Fast increased fidelity samplers for approximate Bayesian Gaussian process regression.

Area of Science:

• Computational statistics
• Bayesian non-parametrics
• Machine learning

Background:

• Gaussian processes (GPs) are fundamental in Bayesian non-parametric modeling.
• Exact GP computations are computationally intensive, limiting their application to smaller datasets.
• Scalability is a major challenge for GP methods in big data scenarios.

Purpose of the Study:

• To develop a computationally efficient posterior sampling algorithm for Gaussian processes.
• To enable the application of GPs to problems with a large number of observations.
• To improve the scalability of Bayesian non-parametric models.

Main Methods:

• Development of a posterior sampling algorithm utilizing H-matrix approximations.
• Algorithm achieves a computational complexity of O(n log^2 n).
• Modeling d-dimensional surfaces using tensor products of univariate GPs for efficiency.

Main Results:

• The proposed algorithm scales efficiently, overcoming the limitations of exact GPs.
• The Kullback-Leibler divergence between the approximation and the true posterior can be minimized.
• Demonstrated performance of the fast increased fidelity approximate GP (FIFA-GP) on simulated and real-world data.

Conclusions:

• The FIFA-GP algorithm offers a scalable solution for Bayesian non-parametric modeling with GPs.
• H-matrix approximations provide a viable approach to reduce computational complexity.
• The method enhances the applicability of GPs in data-intensive scientific research.