Content This is the code repository for the research publication "Sparse Additive Gaussian Process" by Hengrui Luo, Giovanni Nattino and Matthew T. Pratola. The manuscript of this paper can be accessed at https://arxiv.org/abs/1908.08864.

• In Python folder, we provided a set of illustrative code that serves as a proof of concept, and also a set of robust code that can be executed for large datasets.
• In R folder, we provided user-friendly R code with more features like adaptive Metropolis-Hasting step-width. However, we point out that its computational efficiency is not comparable to Python version.

Abstract In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive partitioning (RP) scheme. Within each RP partition, a sparse GP (SGP) regression model is fitted. A Bayesian additive framework then combines multiple layers of partitioned SGPs, capturing both global trends and local refinements with efficient computations. The model addresses both the problem of efficiency in fitting a full Gaussian process regression model and the problem of prediction performance associated with a single SGP. Our approach mitigates the issue of pseudo-input selection and avoids the need for complex inter-block correlations in existing methods. The crucial trade-off becomes choosing between many simpler local model components or fewer complex global model components, which the practitioner can sensibly tune. Implementation is via a Metropolis-Hasting Markov chain Monte-Carlo algorithm with Bayesian back-fitting. We compare our model against popular alternatives on simulated and real datasets, and find the performance is competitive, while the fully Bayesian procedure enables the quantification of model uncertainties.

Citation We provided both iPynb illustrative code, Python/R production code for reproducible and experimental purposes under LICENSE. Please cite our paper using following BibTeX item:

@article{luo2019sparse,
    title={Sparse Additive Gaussian Process Regression},
    author={Hengrui Luo and Giovanni Nattino and Matthew T. Pratola},
    year={2019},
    eprint={1908.08864},
    archivePrefix={arXiv},
    primaryClass={math.ST}
}

Thank you again for the interest and please reach out if you have further questions.