{"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/method-of-moments-for-estimation-of-noisy","title":"Method of Moments for Estimation of Noisy Curves","arxiv_id":"2410.23220","date":"2024-10-30","proceeding":null,"authors":["Phillip Lo","Yuehaw Khoo"],"abstract":"In this paper, we study the problem of recovering a ground truth high dimensional piecewise linear curve $C^*(t):[0, 1]\\to\\mathbb{R}^d$ from a high noise Gaussian point cloud with covariance $\\sigma^2I$ centered around the curve. We establish that the sample complexity of recovering $C^*$ from data scales with order at least $\\sigma^6$. We then show that recovery of a piecewise linear curve from the third moment is locally well-posed, and hence $O(\\sigma^6)$ samples is also sufficient for recovery. We propose methods to recover a curve from data based on a fitting to the third moment tensor with a careful initialization strategy and conduct some numerical experiments verifying the ability of our methods to recover curves. All code for our numerical experiments is publicly available on GitHub.","url_abs":"https://arxiv.org/abs/2410.23220v1","url_pdf":"https://arxiv.org/pdf/2410.23220v1.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":"method-of-moments-for-estimation-of-noisy","repo_url":"https://github.com/PhillipLo/curve-recovery-public","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[],"methods":[],"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}