Bayesian shape-constrained curve-fitting with Gaussian processes
prior elicitation and computation
Keywords:
Bayesian shape-constrained curve-fitting, Gaussian processes, prior elicitation, computationAbstract
In many applications, one is interested in reconstructing a function \( f \) when only few (potentially very noisy) evaluations \( f(x) \) are available, usually due to budget restrictions. When information about the “shape” of \( f \) is available, e.g., whether it is monotonic, convex/concave, etc., it is desirable to include this information into the curve-fitting procedure. Here we build on the Gaussian process literature to propose a comprehensive framework for flexibly modeling \( f \) and its first two derivatives given evaluations of \( f \), \( f' \), \( f'' \) at potentially irregular grids. We show how to include shape-constraints in a principled way through the prior and apply the developed methods to function emulation for noisy Markov chain Monte Carlo.
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References
J. R. Gardner, G. Pleiss, D. Bindel, K. Q. Weinberger, and A. G. Wilson. GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration. 2021. arXiv:1809.11165 [cs.LG].
C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning series. MIT Press, 2005. ISBN: 9780262182539.
J. Riihimäki and A. Vehtari. “Gaussian processes with monotonicity information”. In: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics. Ed. by Yee Whye Teh and Mike Titterington. Vol. 9. Proceedings of Machine Learning Research. Chia Laguna Resort, Sardinia, Italy: PMLR, May 2010, pp. 645–652.
X. Wang and J. O. Berger. “Estimating Shape Constrained Functions Using Gaussian Processes”. In: SIAM/ASA Journal on Uncertainty Quantification 4.1 (2016), pp. 1–25. doi:10.1137/140955033.
