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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence

Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression

February 1, 2023

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Authors

Tong Teng

National University of Singapore


Jie Chen

Shenzhen University


Yehong Zhang

National University of Singapore


Bryan Kian Hsiang Low

National University of Singapore


DOI:

10.1609/aaai.v34i04.6061


Abstract:

This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due to many kernels being evaluated simultaneously by our VBKS algorithm, we show that the variational lower bound of the log-marginal likelihood can be decomposed into an additive form such that each additive term depends only on a disjoint subset of the variational variables and can thus be optimized independently. Stochastic optimization is then used to maximize the variational lower bound by iteratively improving the variational approximation of the exact posterior belief via stochastic gradient ascent, which incurs constant time per iteration and hence scales to big data. We empirically evaluate the performance of our VBKS algorithm on synthetic and massive real-world datasets.

Topics: AAAI

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HOW TO CITE:

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression Proceedings of the AAAI Conference on Artificial Intelligence (2020) 5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression AAAI 2020, 5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low (2020). Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression. Proceedings of the AAAI Conference on Artificial Intelligence, 5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression. Proceedings of the AAAI Conference on Artificial Intelligence 2020 p.5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. 2020. Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression. "Proceedings of the AAAI Conference on Artificial Intelligence". 5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. (2020) "Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression", Proceedings of the AAAI Conference on Artificial Intelligence, p.5997-6004

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low, "Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression", AAAI, p.5997-6004, 2020.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. "Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression". Proceedings of the AAAI Conference on Artificial Intelligence, 2020, p.5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. "Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression". Proceedings of the AAAI Conference on Artificial Intelligence, (2020): 5997-6004.

Tong Teng||Jie Chen||Yehong Zhang||Bryan Kian Hsiang Low. Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression. AAAI[Internet]. 2020[cited 2023]; 5997-6004.


ISSN: 2374-3468


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