Distributed Heterogeneity Learning for Generalized Partially Linear Models with Spatially Varying Coefficients

Area of Science:

• Spatial statistics
• Econometrics
• Environmental science

Background:

• Spatial heterogeneity is crucial in various scientific fields.
• Spatially varying coefficient models address heterogeneity but reduce parsimony.
• Large spatial datasets pose computational challenges.

Purpose of the Study:

• Develop generalized partially linear spatially varying coefficient models.
• Introduce a novel distributed heterogeneity learning (DHL) method for large datasets.
• Balance model flexibility and parsimony while improving scalability.

Main Methods:

• Generalized partially linear spatially varying coefficient models.
• Distributed heterogeneity learning (DHL) using bivariate spline smoothing.
• Scalable, communication-efficient algorithm design.

Main Results:

• DHL achieves near-linear speedup for large spatial datasets.
• Theoretical guarantees for DHL: asymptotic normality and optimal convergence rates.
• DHL demonstrates effectiveness in simulations and real-world U.S. loan data.

Conclusions:

• The proposed DHL method offers a flexible, parsimonious, and scalable approach to spatial regression.
• DHL effectively handles large-scale spatial data challenges.
• Rigorous theoretical support validates the DHL framework's performance.