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Scaling Gaussian Process Regression with Derivatives
David Eriksson · Kun Dong · Eric Lee · David Bindel · Andrew Wilson

Thu Dec 07:45 AM -- 09:45 AM PST @ Room 210 #56
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$ dimensions requires linear solves and log determinants with an ${n(d+1) \times n(d+1)}$ positive definite matrix-- leading to prohibitive $\mathcal{O}(n^3d^3)$ computations for standard direct methods. We propose iterative solvers using fast $\mathcal{O}(nd)$ matrix-vector multiplications (MVMs), together with pivoted Cholesky preconditioning that cuts the iterations to convergence by several orders of magnitude, allowing for fast kernel learning and prediction. Our approaches, together with dimensionality reduction, allows us to scale Bayesian optimization with derivatives to high-dimensional problems and large evaluation budgets.

Author Information

David Eriksson (Cornell University)
Kun Dong (Cornell University)
Eric Lee (Cornell University)
David Bindel (Cornell University)
Andrew Wilson (Cornell University)

I am a professor of machine learning at New York University.

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