Edward Shao | Searcharxiv

arXiv2026

Fast distance computation of multivariate distributions via nonparanormal transport

With the increasing availability of data objects in the form of probability distributions, there is a growing need for statistical methods tailored to distributional data. Distance measures, especially the pairwise distance matrix between data objects, provide the foundation for a wide range of modern data analysis methods, such as clustering, multidimensional scaling, and distance-based regression, among others. The Wasserstein distance is commonly used with distributional data due to its compelling optimal transport property. However, while the Wasserstein distance can be efficiently computed for univariate distributions, its application to multivariate distributions is limited due to high computational costs. To address these scalability issues, we introduce the Nonparanormal Transport (NPT) metric, a closed-form distance based on the flexible nonparanormal distribution family for modeling skewed and non-Gaussian multivariate data. Simulation studies demonstrate that NPT maintains a high level of agreement with the Wasserstein distance, while being at least 1000 times faster than its efficient variants when computing a 100-distribution pairwise distance matrix in both 2 and 5 dimensions. We illustrate the utility of NPT through a multidimensional scaling analysis of bivariate oxygen desaturation distributions of 723 individuals with sleep apnea in the Sleep Heart Health Study.

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arXiv2025

svc: An R package for Spatially Varying Coefficient Models

Traditional regression models assume stationary relationships between predictors and responses, failing to capture the spatial heterogeneity present in many environmental, epidemiological, and ecological processes. To address this limitation, we develop a scalable Bayesian framework for spatially varying coefficient (SVC) models, implemented in the \pkg{svc} R package (available at https://github.com/jdta95/svc), which allows regression coefficients to vary smoothly over space. Our approach combines three key computational innovations: (1) a subset Gaussian process approximation that reduces the computational burden from $O(n^3)$ to $O(m^3)$ with $m<n$, while maintaining predictive accuracy; (2) a robust adaptive Metropolis (RAM) algorithm that automatically tunes proposal distributions for efficient MCMC sampling of spatial range parameters; and (3) optimized linear algebra operations leveraging precomputed distance matrices and Cholesky decompositions to accelerate covariance calculations. We present the model's theoretical foundation, prior specification, and Gibbs sampling algorithm, with a focus on practical implementation for large spatial datasets. Simulation studies demonstrate that our method outperforms existing approaches in computational efficiency while maintaining competitive estimation accuracy. We illustrate its application in an analysis of land surface temperature (LST) data, revealing spatially varying effects of vegetation and emissivity that would be obscured by traditional regression techniques. The \pkg{svc} package provides researchers with a flexible, efficient tool for uncovering and quantifying nonstationary spatial relationships across diverse scientific domains.

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