{"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/on-the-sample-complexity-of-privately-1","title":"On the Sample Complexity of Privately Learning Axis-Aligned Rectangles","arxiv_id":"2107.11526","date":"2021-07-24","proceeding":"NeurIPS 2021 12","authors":["Menachem Sadigurschi","Uri Stemmer"],"abstract":"We revisit the fundamental problem of learning Axis-Aligned-Rectangles over a finite grid $X^d\\subseteq{\\mathbb{R}}^d$ with differential privacy. Existing results show that the sample complexity of this problem is at most $\\min\\left\\{ d{\\cdot}\\log|X| \\;,\\; d^{1.5}{\\cdot}\\left(\\log^*|X| \\right)^{1.5}\\right\\}$. That is, existing constructions either require sample complexity that grows linearly with $\\log|X|$, or else it grows super linearly with the dimension $d$. We present a novel algorithm that reduces the sample complexity to only $\\tilde{O}\\left\\{d{\\cdot}\\left(\\log^*|X|\\right)^{1.5}\\right\\}$, attaining a dimensionality optimal dependency without requiring the sample complexity to grow with $\\log|X|$.The technique used in order to attain this improvement involves the deletion of \"exposed\" data-points on the go, in a fashion designed to avoid the cost of the adaptive composition theorems. The core of this technique may be of individual interest, introducing a new method for constructing statistically-efficient private algorithms.","url_abs":"https://arxiv.org/abs/2107.11526v1","url_pdf":"https://arxiv.org/pdf/2107.11526v1.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":"on-the-sample-complexity-of-privately-1","repo_url":"https://github.com/sadigurs/sadigurs.github.io","is_official":0,"mentioned_in_paper":0,"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}