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Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
Type: Contributed
Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #318301
Title: Fast Correlation-Based Sparse Inverse Cholesky Factorization for Gaussian Processes
Author(s): Myeongjong Kang* and Matthias Katzfuss
Companies: Texas A&M University and Texas A&M University
Keywords: Gaussian process; large datasets; covariance approximation; computational complexity; sparsity; spatial statistics

Gaussian processes are widely used models in a variety of fields such as statistics and machine learning. To achieve computational feasibility for large datasets, a popular approach is the Vecchia approximation, which is an ordered conditional approximation of the data vector that implies a sparse Cholesky factor of the precision matrix. For this purpose, the observations can be ordered using a maximum-minimum-distance algorithm, and the sparsity is determined by nearest-neighbor conditioning. Both ordering and conditioning are typically carried out based on Euclidean distance of the corresponding inputs. Here, we propose instead to use a correlation-based distance metric, resulting in a general class of correlation-based Vecchia approximations. Our approach can greatly improve the approximation accuracy and is widely applicable including general covariance matrices obtained based on non-Euclidean inputs. Moreover, it can be understood in terms of the Euclidean-based approach on a deformed input space and carried out in quasilinear time in the size of the dataset. We demonstrate the advantages of our method in several simulation scenarios as well as a real data application.

Authors who are presenting talks have a * after their name.

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