Fast methods for training Gaussian processes on large datasets.

Area of Science:

• Machine Learning
• Computational Statistics
• Bayesian Inference

Background:

• Gaussian process regression (GPR) is a powerful non-parametric Bayesian method for data interpolation and fitting.
• A significant limitation of GPR is its high computational cost with large datasets, hindering wider adoption.
• Bayesian model comparison, particularly for covariance functions, is computationally intensive within GPR.

Purpose of the Study:

• To derive methods for accelerating the learning phase of Gaussian process regression.
• To enhance the efficiency of Bayesian model comparison for different covariance functions in GPR.
• To reduce the computational burden associated with large-scale GPR applications.

Main Methods:

• Derivation of novel computational shortcuts for the GPR learning stage.
• Application of derived techniques to both synthetic and real-world datasets.
• Quantitative comparison of computational speed-up against traditional nested sampling for model evidence evaluation.

Main Results:

• Significant speed-up achieved in the learning stage of GPR algorithms.
• Demonstrated efficiency gains in performing Bayesian model comparison for covariance functions.
• Quantified performance improvements compared to nested sampling methods.

Conclusions:

• The derived techniques effectively reduce computational costs in Gaussian process regression.
• These advancements make GPR a more practical tool for analyzing large and complex datasets.
• The methods facilitate more efficient Bayesian model comparison, aiding in model selection for GPR.