aiqbench analysis
This research introduces a differentiable framework for nonparametric regression on spatial data, enabling joint learning of cluster partitions and local response functions via neural networks. By employing annealed softmax relaxation and specific penalties to handle discrete assignments, the method achieves prediction rates comparable to oracle estimators even when regression surfaces shift abruptly across boundaries. The approach is particularly relevant for applications involving nonlinear effects, unequal region sizes, or spatially correlated errors where traditional fixed-partition models fall short.
A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment
arXiv:2608.14968v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
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 (pending registration)
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