Gaussian Process Regression

Gaussian process regression is a Bayesian technique for function approximation. It requires the specifying a prior over functions, and a likelihood for the data. There are a variety of ways to tune the parameters involved and you can play with them in the applet below. The red line is the function being approximated, the blue line is the GP posterior mean, and the grey regions bound the area within one standard deviation of the mean.

Correlation Length:

200000

Signal Size:

200000

Noise:

200000

Research Focus: Experimental Design

My research in Gaussian process regression concerns the topic of experimental design. I design algorithms which search for input parameter locations which yield the most information about the underlying simulation we are trying to approximate

Non-concave domain with holes (red region) for which we can design experiments (black points) with many desirable properties
These algorithms are based on adding experiments in locations which minimize the total uncertainty of the surrogate. Uncertainty is measured by the integrated variance of the posterior, i.e., the area inside the grey region in the applet above. My paper detailing the algorithm can be found below. Also in the paper is a theoretical and numerical discussion about the relationship between polynomial chaos expansions and Gaussian process regression. As part of this paper, I have written a python package for GP regression and experimental design GPEXP which is available on github

See the paper …

A.A. Gorodetsky and Y.M. Marzouk. (2016) Mercer Kernels and Integrated Variance Experimental Design: Connections Between Gaussian Process Regression and Polynomial Approximation SIAM/ASA Journal on Uncertainty Quantification, 4(1), 796–828. (download)

See the code …

Experimental design for GP regression (Github)

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