Splitting Gaussian processes for computationally-efficient regression.

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Gaussian processes (GPs) are powerful kernel methods for regression.
• Standard GPs exhibit cubic time complexity, limiting scalability with large datasets.
• Efficient updating of GP models is crucial for practical applications.

Purpose of the Study:

• To develop a scalable Gaussian process regression algorithm.
• To address the computational limitations of standard GP models.
• To introduce a localized Gaussian process regression model with improved efficiency.

Main Methods:

• Propose an algorithm for sequential input space partitioning.
• Fit localized Gaussian processes to disjoint regions.
• Achieve a model with tightly bounded update time complexity.

Main Results:

• The algorithm demonstrates superior time and space complexity compared to existing methods.
• The localized GP model achieves linear memory complexity.
• Theoretical continuity properties of the model are established.

Conclusions:

• The proposed localized Gaussian process regression model offers significant scalability improvements.
• The algorithm enables efficient model updating with bounded time complexity.
• The model's efficacy is validated on multi-dimensional regression tasks.