Team: S. Foucart, F. Narcowich, R. Tuo (lead)

Synopsizing points

• Sampling inequalities and optimal recovery in reproducing kernel Hilbert spaces

• Sparse representation of covariance matrices

• Approximation theory for Gaussian process models with non-Gaussian distributed observations

Related grants

• NSF CDS&E-MSS: Sparsely Activated Bayesian Neural Networks from Deep Gaussian Processes, 2023-26 (PI: Rui Tuo)

Recent relevant papers

• L. Ding, R. Tuo. A general theory for kernel packets: from state space model to compactly supported basis. (arXiv)

• R. Tuo, L. Zou. Asymptotic theory for linear functionals of kernel ridge regression. (arXiv)

• A. Prakash, R. Tuo, Y. Ding. Gaussian process aided function comparison using noisy scattered data. Technometrics, 64/1, 92-102, 2022. (doi)

• H. Chen, L. Ding, R. Tuo. Kernel packet: an exact and scalable algorithm for Gaussian process regression with Matérn correlations. Journal of Machine Learning Research, 23/127, 1-32, 2022. (link)

• R. Tuo, S. He, A. Pourhabib, Y. Ding, J. Z. Huang. A reproducing kernel Hilbert space approach to functional calibration of computer models. Journal of the American Statistical Association, 2021. (doi)

• R. Tuo, W. Wang. Uncertainty quantification for Bayesian optimization. International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research, 151, 2862-2884, 2022. (link)

• A. Amir, D. Levin, F. J. Narcowich, J. D. Ward. Meshfree extrapolation with application to enhanced near-boundary approximation with local Lagrange kernels. Foundations of Computational Mathematics, 22, 1–34, 2022. (doi)