A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment

[2608.14968] A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2608.14968 (stat) [Submitted on 15 Aug 2026] Title: A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment Authors: Kexuan Li , Weidong Ma View a PDF of the paper titled A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment, by Kexuan Li and Weidong Ma View PDF HTML (experimental) Abstract: We consider nonparametric regression when the association between a response and its covariates changes across an unknown partition of a spatial domain. The proposed estimator learns the partition and the cluster-specific regression functions jointly. A neural network depending only on location determines cluster membership, while separate neural networks describe the covariate--response relationship within the clusters. An annealed softmax relaxation permits gradient-based estimation of the otherwise discrete assignments. Graph-Laplacian and occupancy penalties are used to discourage fragmented regions and degenerate solutions. We establish identifiability up to label permutation, bound partition error under a margin condition, and decompose prediction risk into regression and assignment components. The resulting rate agrees with that of an oracle estimator when the partition is estimated sufficiently accurately. Simulations show that joint estimation is useful when regression surfaces change abruptly across spatial boundaries, including settings with nonlinear effects, unequal region sizes, preferential sampling, and spatially correlated errors. Finally, a real data analysis is provided to demonstrate the validity and effectiveness of the proposed method. Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:2608.14968 [stat.ML] (or arXiv:2608.14968v1 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2608.14968 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kexuan Li [ view email ] [v1] Sat, 15 Aug 2026 01:39:56 UTC (1,143 KB) Full-text links: Access Paper: View a PDF of the paper titled A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment, by Kexuan Li and Weidong Ma View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2026-08 Change to browse by: cs cs.LG stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from

Related documents

• A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment#612405
• A Functorial Formulation of Neighborhood Aggregating Deep Learning#138917
• How to Achieve the Intended Aim of Deep Clustering Now, without Deep Learning#670483
• How to Achieve the Intended Aim of Deep Clustering Now, without Deep Learning#668418
• Microclimate spatio-temporal prediction using deep learning and land use data#678141