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

• URL: http://arxiv.org/abs/2608.14968v1
• Date: Sat, 15 Aug 2026 01:39:56 GMT
• Title: A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment
• Abstract summary: A nonparametric estimator is proposed to learn the partition and the cluster-specific regression functions jointly.<n>A real data analysis is provided to demonstrate the validity and effectiveness of the proposed method.
• Score: 2.5782420501870296
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening [1.4773309126683776]
  We consider dimensionality reduction for high-dimensional observations accompanied by a supplied partition into two or more clusters.<n>The proposed procedure compares the cluster-specific empirical distribution functions through a several-sample Kolmogorov-Smirnov separation statistic.<n>We formalize the resulting marginal cluster support and establish simultaneous finite-sample concentration over all coordinates.
  arXiv  Detail & Related papers  (2026-09-06T21:58:59Z)
• Distinguishing case-mix from context heterogeneity in prognostic regression model synthesis settings [0.0]
  Prognostic regression models often synthesize data from multiple sites.<n>Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center.<n>Analysts must decide whether one regression model represents all sites or whether site-specific models are needed.
  arXiv  Detail & Related papers  (2026-08-13T07:04:53Z)
• Efficient Covariance Estimation for Sparsified Functional Data [51.69796254617083]
  proposed Random-knots (Random-knots-Spatial) and B-spline (Bspline-Spatial) estimators of the covariance function are computationally efficient.<n>Asymptotic pointwise of the covariance are obtained for sparsified individual trajectories under some regularity conditions.
  arXiv  Detail & Related papers  (2025-11-23T00:50:33Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Benign Overfitting and the Geometry of the Ridge Regression Solution in Binary Classification [75.01389991485098]
  We show that ridge regression has qualitatively different behavior depending on the scale of the cluster mean vector.<n>In regimes where the scale is very large, the conditions that allow for benign overfitting turn out to be the same as those for the regression task.
  arXiv  Detail & Related papers  (2025-03-11T01:45:42Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Semiparametric Regression for Spatial Data via Deep Learning [17.63607438860882]
  We use a sparsely connected deep neural network with rectified linear unit (ReLU) activation function to estimate the unknown regression function. Our method can handle well large data set owing to the gradient descent optimization algorithm.
  arXiv  Detail & Related papers  (2023-01-10T01:55:55Z)
• Communication-Efficient Distributed Quantile Regression with Optimal Statistical Guarantees [2.064612766965483]
  We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. The difficulties are resolved through a double-smoothing approach that is applied to the local (at each data source) and global objective functions. Despite the reliance on a delicate combination of local and global smoothing parameters, the quantile regression model is fully parametric.
  arXiv  Detail & Related papers  (2021-10-25T17:09:59Z)
• Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence [15.988679065054498]
  We propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial nonstationarity, local homogeneity, and outliers. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2021-09-01T16:29:46Z)
• Spatially Adaptive Inference with Stochastic Feature Sampling and Interpolation [72.40827239394565]
  We propose to compute features only at sparsely sampled locations. We then densely reconstruct the feature map with an efficient procedure. The presented network is experimentally shown to save substantial computation while maintaining accuracy over a variety of computer vision tasks.
  arXiv  Detail & Related papers  (2020-03-19T15:36:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.