayesian-multi-scale-modeling-of-factor","repo_url":"https://github.com/moran-xu/MultiscaleFactorHMC","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}