Decomposed Gaussian Processes for Efficient Regression Models with Low Complexity.

Area of Science:

• Machine Learning
• Statistical Modeling
• Computational Mathematics

Background:

• Gaussian process regression (GPR) is powerful but computationally intensive for large datasets (N≫1).
• Traditional GPR methods face scalability challenges due to cubic complexity in computation and memory.
• Efficient inference and learning are crucial for applying GPR to big data problems.

Purpose of the Study:

• To develop a computationally efficient Gaussian process regression model for large-scale observational data.
• To introduce a novel covariance construction method that improves scalability.
• To reduce the computational and memory complexity of GPR.

Main Methods:

• Proposing a flexible covariance construction based on differential operators.
• Proving the convergence of the proposed method.
• Developing an optimized implementation for reduced computational and memory footprints.

Main Results:

• Achieved computational cost of O(Nm2) for inference and O(m3) for learning, a significant improvement over the canonical O(N3).
• Reduced memory requirements to O(m2) from O(N2).
• Demonstrated effectiveness through simulations and real-world data experiments.

Conclusions:

• The proposed Gaussian process regression method offers a scalable and efficient solution for large datasets.
• The novel covariance construction significantly enhances computational performance and memory efficiency.
• This method provides a competitive alternative to existing cutting-edge techniques for large-scale GPR.