Spiked Dirichlet Process Priors for Gaussian Process Models.

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Gaussian process (GP) models are powerful tools for regression and classification.
• Variable selection is crucial for improving the interpretability and performance of GP models.
• Existing Bayesian variable selection methods for GPs have limitations in handling complex covariate structures.

Purpose of the Study:

• To develop a novel Bayesian variable selection framework for Gaussian process models.
• To introduce nonparametric treatments of covariance parameter distributions using Dirichlet process (DP) priors.
• To induce covariate clustering for enhanced model performance and interpretability.

Main Methods:

• Employing spiked Dirichlet process (DP) prior constructions over set partitions of covariates.
• Evaluating two DP prior constructions: one clustering all covariates, the other clustering selected covariates.
• Utilizing novel combinations and extensions of existing algorithms for posterior inference with DP prior models.

Main Results:

• The proposed framework induces a nonparametric clustering of covariates within the GP covariance matrix.
• Simulation results demonstrate a reduction in posterior sampling variability.
• Enhanced prediction performances were observed compared to existing methods.

Conclusions:

• The developed Bayesian variable selection framework effectively clusters covariates in GP models.
• The novel DP prior constructions lead to improved prediction accuracy and reduced uncertainty.
• This approach offers a promising direction for enhancing GP model performance in complex datasets.