A0557
Title: Parallel approximations of the Tukey g-and-h likelihoods and predictions for non-Gaussian geostatistics
Authors: Sagnik Mondal - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Sameh Abdulah - King Abdullah University of Science and Technology (Saudi Arabia)
Hatem Ltaief - KAUST (Saudi Arabia)
Ying Sun - KAUST (Saudi Arabia)
Marc Genton - KAUST (Saudi Arabia)
David Keyes - King Abdullah University of Science and Technology (Saudi Arabia)
Abstract: Gaussian random fields are among the most popular models to describe spatial data. However, the assumption of Gaussianity in real data is unrealistic since data may show signs of skewness and heavy tails. We consider the Tukey g-and-h (TGH) non-Gaussian random field that shows more robustness in modeling spatial data by including two parameters to incorporate skewness and heavy tail features. This modeling process involves generating a dense symmetric positive definite matrix with $O(n^2)$ space complexity and $O(n^3)$ operational complexity, where $n$ represents the number of spatial locations. On a large scale, this modeling process becomes prohibitive with standard methods. This work provides a parallel high-performance implementation of the TGH random field's inference on state-of-the-art hardware architectures. The implementation permits running the exact non-Gaussian modeling process for a large number of geospatial locations. We also provide a Tile Low-Rank approximation implementation that can accelerate the execution compared to the exact solution by around 7.29X and 2.96X on shared memory and distributed memory systems, respectively, using up to 810K spatial locations.
