{"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/coresets-for-decision-trees-of-signals","title":"Coresets for Decision Trees of Signals","arxiv_id":"2110.03195","date":"2021-10-07","proceeding":"NeurIPS 2021 12","authors":["Ibrahim Jubran","Ernesto Evgeniy Sanches Shayda","Ilan Newman","Dan Feldman"],"abstract":"A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to a given matrix $D$ of $N$ entries (labels) is the sum of squared differences over every label in $D$ and its assigned label by $t$. Given an error parameter $\\varepsilon\\in(0,1)$, a $(k,\\varepsilon)$-coreset $C$ of $D$ is a small summarization that provably approximates this loss to \\emph{every} such tree, up to a multiplicative factor of $1\\pm\\varepsilon$. In particular, the optimal $k$-tree of $C$ is a $(1+\\varepsilon)$-approximation to the optimal $k$-tree of $D$. We provide the first algorithm that outputs such a $(k,\\varepsilon)$-coreset for \\emph{every} such matrix $D$. The size $|C|$ of the coreset is polynomial in $k\\log(N)/\\varepsilon$, and its construction takes $O(Nk)$ time. This is by forging a link between decision trees from machine learning -- to partition trees in computational geometry. Experimental results on \\texttt{sklearn} and \\texttt{lightGBM} show that applying our coresets on real-world data-sets boosts the computation time of random forests and their parameter tuning by up to x$10$, while keeping similar accuracy. Full open source code is provided.","url_abs":"https://arxiv.org/abs/2110.03195v1","url_pdf":"https://arxiv.org/pdf/2110.03195v1.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":"coresets-for-decision-trees-of-signals","repo_url":"https://github.com/ernestosanches/decision-trees-coreset","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"coresets","method_name":"Coresets"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}