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    Area of Science:

    • Machine Learning
    • Statistical Modeling

    Background:

    • Large-scale Gaussian process (GP) modeling is crucial in machine learning.
    • Standard GP methods (maximum likelihood, best linear unbiased predictor) are limited by single-computer constraints.
    • Existing approximate methods often prioritize computational over statistical efficiency.

    Purpose of the Study:

    • Develop an optimal composite likelihood (OCL) scheme for distributed GP modeling.
    • Minimize information loss in parameter estimation and prediction for large-scale GPs.
    • Provide accurate and efficient solutions for supercomputing practitioners.

    Main Methods:

    • Developed an optimal composite likelihood (OCL) scheme.
    • Introduced the best linear unbiased block predictor (BLUBP) for partitioned data.
    • Conducted numerical examples to evaluate performance.

    Main Results:

    • The OCL scheme minimizes information loss in parameter estimation.
    • The BLUBP achieves minimum prediction variance for partitioned data.
    • Proposed methods demonstrate superior accuracy compared to traditional counterparts.

    Conclusions:

    • The OCL scheme offers an accurate and statistically efficient approach for distributed GP modeling.
    • The BLUBP provides a highly accurate prediction method for large-scale datasets.
    • This work bridges the gap between computational efficiency and statistical accuracy in GP modeling.