Parameter space exploration with Gaussian process trees

  • Authors:
  • Robert B. Gramacy;Herbert K. H. Lee;William G. Macready

  • Affiliations:
  • University of California, Santa Cruz, CA;University of California, Santa Cruz, CA;University Affiliated Research Center, Moffett Field, CA

  • Venue:
  • ICML '04 Proceedings of the twenty-first international conference on Machine learning
  • Year:
  • 2004

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Abstract

Computer experiments often require dense sweeps over input parameters to obtain a qualitative understanding of their response. Such sweeps can be prohibitively expensive, and are unnecessary in regions where the response is easy predicted; well-chosen designs could allow a mapping of the response with far fewer simulation runs. Thus, there is a need for computationally inexpensive surrogate models and an accompanying method for selecting small designs. We explore a general methodology for addressing this need that uses non-stationary Gaussian processes. Binary trees partition the input space to facilitate non-stationarity and a Bayesian interpretation provides an explicit measure of predictive uncertainty that can be used to guide sampling. Our methods are illustrated on several examples, including a motivating example involving computational fluid dynamics simulation of a NASA reentry vehicle.