An R Package for Multivariate Penalized Splines on Triangulations with Global & Distributed Learning

Music City Center 

The MPST (Multivariate Penalized Spline over Triangulation) package provides a robust and efficient framework for statistical modeling of large-scale 2D and 3D data. Using advanced multivariate penalized splines, MPST effectively handles irregular domains, noisy observations, and sparse datasets. It supports global and distributed learning, enabling seamless large-scale analysis. Its distributed framework employs domain decomposition, partitioning data into subsets based on triangulation, processing them in parallel, and integrating results efficiently. This approach enhances computational performance without sacrificing accuracy. A key strength of MPST is its ability to achieve precise local fitting with varying smoothness across subdomains, ensuring smooth global transitions and overcoming traditional spline limitations. Additionally, MPST provides user-friendly 2D and 3D visualization tools, aiding result interpretation. Numerical studies show MPST outperforms existing smoothing methods in accuracy, efficiency, and scalability. By integrating state-of-the-art smoothing techniques with distributed computing, MPST is a powerful tool for complex, high-dimensional data modeling.

Complex multidimensional data

Computational efficiency

Distributed learning

Nonparametric smoothing

Multivariate spline smoothing

MPST package 

Section on Nonparametric Statistics