Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion

[2411.12965] Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion Skip to main content Search Submit Donate Log in Statistics > Machine Learning arXiv:2411.12965 (stat) [Submitted on 20 Nov 2024 ( v1 ), last revised 24 Aug 2026 (this version, v3)] Title: Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion Authors: Tathagata Sadhukhan , Manit Paul , Raaz Dwivedi View PDF HTML (experimental) Abstract: Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying data is sufficiently smooth and the missingness probabilities are lower bounded. Here we analyze NN with non-smooth non-linear functions with vast amounts of missingness. In particular, we consider matrix completion settings where the entries of the underlying matrix follow a latent non-linear factor model, with the non-linearity belonging to a \Holder function class that is less smooth than Lipschitz. Our results establish following favorable properties for a suitable two-sided NN: (1) The mean squared error (MSE) of NN adapts to the smoothness of the non-linearity, (2) under certain regularity conditions, the NN error rate matches the rate obtained by an oracle equipped with the knowledge of both the row and column latent factors, and finally (3) NN's MSE is non-trivial for a wide range of settings even when several matrix entries might be missing deterministically. We support our theoretical findings via extensive numerical simulations and a case study with data from a mobile health study, HeartSteps. Comments: 40 pages, 14 figures Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME) Cite as: arXiv:2411.12965 [stat.ML] (or arXiv:2411.12965v3 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2411.12965 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tathagata Sadhukhan [ view email ] [v1] Wed, 20 Nov 2024 01:40:53 UTC (4,437 KB) [v2] Mon, 1 Sep 2025 20:44:58 UTC (1,026 KB) [v3] Mon, 24 Aug 2026 23:33:58 UTC (1,025 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2024-11 Change to browse by: cs cs.LG math math.ST stat stat.ME stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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