{"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/kllr-a-scale-dependent-multivariate-model","title":"KLLR: A scale-dependent, multivariate model class for regression analysis","arxiv_id":"2202.09903","date":"2022-02-20","proceeding":null,"authors":["Arya Farahi","Dhayaa Anbajagane","August Evrard"],"abstract":"The underlying physics of astronomical systems governs the relation between their measurable properties. Consequently, quantifying the statistical relationships between system-level observable properties of a population offers insights into the astrophysical drivers of that class of systems. While purely linear models capture behavior over a limited range of system scale, the fact that astrophysics is ultimately scale-dependent implies the need for a more flexible approach to describing population statistics over a wide dynamic range. For such applications, we introduce and implement a class of Kernel-Localized Linear Regression (KLLR) models. KLLR is a natural extension to the commonly-used linear models that allows the parameters of the linear model -- normalization, slope, and covariance matrix -- to be scale-dependent. KLLR performs inference in two steps: (1) it estimates the mean relation between a set of independent variables and a dependent variable and; (2) it estimates the conditional covariance of the dependent variables given a set of independent variables. We demonstrate the model's performance in a simulated setting and showcase an application of the proposed model in analyzing the baryonic content of dark matter halos. As a part of this work, we publicly release a Python implementation of the KLLR method.","url_abs":"https://arxiv.org/abs/2202.09903v2","url_pdf":"https://arxiv.org/pdf/2202.09903v2.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":"kllr-a-scale-dependent-multivariate-model","repo_url":"https://github.com/afarahi/kllr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","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}